*^,i » *4 -
t>«.
HQ).J^' •■^- • 'i'»i a .."i> .ii.v.ivr.i. .'._.jr.'>rvr;.v.'. -■ -• — —- ; . ■.^-— •■ -,-
•.^nv;
.• . H\'* ^o%..'^"T vj't'JcTKv.^/ '<.v^•^^.^•v^ >v. -. ;^
Ac
CORNELL
UNIVgRSFTY
LIBRARY
GOLDWIN SMITH
HALL
FROM THE FUND GIVEN BY
GOLDWIN SMITH
1909
Cornell University Library
BC 91.M641874
A system of logic, ' atjocina^^^^
3 1924 014 688 257
Cornell University
Library
The original of tiiis book is in
tine Cornell University Library.
There are no known copyright restrictions in
the United States on the use of the text.
http://www.archive.org/details/cu31924014688257
A SYSTEM OF LOaiC,
RATIOCINATIVE AND mDUCTITE:
BEING A
CONNECTED VIEW OF THE PRINCIPLES OF EVIDENCE
AND THE
METHODS OF SCIENTIFIC INVESTIGATION.
BY
JOHN STUART MILL
EIGHTH EDITION.
HARPEK & BROTHERS PUBLISHERS,
NEW YORK AND LONDON,
' ' I', W i) w
- , .'iff
G^^.Vi^
PREFACE TO THE FIRST EDITION.
This book makes no pretense of giving to the world a new theory of the
intellectual operations. Its claim to attention, if it possess any, is ground-
ed on the fact that it is an attempt, not to supersede, but to embody and
systematize, the best ideas which have been either promulgated on its sub-
ject by speculative writers, or conformed to by accurate thinkers in tbeir
scientific inquiries.
To cement together the detached fragments of a subject, never yet treat-
ed as a whole ; to harmonize the true portions of discordant theories, by
supplying the links of thought necessary to connect them, and by disentan-
gling them from the errors with which they are always more or less inter-
woven, must necessarily require a considerable amount of original specula-
tion. To other originality than this, the present work lays no claim. In
the existing state of the cultivation of the sciences, there would be a very
strong presumption against any one who should imagine that he had effect-
ed a revolution in the theory of the investigation of truth, or added any
fundamentally new process to the practice of it. The improvement which
remains to be effected in the methods of philosophizing (and the author be-
lieves that they have much need of improvement) can only consist in per-
forming more systematically and accurately operations with which, at least
in their elementary form, the human intellect, in some one or other of its
employments, is already familiar.
In the portion of the work which treats of Ratiocination, the author has
not deemed it necessary to enter into technical details which may be ob-
tained in so perfect a shape from the existing treatises on what is termed
the Logic of the Schools. In the contempt entertained by many modern
philosophers for the syllogistic art, it will be seen that he by no means par-
ticipates; though the scientific theory on which its defense is usually rest-
ed appears to him erroneous : and the view which he has suggested of the
nature and functions of the Syllogism may, perhaps, afford the means of
conciliating the principles of the art with as much as is well grounded in
the doctrines and objections of its assailants.
The same abstinence from details could not be observed in the First
Book, on Names and Propositions ; because many useful principles and dis-
iv PREFACE.
tinctions which were contained in the old Logic have been gradually omit-,
ted from the writings of its later teachers; and it appeared desirable both(
to revive these, and to reform and rationalize the philosophical foundation
on which they stood. The earlier chapters of this preliminary Book will
consequently appear, to some readers, needlessly elementary and scholastic.
But those who know in what darkness the nature of our knowledge, and
of the processes by which it is obtained, is often involved by a confused
apprehension of the import of the different classes of Words and Asser-
tions, will not regard these discussions as either frivolous, or irrelevant to
the topics considered in the later Books.
On the subject of Induction, the task to be performed was that of gener-
alizing the modes of investigating truth and estimating evidence, by which
so many important and recondite laws of nature have, in the various sci-
ences, been aggregated to the stock of human knowledge. That this is not
a task free from difficulty may be presumed from the fact that even at a
very recent period, eminent writers (among whom it is suiEcient to name
Archbishop Whately, and the author of a celebrated article on Bacon in the
Edinburgh lieview) have not scrupled to pronounce it impossible.* The
author has endeavored to comhat their theory in the manner in which Di-
ogenes confuted the skeptical reasonings against the possibility of motion ;
remembering that Diogenes's argument would have been equally conclu-
sive, though his individual perambulations might not have extended be-
yond the circuit of his own tub.
Whatever may be the value of what the author has succeeded in effect-
ing on this branch of his subject, it is a duty to acknowledge that for much
of it he has been indebted to several important treatises, partly historical
and partly philosophical, on the generalities and processes of physical sci-
ence, which have been published within the last few years. To these trea-
tises, and to their authors, he has endeavored to do justice in the body of
the work. But as with one of these writers. Dr. Whewell, he has occasion
frequently to express differences of opinion, it is more particularly incum-
bent on him in this place to declare, that without the aid derived from the ;
* In the later editions of Archbishop Whately's "Logic," he states his meaning to be, not i
that " rules " for the ascertainment of truths by inductive investigation can not be laid down,
or that they may not be "of eminent service," but that they "must always be comparatively!
vague and general, and incapable of being built up into a regular demonstrative theoiy like!
that of the Syllogism." (Book iv., ch. iv., § 3.) And he observes, that to devise a system
for thi« purpose, capable of being "brought into a scientific form," would be an achievement
which "he must be more sanguine than scientific who expects." (Book iv., ch. ii,, § 4.) Tou
effect this, however, being the express object of the portion of the present work which treatj
of Induction, the words inthe text are no overstatement of the difference of opinion between
Archbishop Whately and me on the subject.
PREFACE. V
facts and ideas contained in that gentleman's " History of the Inductive
Sciences," the corresponding portion of this work would probably not have
been written.
The concluding Book is an attempt to contribute toward the solution of
a question which the decay of old opinions, and the agitation that disturbs
European society to its inmost depths, render as important in the present
day to the practical interests of human life, as it must at all times be to the
completeness of our speculative knowledge — viz. : Whether moral and so-
cial phenomena are really exceptions to the general certainty and uniformi-
ty of the course of nature ; and how far the methods by which so many of
the laws of the physical world have been numbered among truths irrevo-
cably acquired and universally assented to, can be made instrumental to
the formation of a similar body of received doctrine in moral and political
fcience.
PREFACE TO THE THIRD AND FOURTH EDITIONS.
Several criticisms, of a more or less controversial character, on this
"work, have appeared since the publication of the second edition ; and Dr.
Whewell has lately published a reply to those parts of it in which some of
his opinions were controverted.*
I have carefully reconsidered all the points on which my conclusii.. ^
have been assailed. But I have not to announce a change of opinion on
any matter of importance. Such minor oversights as have been detected,
cither by myself or by my critics, I have, in general silently, corrected : but
it is not to be inferred that I agree with the objections which have been
made to a passage, in every instance in which I have altered or canceled it.
I have often done so, merely that it might not remain a stumbling-block,
when the amount of discussion necessary to place the matter in its true
light would have exceeded what was suitable to the occasion.
To several of the arguments which have been urged against me, I have
thought it useful to reply with some degree of minuteness ; not from any
taste for controversy, but because the opportunity was favorable for pla-
•cing my own conclusions, and the grounds of them, more clearly and com-
pletely before the reader. Truth on these subjects is militant, and can
only establish itself by means of conflict. The most opposite opinions can
make a plausible show of evidence while each has the statement of its own
<3ase ; and it is only possible to ascertain which of them is in the right, af-
ter hearing and comparing what each can say against the other, and what
the other can urge in its defense.
Even the criticisms from which I most dissent have been of great serv-
ice to me, by showing in what places the exposition most needed to be
improved, or the argument strengthened. And I should have been well
pleased if the book had undergone a much greater amount of attack ; as in
that case I should probably have been enabled to improve it still more than
I believe I have now done.
In the subsequent editions, the attempt to improve the work by addi-
tions and corrections, suggested by criticism or by thought, has been con-
* Now forming a chapter in his volume on "The Philosophy of Discovery."
VlU PREFACE.
tinued. The additions and corrections in the present (eighth) edition,
which are not very considerable, are chiefly such as have been suggested
by Professor Bain's " Logic," a book of great merit and value. Mr. Bain's
view of the science is essentially the same with that taken in the present
treatise, the differences of opinion being few and unimportant compared
with the agreements ; and he has not only enriched the exposition by many
applications and illustrative details, but has appended to it a minute and
very valuable discussion of the logical principles specially applicable to
each of the sciences — a task for which the encyclopedical character of his
knowledge peculiarly qualified him. I have in several instances made use
of his exposition to improve my own, by adopting, and occasionally by
controverting, matter contained~in his treatise.
The longest of the additions belongs to the chapter on Causation, and is
a discussion of the question how far, if at all, the ordinary mode of stating
the law of Cause and Effect requires modification to adapt it to the new
doctrine of the Conservation of Force — a point stiU more fully and elabo-
rately treated in Mr. Bain's work.
CONTENTS.
INTKODUCTION.
PAGE
5 1. A definitloii at the commencement of a sub-
ject mnst be provisional 17
2. Is logic the'art and science of reasoning f. 17
3. Or the art and science of the pursuit of
truth P 18
4. Logic is concerned with inferences, not
with intuitive truths 19
5. Relation of logic to the other sciences 21
S. Its utility, how shown 22
T. Definition of logic stated and illustrated.. 23
BOOK I.
OF NAMES AND PROPOSITIONS.
CiiAPTKB I. Of the Necessity of commencing with an
Analysis of Language.
i 1. Theory of names, why a necessary part of
logic 26
2. First step in the analysis of Propoaitione,. 27
3. Kames mnst be studied before Things.... 28
Chap'ikb II. Of Names.
H. Namesarenamesof things, not of onrideas 29
2. Words which are not names, but parts of
names 30
3. General and Singular names 32
4. Concrete and Abstract 33
6. Connotative and Non-connotative 34
6. Positive and Negative 41
7. Eelative and Absolute 42
8. Uuivocal and ^qnivocal 44
Chapteb IIL Of the Things demoted by Names.
i 1. Necessity of an enameration of Namable
Things. The Categories of Aristotle. ... 45
2. Amhignityof the most general names 46
3. Feelings, or states of conscionsness 48
4. Feelings mnst be distinguished from their
physical antecedents. Perceptions, what. 49
5. Volitions, and Actions, what 51
6. Substance and Attribute SI
7. Body 62
8. Mind 66
9. Qualities 67
10. Relations 69
11. Resemblance. 60
12. Quantity 62
13. All 'attributes of bodies are grounded on
states of consciousness 63
14. 8o also all attributes of mind 64
16. Recapitulation 64
PAGE
Chapter IV.., Of Propositions,
i 1. Nature and office of the copula 60
2. Affirmative and Negative propositions 67
3. Simple and Complez 6*
4. Universal, Particular, and Singular. 71
Chapter V. Of the Invport gf I^o^Q^i^t^.
% 1. Doctrine that a proposition is the expres-
sion of a^ relation between two ideas 73
2. — that it is the expression of a relation be-
tween the meanings of two names 75
3. — that it consists in referring something
to, or excluding something fi-om, a class. 77
4. What it really is 80
5. It asserts (or denies) a sequence, a co-exiat-
ence, a simple existence, a causation 81
6. — or a resemblance 83
7. Propositions of which the terms are ab-
stract ". 86
Chapter VI. Of ProposiUons merely Verbal,
§ 1. Essential and Accidental propositions 8*
2. All essential propositions are Identical
propositions 89
3. Individuals have no essences 91
4. Real propositions, how distinguished tvom
verbal 92
8. Two modes of representing the import of
a Real proposition 93
Chapteb VII. Of'th^ Nature of Classification^ and
the Five Predicables.
§ 1. Classification, how connected with Naming 94
2. The Predicables, what 95
3. G«nus and Species 95
4. Kinds have a real existence in nature 97
6. Differentia 100
6. Differentiae for general purposes, and difi'er-
entise for special or technical purposes. . . 101
7. Proprinm 103
8. Accidens 104
Chapter Vni. Of Definition.
§ 1. A definition, what 105-
2. Every name can be defined, whose meaning
is susceptible of analysis 10&
3. Complete, how distinguished from incom-
plete definitions 107
4. — and from descriptions 108
6. What are called definitions of Things, are
definitions of Names with an implied as-
sumption of the existence of Things cor-
responding to them Ill
6. — even when Such things do not in reality
exist 11*
CONTENTS.
iT. DefinitioBB, though of names only, mnstbe
grouuded on knowledge of the corre-
sponding things IIT
BOOK n.
OF REASONING.
Chapteb I. Of Inference, or Reaaoming, in general.
5 1. Retrospect of the preceding book 121
2. Inferences improperly so called 122
3. Inferences proper, distinguished into in-
dactions and ratiocinations 125
Chapter II. Of Ratiocination, or Byllogia/m,
<1. Analysis of the Syllogism 126
2. The didvmh de omni not the foundation of
reasoning, but a mere identical proposi-
tion 132
3. What is the really fundamental axiom of
Batiocination .' 136
. 4. The other form of the axiom 137
Chapteb III. Of the Functions, and Logical Value
of the Syllogism,
H. Is the Syllogism a pettiiojjrincipw/ 139
2. Insufficiency of the common theory 139
3. All inference is from particulars to partic-
ulars 141
4. General propositions are a record of such
inferences, and the rules of the syllogism
are rules for the interpretation of the
record 146
5. The syllogism not the type of I'easonlng,
but a test of it 148
6. The true type, what 151
J. Relation between Induction and Deduc-
tion 153
8. Objections answered 1S4
9. Of Formal Logic, and its relation to the
Logic of Truth 156
CuAPTEE rv. Of Trains of Reatonint), and Dedvxt-
ive Sciences.
41. For what purpose trains of reasoning exist. 15S
2. A train of reasoning is a series of induct-
ive inferences 168
3. — from particulars to particulars through
marks of marks 160
4. Why there are deductive sciences 161
6. Why other sciences still remain experi-
mental ■ 164
6. Experimental sciences may become deduct-
ive by the progress of experiment 165
7. In what manner this usually takes place. . 166
Chaptee V. Of Demonstration, and Neceesarg
Truths.
S 1. The Theorems of geometry are necessary
truths only in the sense of necessarily fol-
lowing from hypotheses 168
2. Those hypotheses are real facts with some
of their circumstances exaggerated or
omitted ITO
3. Some of the first principles of geometry are
axioms, and these are not hypothetical. . ITl
4. ~ but are experimental truths. 172
§6. An objection answered 174
6. Dr. Whewell's opinions on axioms exam-
ined 176
Chapiee VI. The same Subject continued.
51. All deductive sciences are inductive 1ST
2. The propositions of the science of number
are not verbal, but generalizations from
experience 188
3. In what sense hypothetical 191
4. The characteristic property of demonstra-
tive science is to be hypothetical 192
6. Definition of demonstrative evidence 193
Chapteb VII. Exatnination ofaoTne Opinions ojh
posed to the preceding doctrines.
5 1. Doctrine of the Universal Postulate. ...... 193
2. The test of inconceivability does not' rep-
resent the aggregate of past experience. . 195
3. — nor is implied in every process of
thought ., 197
4. Objections answered '. 201
6. Sir W. Hamilton's opinion on the Princi-
ples of Contradiction and Excluded Mid-
dle 204
BOOK m.
OF INDUCTION.
y
Chapteb I. Preliminary Observations on Induc-
tion in general.
§ 1, Importance of an Inductive Logic 207
2. The logic of science is also that of business
and life 203
Chapteb II. Of Inductions itnproperly so called.
} 1. Inductions distinguished from verbal trans-
formations 210
2. — frominductions,falselysocalled,inmath-
ematlcs 212
3. — and from descriptions 213
4. Examination of Dr. Whewell's theory of
Induction 214
6. Further Illustration of the preceding re-
marks 221
Chapter III. Of the Ground of Induction. ^
5 1. Axiom of the uniformity of the course of
nature 223
2. Not true in every sense. Induction per
enwmerationem simplicem 2-**
B. The question of Inductive Logic stated. ... 227
Chapteb IV. Of Laws of Nature.
§ 1. The general regularity In nature is a tissue
of partial regularities, called laws 229
2. Scientific induction must be grounded on
previous spontaneous Inductions 23'^
3. Are there any inductions fitted to be a test
of all others f 231
Chapteb V. Of the Law of Universal Causation,
5 1. The universal law of successive phenomena
Is the Law of Causation 234
2. — i. e., the law that every consequent has
an invariable antecedent asd
CONTENTS.
XI
PAGE
[3. The cause of a phenomenon is the asBem-
blflge of its conditions 237
4. The distinction of agent and patient illu-
sory 241
6. Case in which the effect consists in giving
a property to an object 243
6. The cause is not the invariable antecedent,
bnt the unconditional invariable anteced-
ent 244
7. Can a cause be simaltaueous with its ef~
feet? 247
8. Idea of a Permanent Cause, or original nat-
ural agent 248
9. Uniformities of co- existence between ef-
fects of different permanent causes, are
not laws 251
10. Theory of the Conservation of Force 251
11. Doctrine that volition is an efficient cause,
examined 255
CuAPTEK VI. Of tJie Composition of Causes.
i 1. Two modes of the conjunct action of causes,
the mechanical and the chemical 266
2. The .composition of causes the general
rule ; the other case exceptional 268
8. Are effects proportional to their causes?. . 270
Chaptee VIL Of Observation and Experiment.
5 1. The first step of inductive inquiry is a men-
tal analysis of complex phenomena into
their elements 272
2. The next is an actual separation of those
elements 273
3. Advantages of experiment over observa-
tion 274
4. Advantages of observation over experi-
ment 276
Chapter VIIL Of the Four Methods of Eaperi-
mental Inquiry.
51. Method of Agreement 278
2. Method of Difference 280
3. Mutual relation of these two methods 281
4. Joint Method of Agreement and Difference. 283
5. Method of Residues 284
6. Method of Concomitant Variations 285
7. Limitations of this last method 289
Chapter IX. ]Hiscella/}ieous Examples of the Four
Methods,
§ 1. Liebig's theory of metallic poisons 292
2. Theory of induced electricity. 294
3. Dr. Wells's theory of dew 296
4. Dr. Brown-Sequard's theoiy of cadaveric
rigidity 301
5. Examples of the Method of Residues 305
6. Dr. Whewell's objections to the Four
Methods 307
Chaptee X. Of Plurality of Causes ; and of the
Fntermixture of Effects.
8 1, One effect may have several causes 311
2. — which is the source of a characteristic
imperfection of the Method of Agree-
ment 311
3. Plurality of Causes, how ascertained 314
4. Concurrence of Causes which do not com-
pound their effects 315
6. Difficulties of the investigation, when
causes compound their effects 317
FAOB
§6. Three modes of investigating the laws of
complex effects 320
7. The method of simple observation inap-
plicable 321
8. The purely experimental method inappli-
cable 322
Chapter XI. Of the Deductive Method.
§1. First stage; ascertainment of the laws of
the separate causes by direct indnction. . 325
2. Second stage ; ratiocination from the sim-
ple laws of the complex cases 328
3. Third stage ; verification by specific expe-
rience 329
Chapter XII, Of the Explanation of Laws of Na-
ture.
§ 1. Explanation defined 332
2. First mode of explanation, by resolving the
law of a complex effect into the laws of
the concurrent causes and the fact of
their co-existence 332
3. Second mode ; by the detection of an in-
termediate link in the sequence 332
4 Laws are always resolved into laws more
general than themselves 333
5. Third mode ; the subsumption of less gen-
eral laws under a more general one 335
6. What the explanation of a law of nature
amounts to 337
Chapter XIII. Miscellaneous Exa/mples of the Ex-
planation of Laws of Nature.
§ 1. The general theories of the sciences 338
2. Examples from chemical speculations 339
3. Example from Dr. Brown - Si^quard's re-
searches on the nervous system 340
4. Examples of following newly - discovered
laws into their complex manifestations.. 341
5. Examples of empirical generalizations, af-
terward confirmed and explained deduct-
ively 342
6. Example from mental science 343
7. Tendency of all the sciences to become de-
ductive 344
Chapter XIV. Of the Limits to the Explanation
of Laws of Nature; and of Hypotheses.
§ 1. Can all the sequences in nature be resolva-
ble into one law? 345
2. Ultimate laws can not be less numerous
than the distinguishable feelings of our
nature 346
3. In what sense ultimate facts can be ex-
plained 348
4. The proper use of scientific hypotheses 849
5. Their indispensableness 353
6. The two degrees of legitimacy in hypoth-
eses 355
7. Some inquiries apparently hypothetical are
really inductive 359
Chapter XV. Of Progressive Ejects ; and of the
Continued Action of Causes,
51. How a progressive effect results from the
simple continuance of the cause 361
2. — and from the progressiveness of the
cause 363
3. Derivative laws generated from a single
ultimate law 365 '
xu
CONTENTS.
PAGE
Chaptee XVI. Of Empirical Laws.
{ 1. Definitlou of au empirical law. 366
2. Derivative laws commonly depeud on col-
locations 367
3. The collocations of the permanent causes
are not reducible to any law 367
4. Hence empirical laws can not be relied on
beyond the limits of actual experience. . . 368
Gw Generalizations which rest only on the
Method of Agreement can only be re-
ceived as empirical laws 369
6. Signs from which an observed uniformity
of sequence may be presumed to be re-
solvable 369
T. Two kinds of empirical laws 371
Chaptee XVII. Of Cha/nce, and its ElimiTiation.
51. The proof of empirical laws depends on
the theory of chance 372
2. Chance deliued and characterized 373
3. The elimination of chance 376
4. Discovery of residual phenomena by elim-
inating chance 377
5. The doctrine of chances 378
Chaptek XVIII. Of the Calculation of Chances.
§1. Foundation of the doctrine of chances, as
taught by mathematics 379
2. The doctrine tenable 380
3. On what foundation it really rests 381
4. Its ultimate dependence on causation 383
6. Theorem of the doctrine of chances which
relates to the cause of a given event. . . - . 385
6. How applicable to the elimination of
chance 386
Chaptee XIX. Of the Extension of Derivative Laws
to Adjacent Cases.
§ 1. Derivative laws, when not casual, are al-
most always contingent on collocations.. 388
2. On what grounds they can be extended to
cases beyond the bounds of actual expe-
rience 389
3. Those cases must be adjacent cases 390
Chapter XX. Of Analogy.
5 1. Various senses of the word analogy 393
2. Nature of analogical evidence 393
3. On what circumstances its value depends. . 396
Chapter XXI. Of the Evidence of the Law of Uni-
versal Causation.
il. The law of causality does not rest on an
instinct 397
2. — but on an induction by simple enumera-
tion 400
3. In what cases such induction is allowable. 402
4. The universal prevalence of the law of cau-
sality, on what grounds admissible 403
Chapteb XXII. Of Uniformities of Co-existence
not dependent on Causation.
§1. XTnifonnities of co-existence which result
from laws of sequence 406
2. The properties of Kinds are uniformities
of co-existence 408
3. Some are derivative, others ultimate 409
4. No imiversal axiom of co-existence 410
6. The evidence of uniformities of co-exist-
ence, how measured 411
PAGBT-
§ 6. When derivative, their evidence is that of
empirical laws 412
7. So also when ultimate 413^
8. The evidence stronger in proportion as the
law is more general 413
9. Every distinct Kind must be examined.... 414
Chaptee XXIII. Of Approximate Generalizations^
and Probable Evidence.
§ 1. The inferences called probable, rest on ap-
proximate generalizations 416^
2. Approximate generaKzations less useful
in science than in life 416-
3. In what cases they may be resorted to 417
4. In what manner proved 41&
5. With what precautions employed 420-
6. The two modes of combining probabilities, 421
7. How approximate generalizations may be
converted into accurate generalizations
equivalent to them 433:
Chaptee XXIV. Of the Remaining Laws of Na-
ture.
51. Propositions which assert mere existence. 425-
2. Kesemblance, considered as a subject of
science 426-
3. The axioms and theorems of mathematics
comprise the principal laws of resem-
blance 427"
4. — and those of order in place, and rest on
induction by simple enumeration 42S
5.. The propositions of arithmetic afl&rm the
modes of formation of some given num-
ber 429^
6. Those of algebra affirm the equivalence
of different modes of formation of num-
bers generally 433"
7. The propositions of geometry are laws of
outward nature 433
8. Why geometry is almost entirely deduct-
ive 436
9. Function of mathematical truths in the
other sciences, and limits of that function. 43fr
Chapter XXV. Of the Grounds of Disbelief.
5 1. Improbability and impossibility 438-
2. Examination of Hume's doctrine of mir-
acles 43ft
3. The degrees of improbability correspond
to differences in the nature of the gener-
alization with which an assertion con-
flicts 441
4. A fact is not incredible because the chances
are against it 443-
6. Are coincidences less credible than other
facts? 444
6. An opinion of Laplace examined 44ft
BOOK IV.
OF OPERATIONS SUBSIDIARY TO IN-
DUCTION.
'^ Chapter I. Of Observation aind Description,
§ 1. Observation, how far a subject of logic 449
2. A great part of what seems observation is
really inference 450
CONTENTS.
xm
PAGE
^»- The description of an obfiervation afflrme
mote thau is cuulained in the observa-
tion 452
4. — namely, an agreement among phenom-
ena; and the comparison of phenomena
to ascertain such agreements is a prelim-
inary to induction 453
-CJhaptkb n. Of A &8iracWon, <yr the Formation of
■^ Coiweptions.
41. The comparison which is a preliminary to
induction implies general conceptions... 465
2. — bat these need not be pre-existent 456
3. A general conception, originally the result
of a comparison, becomes itself the type
of comparison 45S
4. What is meant by appropriate conceptions. 459
5. — and by clear conceptions 461
6. Farther illustration of the subject 462
Chaptee in. Of Xaming as Subsidiary to Induc-
tion.
41. The fiindamental property of names as an
instrument of thought 464
2. Names are not indispensable to induc-
tion 465
3. In what manner subservient to it 466
4. General names noi a mere contrivance to
economize the use of language 466
C^HiPTEE r^ Of the Requisites of a Philosophical
' ^Hangudge, and the Prind/ples of Definition,
4 1. First requisite of philosophical language,
a steady and determinate meaning for ev-
ery general name 467
2. Names iu common use have often a loose
connotation 467
3. — which the logician should fix, with as
little alteration as possible 469
■4. Why definition is often a question not of
words but of things 470
6. How the logician should deal with the
transitive applications of words 472
€. Evil consequences of casting oflF any por-
tion of the customary connotation of
words 476
Chaptbe V. On the, Nature^ History of the Varia-
tions in the Meaning of Terms.
41. How circumstances originally accidental
become incorporated into the meaning of
words 480
2. — and sometimes become the whole mean-
ing 481
3. Tendency of words to become generalized. 482
4. — and to become specialized 486
Chapteb VL The Principles of Philosophical Lan-
guage fa/rther cvnMdered.
§1. Second requisite of philosophical language,
a name for every Important meaning — 487
5. — viz., first, an accurate descriptive ter-
minology. 487
3. — secondly, a name for each of the more
important results of scientific abstrac-
tion 490
'4. — thirdly, a nomenclature, or system of
the names of Kindi^ 491
& Peculiar nature of the connotation of
names which belong to a nomenclature.. 493
PAGB
§ 6. In what cases language may, and may not,
be used mechanically 404
C&APTEE VII. Of Classificationf as Subsidiary to
''^ Induction.
51. Classification as here treated of, wherein
different from the classification implied
in naming 497
2. Theory of natural groups 498
3. Are natural groups giveu by type, or by
definition ? 50I
4. Kinds are natural groups 502
5. How the uames of Kinds should be con-
structed 605
Chaptes Till. Of Classification by Series,
51. Natural groups should be arranged in a
^ natural series 507
3. The arrangement should follow the de-
grees of the main phenomenon 608
3. — which implies the assumption of a type
species 509
4. How the divisions of the series should be
determined 510
6. Zoology affords the compietest type of sci-
entific classification 5II
BOOK V.
ON FALLACIES.
Cbaptee I. Of Fallacies in General.
§1. Theory of fallacies a necessary part of
logic 512
2. Casual mistakes are not fallacies 513
3. The moral sources of erroneous opinion,
how related to the intellectnal 513
Chaptee II. Classification of Fallacies.
§1. On what criteria a classification of fallacies
should be grounded 515
2. The five classes of fallacies 516
3. The reference of a fallacy to one or an-
other class is sometimes arbitrary 518
Chapteb m. Fallacies of Simple In^ecUon, or
A Priori Fallacies.
51. Character of this class of fallacies 520
2. Natural prejadice of mistaking subjective
laws for objective, exemplified in popular
superstitions 521
3. — that things which we think of together
must exist together, and that what is in-
conceivable must be false 623
4. — of ascribing objective existence to ab-
abstractions 527
6. Fallacy of the Sufficient Reason 628
6. Natural prejudice, that the differences in
nature correspond to the distinctions in
language 529
7. Prejudice, that a phenomenon can not have
more than one cause 532
8. — that the conditions of a phenomenon
must resemble the phenomenon 533
Cuaptee IV. Fallacies 0/ ObservatioTU
§1. Non-observation, and Mal-observation ^8
xlv
CONTENTS.
PAOB
{ 2. Non - observation of inBtances, and non-
observation of circnmstances 638
3. Examples of the former 539
4. —and of the lattet. B42
6. Mat-observation characterized and exem-
plified S45
Chapteb V. Fallacies of Oeneralization.
51. Character of the class 547
2. Certain kinds of generalization mast al-
ways be groundless B4T
3. Attempts to resolve phenomena radically-
different into the same 648
4. Fallacy of mistaking empirical for casual
laws 649
6. Post hoc^ ergo propter hoc; and the dedact-
ive fallacy corresponding to it 661
6. Fallacy of False Analogies 853
7. Function of metaphors in reasoning 657
8. How fallacies of geueralization grow out
V of bad classification 668
Chapter VI. Fallacies of Batiodnatimi.
{1. Introductory Remarks 669
2. Fallacies in the conversion and aequipol-
lency of propositions 659
3. — in the syllogistic process 660
4. Fallacy of changing the premises 661
Chaptee VII. Fallacies of Confusion.
i 1. Fallacy of Ambiguous Terms 663
2. — of Petitio Principii 670
3. — of Ignoratio Blenchi 676
BOOK VI.
ON THE LOGIC OP THE MORAL SCI-
ENCES.
Chapter I, Introduct^rry R&mofrks,
5 1. The backward state of the Moral Sciences
can only he remedied by applying to them
the methods of Physical Science, duly ex-
tended and generalized 579
2. Huw far this can be attempted in the pres-
ent work 680
Chapter II. Of Liberty and Necessity.
51. Are human actions subject to the law of
causality? 681
2. The doctrine commonly called Philosoph-
ical Necessity, in what sense true 681
3. Inappropriateness and pernicious effect of
the term Necessity 583
1. A motive not always the anticipation of a
pleasure or a pain 586
Chapter III. That there is, or may be, a Science of
Bwman Nature.
S 1. There may be sciences which are not exact
sciences 686
2. To what scientific type the Science of Hu-
man Nature corresponds 688
Chapter IV. Of the Laws of Mind.
! 1. What is meant by Laws of Mind 689
2. Is there s Science of Psychology F 690
PASB
53. The pr'ncipal invertigatlons cf Psychology
characterized 691
4. Kelation of mental facto to physical con-
ditions 694
Chapter V. Of Ethology, or the Science of the For
ma/ion of Character.
§1. The Empirical Laws of Human Nature 69*
2. — are merely approximate generalizations.
The universal laws are those of the for-
mation of character 69T
3. The laws of the foi-mation of character can
not be ascertained by observation and
experiment 599
4. — but must be studied deductively 601
6. The principles of Ethology are the axio-
Tnata media of mental science 603
6. Ethology characterized 604
Chapter VI. General Considerations on the Social
Science.
5 1. Are Social Phenomena a subject of Sci-
ence? 606
2. Of what nature the Social Science must
be. 607
Chapter VII. Of the Cheynical or Experitnental
Method in the Social Science.
51. Characters of the mode of thinking which
deduces political doctrines from specific
experience 608
2. In the Social Science experiments are im-
possible 610
3. — the Method of Difference inapplicable. . 610
4. — and the Methods of Agreement, and of
Concomitant Variations, inconclusive. ... 611
5. The Method of Kesidnes also inconclusive,
aud presupposes Deduction 612
Chapter VIII. Of the Geometrical, or Abstract
Method.
6 1. Characters of this mode of thinking 614
2. Examples of the Geometrical Method 615
3. The interest-philosophy of the Bentham
school 616
Chapter IX. Of the Physical, or Concrete Deductive
Method.
5 1. The Direct and Inverse Deductive Meth-
ods 619
2. Diflftculties of the Direct Deductive Meth-
od in the Social Science 621
3. To what extent the dift'erent branches of
sociological speculation can be studied
apart. Political Economy characterized. 62^
4. Political Ethology, or the science of nation-
al character 02&
6. The Empirical Laws of the Social Sci-
ence 628
6. The Verification of the Social Science 62»
Chapter S. Of the Inverse Deductive, or Historical
Method.
5 1. Dittinction between the general Science of
Society, and special sociological inquiries. 030
2. What is meant by a State of Society f 631
3. TheProgressivenessof Man and Society.. 681
4. The laws of the succession of states of so-
ciety can only be ascertained by the In-
verse Deductive Method 63*:
CONTENTS.
XV
FAOB
§5. Social Statics, or the science of the Co-ex-
istences of Social Phenomena 635
6. Social Dynamics, or the science of the Suc-
ceesi<ms of Social Phenomena. 639
7. Outlines of the Historical Method 640
8. Patnre prospects of Sociological Inquiry. . 642
CoAPTEB XL Addi^umal Elucidations of the Sci-
eiux of History.
S 1. The subjection of historical facts to uni-
form laws is verified by statistics 644
2. — does not imply the insignificance of
moral causes 646
3. — nor the Inefflcacy of the characters of
indlridaals and of the acts of govern-
ments 647
«. The historical importance of eminent men
PAGB
and of the policy of governments lllns-
trated 650
Ghapteb Xn. 0/ the Logic of Practice, or Art ; in-
clvdiTig Morality and Policy.
§ 1. Morality not a Science, but an Art 662
5. Belation between rules of art and the the-
orems of the correspondiug science 653
3. What is the proper fauction of rules of art ? 654
4. Art can not be deductive 655
B. Every Art consists of truths of Science, ar-
ranged iu the order suitable for some prac-
tical use 655
6. Teleology, or the Doctrine of Ends Oi.0
7. Necessity of an nltimate standard, or first
principle of Teleology 657
8. Conclusion <StW
INTRODUCTION.
§ 1. There is as great diversity among authors in the modes which they
have adopted of defining logic, as in their treatment of the details of it.
This is what might naturally be expected on any subject on which writers
have availed themselves of the same language as a. means of delivering
different ideas. Ethics and jurisprudence are liable to the remark in com-
mon with logic. Almost every writer having taken a different view of
some of the particulars which these branches of knowledge are usually
understood to include ; each has so framed his definition as to indicate
beforehand his own peculiar tenets, and sometimes to beg the question in
their favor.
This diversity is not so much an evil to be complained of, as an inevita-
ble and in some degree a proper result of the imperfect state of those
sciences. It is .not to be expected that there should be agreement about
the definition of any thing, until there is agreement about the thing itself.
To define, is to select from among all the properties of a thing, those which
shall be undei'stood to be designated and declared by its name; and the
properties must be well known to us before we can be competent to deter-
mine which of them are fittest to be chosen for this purpose. According-
ly, in the case of so complex an aggregation of particulars as are compre-
hended in any thing which can be called a science, the definition we set
out with is seldom that which a more extensive knowledge of the subject
shows to be the most appropriate. Until we know the particulars them-
selves, we can not fix upon the most correct and compact mode of circum-
scribing them by a general description. It was not until after an extensive
and accurate acquaintance with the details of chemical phenomena, that it
was found possible to frame a rational definition of chemistry; and the
definition of the science of life and organization is still a matter of dispute.
So long as the sciences are imperfect, the definitions must partake of their
imperfection ; and if the former are progressive, the latter ought to be so
too.. As much, therefore, as is to be expected from a definition placed at
the commencement of a subject, is that it should define the scope of our
inquiries : and the definition which I am about to offer of the science of
logic, pretends to nothing more than to be a statement of the question
which I have put to myself, and which this book is an attempt to resolve.
The reader is at liberty to object to it as a definition of logic; but it is at
all events a correct definition of the subject of this volume.
§ 2. Logic has often been called the Art of Reasoning. A writei-* who
has done more than any other person to restore this study to the rank from
which it had fallen in the estimation of the cultivated class in our own
country, has adopted the above definition with an amendment ; he has de-
* Archbishop Whately.
2
18 INTRODUCTION.
fined Logic to be the Science, as well as the Art, of reasoning; meaning
by the former term, the analysis of the mental process which takes place
whenever we reason, and by the latter, the rules, grounded on that analy-
sis, for conducting the process correctly. There can be no doubt as to the
propriety of the emendation. A right understanding of the mental process
itself, of the conditions it depends on, and the steps of which it consists,
is the only basis on which a system of rules, fitted for the direction of the
process, can possibly be founded. Art necessarily presupposes knowledge ;,
art, in any but its infant state, presupposes scientific knowledge : and if ev-
ery art does not bear the name of a science, it is only because several sci-
ences are often necessary to form the groundwork of a single art. So com-
plicated are the conditions which govern our practical agency, that to ena-
ble one thing to be done, it is often requisite to know the nature and prop-
erties of many things.
Logic, then, comprises the science of reasoning, as well as an art, found-
ed on that science. But the word Reasoning, again, like most other scien-
tific terms in popular use, abounds in ambiguities. In one of its accepta-
tions, it means syllogizing ; or the mode of inference which may be called
(with sufficient accuracy for the present purpose) concluding from generals-
to particulars. In another of its senses, to reason is simply to infer any
assertion, from assertions already admitted : and in this sense induction is
as much entitled to be called reasoning as the demonstrations of geometry!;
Writers on logic have generally preferred the former acceptation of th«
term : the latter, and more extensive signification is that in which I meai)
to use it. I do this by virtue of the right I claim for every author, to give
whatever provisional definition he pleases of his own subject. But suffi-,
cient reasons will, I believe, unfold themselves as we advance, why this-
should be not only the provisional but the final definition. It involves, at
all events, no arbitrary change in the meaning of the word ; for, with the
general usage of the English language, the wider signification, I believe,
accords better than the more restricted one.
§ 3. But reasoning, even in the widest sense of which the word is sus-
ceptible, does not seem to comprehend all that is included, either in the
best, or even in the most current, conception of the scope and province of
our science. The employment of the word Logic to denote the theory of
Argumentation, is derived from the Aristotelian, or, as they are commonly
termed, the scholastic, logicians. Yet even with them, in their systematic
treatises, Argumentation was the subject only of the third part : the two
former treated of Terms, and of Propositions ; under one or other of which
heads were also included Definition and Division. By some, indeed, these
previous topics were professedly introduced only on account of their con-
nection with reasoning, and as a preparation for the doctrine and rules of
the syllogism. Yet they were treated with greater minuteness, and dwelt
on at greater length, than was required for that purpose alone. More re-^
cent writers on logic have generally understood the term as it was employ-
ed by the able author of the Port Royal Logic ; viz., as equivalent to the
Art of Thinking. Nor is this acceptation confined to books, and scientific!
inquiries. Even in ordinary conversation, the ideas connected with the'
word Logic include at least precision of language, and accuracy of classifi-!
cation : and we perhaps oftener hear persons speak of a logical arrange-*
ment, or of expressions logically defined, than of conclusions logically de^,'
duced from premises. Again, a man is often called a great logician or a>
DEFINITION AND PROVINCE OF LOGIC. 19
man of powerful logic, not for the accuracy of his deductions, but for the
extent of his command over premises ; because the general propositions
required for explaining a difficulty or refuting a sophism, copiously and
promptly occur to him : because, in short, his knowledge, besides being
ample, is well under his command for argumentative use. Whether, there-
fore, we conform to the practice of those who have made the subject their
particular study, or to that of popular writers and common discourse, the
province of logic will include several operations of the intellect not usually
considered to fall within the meaning of the terms Reasoning and Argu-
mentation.
These various operations might be brought within the compass of the
science, and the additional advantage be obtained of a very simple defini-
tion, if, by an extension of the term, sanctioned by high authorities, we
were to define logic as the science which treats of the operations of the hu-
man understanding in the pursuit of truth. For to this ultimate end, nam-
ing, classification, definition, and all other operations over which logic has
ever claimed jurisdiction, are essentiaUy subsidiaiy. They may all be re-
garded as contrivances for enabling a person to know the truths which are
needful to him, and to know them at the precise moment at which they are
needful. Other purposes, indeed, are also served by these operations ; for
instance, that of imparting our knowledge to others. But, viewed with re-
gard to this purpose, they have never been considered as within the prov-
ince of the logician. The sole object of Logic is the guidance of one's own
thoughts : the communication of those thoughts to others falls under the
consideration of Rhetoric, in the large sense in which that art was con-
ceived by the ancients ; or of the still more extensive art of Education.
Logic takes cognizance of our intellectual operations only as they conduce
to our own knowledge, and to our command over that knowledge for our
own uses. If there were but one rational being in the universe, that being
might be a perfect logician ; and the science and art of logic would be the
same for that one person as for the whole human race.
§ 4. But, if the definition which we formerly examined included too lit-
tle, that which is now suggested has the opposite fault of including too
much.
Truths are known to us in two ways : some are known directly, and of
themselves; some through the medium of other truths. The former are
the subject of Intuition, or Consciousness ;* the latter, of Inference. The
truths known by intuition are the original premises from which all others
are inferred. Our assent to the conclusion being grounded on the truth of
the premises, we never could arrive at any knowledge by reasoning, unless
something could be Juiown antecedently to all reasoning.
Examples of tniths known to us by immediate consciousness, are our
own bodily sensations and mental feelings. I know directly, and of my
own knowledge, that I was vexed yesterday, or that I am hungry to-day.
Examples of truths which we know only by way of inference, are occur-
rences which took place while we were absent, the events recorded in his-
tory, or the theorems of mathematics. The two former we infer from the
testimony adduced, or from the traces of those past occurrences which still
• I use these terms indiscriminately, because, for the purpose in view, there is no need for
making any distinction between them. But metaphysicians usually restrict the name Intui-
tion to the direct knowledge we are supposed to have of things external to our minds, and
Consciousness to our knowledge of our own mental phenomena.
20 INTRODUCTION.
exist ; the latter, from the premises laid down in books of geometry, undei
the title of definitions and axioms. Whatever we are capable of knowing
must belong to the one class or to the other; must be in the number of the
primitive data, or of the conclusions which can be drawn from these.
With the original data, or ultimate premises of our knowledge; with
their number or nature, the mode in which they are obtained, or the testa
by which they may be distinguished ; logic, in a direct way at least, has,
in the sense in which I conceive the science, nothing to do. These ques-
tions are partly not a subject of science at all, partly that of a very differ-
ent science.
Whatever is known to us by consciousness is known beyond possibility
of question. What one sees or feels, whether bodily or mentally, one can
not but be sure that one sees or feels. No science is required for the pur-
pose of establishing such truths ; no rules of art can render our knowledge
of them more certain than it is in itself. There is no logic for this portion
of our knowledge.
But we may fancy that we see or feel what we in reality infer. A truth,
or supposed truth, which is really the result of a very rapid inference, may
seem to be apprehended intuitively. It has long been agreed by thinkers of
the most opposite schools, that this mistake is actually made in so familiar
an instance as that of the eyesight. There is nothing of which we appear
to ourselves to be more directly conscious than the distance of an object
from us. Yet it has long been ascertained, that what is perceived by the
eye, is at most nothing more than a variously colored surface ; that when
we fancy we see distance, all we really see is certain variations of apparent
size, and degrees of faintness of color; that our estimate of the object's
distance from us is the result partly of a rapid inference from the muscular
sensations accompanying the adjustment of the focal distance of the eye to
objects unequally remote from us, and partly of a comparison (made with
so much rapidity that we are unconscious of making it) between the size
and color of the object as they appear at the time, and the size and coloi
of the same or of similar objects as they appeared when close at hand, oi
when their degree of remoteness was known by other evidence. The per-
ception of distance by the eye, which seems so like intuition, is thus, in re-
ality, an inference grounded on experience ; an inference, too, which we
learn to make ; and which we make with more and more correctness as ouj
experience increases ; though in familiar cases it takes place so rapidly as
to appear exactly on a par with those perceptions of sight which are really
intuitive, our perceptions of color.*
Of the science, therefore, which expounds the operations of the human
understanding in the pursuit of truth, one essential part is the inquiry:
What are the facts which are the objects of intuitiorL-or consciousness, and
what are those which we merely infer ? But this inquiry has never been
considered a portion of logic. Its place is in another and a perfectly dis-
tinct department of science, to which the name metaphysics more particifej
larly belongs : that portion of mental philosophy which attempts to deter-
mine what part of the furniture of the mind belongs to it originally, and
* This important theory has of late been called in question by a writer of deserved reput*?
tion, Mr. Samuel Bailey ; but I do not conceive that the grounds on which it has been ad-
mitted as an established doctrine for a century past, have been at all shaken by that gentle-
man's objections. I have elsewhere said what appeared to me necessary in reply to -his argu-
ments. (^Westmiitster Review for October. 1842; reprinted in "Dissertations and Discus-
sions," Tol. ii.)
DEFINITION AND PROVINCE OF LOGIC. 21
what part is constructed out of materials furnished to it from without. To
this science appertain the great and much debated questions of the exist-
ence of matter ; the existence of spirit, and of a distinction between it and
matter ; the reality of time and space, as things without the mind, and
distinguishable from the objects which are said to exist in them. For
in the present state of the discussion on these topics, it is almost uni-
versally allowed that the existence of matter or of spirit, of space or of
time, is in its nature unsusceptible of being proved ; and that if any thing
is known of them, it must be by immediate intuition. To the same science
belong the inquiries into the nature of Conception, Perception, Memory,
and Belief ; all of which are operations of the understanding in the pursuit
of truth; but with which, as phenomena of the mind, or with the possibili-
ty which may or may not exist of analyzing any of them into si-mpler phe-
nomena, the logician as such has no concern. To this science must also be
referred the following, and all analogous questions : To what extent our in-
tellectual faculties and our emotions are innate — to what extent the result
of association : Whether God and duty are realities, the existence of which
is manifest to us a priori by the constitution of our rational faculty ; or
whether our ideas of them are acquired notions, the origin of which we
are able to trace and explain ; and the reality of the objects themselves -a
question not of consciousness or intuition, but of evidence and reasoning.
The province of logic must be restricted to that portion of our knowl-
edge which consists of inferences from truths previously known ; whether
those antecedent data be general propositions, or particular observations
and perceptions. Logic is not the science of Belief, but the science of
Proof, or Evidence. In so far as belief professes to be founded on proof,
the office of logic is to supply a test for ascertaining whether or not the be-
lief is well grounded. With the claims which any proposition has to be-
lief on the evidence of consciousness — that is, without evidence in the
proper sense of the word — logic has nothing to do.
• § 6. By far the greatest portion of our knowledge, whether of general
truths or of particular facts, being avowedly matter of inference, nearly the
whole, not only of science, but of human conduct, is amenable to the au-
thority of logic. To draw inferences has been said to be the great business
of life. Every one has daily, hourly, and momentary need of ascertaining
facts which he has not directly observed ; not from any general purpose of
adding to his stock of knowledge, but because the facts themselves are of
importance to his interests or to his occupations. The business of the
magistrate, of the military commander, of the navigator, of the physician,
of the agriculturist, is merely to judge of evidence, and to act accordingly.
They all have to ascertain certain facts, in order that they may afterward
apply certain rules, either devised by themselves or prescribed for their
guidance by others ; and as they do this well or ill, so they discharge well
or ill the duties of their several callings. It is the only occupation in which
the mind never ceases to be engaged ; and is the subject, not of logic, but
of knowledge in general.
Logic, however, is not the same thing with knowledge, though the field
of logic is co-extensive with the field of knowledge. Logic is the com-
mon judge and arbiter of all particular investigations. It does not under-
take to find evidence, but to determine whether it has been found. Logic
neither observes, nor invents, nor discovers ; but judges. It is no part of
the business of logic to inform the surgeon what appearances are found to
22 INTRODUCTION.
accompany a violent death. This he must learn from his own experience
and observation, or fi-om that of others, his predecessors in his peculiarly,
pursuit. But logic sits in judgment on the sufficiency of that observation
and experience to justify his rules, and on the sufficiency of his rules to
justify his conduct. It does not give him proofs, but teaches him what
makes them proofs, and how he is to judge of them. It does not teach '
that any particular fact proves any other, but points out to what conditions
all facts must conform, in order that they may prove other facts. To de-
cide whether any given fact fulfills these conditions, or whether facts can
be found which fulfill them in a given case, belongs exclusively to the par-
ticular art or science, or to our knowledge of the particular subject.
It is in this sense that logic is, what it was so expressively called by the
schoolmen and by Bacon, ars artium; the science of science itself. AH
science consists of data and conclusions from those data, of proofs and what
they prove : now logic points out what relations must subsist between data
and whatever can be concluded from them, between proof and every thing
which it can prove. If there be any such indispensable relations, and if
these can be precisely determined, every particular branch of science, as
well as every individual in the guidance of his conduct, is bound to con-
foTm to those relations, under the penalty of making false inferences — of
drawing conclusions which are not grounded in the realities of things.
Whatever has at any time been concluded justly, whatever knowledge has
been acquired otherwise than by immediate intuition, depended on the ob-
servance of the laws which it is the province of logic to investigate. If
the conclusions are just, and the knowledge real, those laws, whether known
or not, have been observed.
§ 6. We need not, therefore, seek any further for a solution of the ques-
tion, so often agitated, respecting the utility of logic. If a science of logic
exists, or is capable of existing, it must be useful. If there be rules to
which every mind consciously or unconsciously conforms in every instance
in which it infers rightly, there seems little necessity for discussing whether
a person is more likely to observe those rules, when he knows the rules, than
when he is unacquainted with them.
A science may undoubtedly be brought to a certain, not inconsiderable,
stage of advancement, without the application of any other logic to it than
what all persons, who are said to have a sound understanding, acquire em-
pirically in the course of their studies. Mankind judged of evidence, and
often correctly, before logic was a science, or they never could have made
it one. And they executed great mechanical works before they understood
the laws of mechanics. But there are limits both to what mechanicians can
do without principles of mechanics, and to what thinkers can do without
principles of logic. A few individuals, by extraordinary genius, or by the
accidental acquisition of a good set of intellectual habits, may work with-
out principles in the same way, or nearly the same way, in which they
would have worked if they had been in possession of principles. But the
bulk of mankind require either to understand the theory of what they are
doing, or to have rules laid down for them by those who have understood-
the theory. In the progress of science from its easiest to its more difficult
problems, each great step in advance has usually had either as its precur-
sor, or as its accompaniment and necessary condition, a corresponding im-
provement in the notions and principles of logic received among the most
advanced thinkers. And if several of the more difficult sciences are still.
DEFINITION AND PKOVINCE OF LOGIC. 23
in so defective a state ; if not only so little is proved, but disputation has
not terminated even about the little which seemed to be so ; the i-eason
perhaps is, that men's logical notions have not yet acquired the degree of
■extension, or of accuracy, requisite for the estimation of the evidence prop-
er to those particular departments of knowledge.
§ 7. Logic, then, is the science of the operations of the understanding
which are subservient to the estimation of evidence : both the process it-
self of advancing from known truths to unknown, and all other intellectual
operations in so far as auxiliary to this. It includes, therefore, the opera-
tion of Naming ; for language is an instrument of thought, as well as a
means of communicating our thoughts. It includes, also. Definition, and
•Classification. For, the use of these operations (putting all other minds
than one's own out of consideration) is to serve not only for keeping our
evidences and the conclusions from them permanent and readily accessible
in the memory, but for so marshaling the facts which we may at any time
be engaged in investigating, as to enable us to perceive more clearly what
■evidence there is, and to judge with fewer chances of error whether it be
suflScient. These, therefore, are operations specially instrumental to the
estimation of evidence, and, as such, are within the province of Logic.
There are other more elementary processes, concerned in all thinking, such
as Conception, Memory, and the like ; but of these it is not necessary that
Logic should take any peculiar cognizance, since they have no special
-connection with the problem of Evidence, further than that, like all other
problems addressed to the understanding, it presupposes them.
Our object, then, will be, to attempt a correct analysis of the intellectual
process called Reasoning or Inference, and of such other mental operations
:as are intended to facilitate this : as well as, on the foundation of this anal-
ysis, and pari passu with it, to bring together or frame a set of rules or
canons for testing the sufficiency of any given evidence to prove any given
•proposition.
With respect to the first part of this undertaking, I do not attempt to
-decompose the mental operations in question into their ultimate elements.
It is enough if the analysis as far as it goes is correct, and if it goes far
enough for the practical purposes of logic considered as an art. The sep-
aration of a complicated phenomenon into its component parts is not like
a connected and interdependent chain of proof. If one link of an argu-
ment breaks, the whole drops to the ground ; but one step toward an anal-
ysis holds good and has an independent value, though we should never be
able to make a second. The results which have been obtained by analytical
chemistry are not the less valuable, though it should be discovered that
all which we now call simple substances are really compounds. All other
things are at any rate compounded of those elements: whether the ele-
ments themselves admit of decomposition, is an important inquiry, but
-does not affect the certainty of the science up to that point.
I shall, accordingly, attempt to analyze the process of inference, and the
processes subordinate to inference, so far only as may be requisite for as-
certaining the difference between a correct and an incorrect performance
of those processes. The reason for thus limiting our design, is evident.
It has been said by objectors to logic, that we do not learn to use our
muscles by studying their anatomy. The fact is not quite fairly stated;
for if the action of any of our muscles were vitiated by local weakness, or
other physical defect, a knowledge of their anatomy might be very neces-
24 INTRODUCTION.
sary for effecting a cure. But we should be justly liable to the criticism
involved in this objection, were we, in a treatise on logic, to carry the anal-
ysis of the reasoning process beyond the point at which any inaccuracy
which may have crept into it must become visible. In learning bodily
exercises (to carry on the same illustration) we do, and must, analyze the
bodily motions so far as is necessary for distinguishing those which ou^^
to be performed from those which ought not. To a similar extent, and no
further, it is necessary that the logician should analyze the mental process^
with which Logic is concerned. Logic has no interest in carrying the anal-
ysis beyond the point at which it becomes apparent whether the operations
have in any individual case been rightly or wrongiy performed: in the
same manner as the science of music teaches us to discriminate between
musical notes, and to know the combinations of which they are susceptible,
but not what number of vibrations in a second correspond to each ; which,
though useful to be known, is useful for totally different purposes. The
extension of Logic as a Science is determined by its necessities as an Art :
whatever it does not need for its practical ends, it leaves to the larger
science which may be said to correspond, not to any particular art, but to
art in general ; the science which deals with the constitution of the human
faculties ; and to which, in the part of our mental nature which concerns
Logic, as well as in all other parts, it belongs to decide what are ultimate
facts, and what are resolvable into other facts. And I believe it will be
found that most of the conclusions arrived at in this work have no neces-
sary connection with any particular views respecting the ulterior analysis.
Logic is common ground on which the partisans of Hartley and of Reid,
of Locke and of Kant, may meet and join hands. Particular and detached
opinions of all these thinkers will no doubt occasionally be controverted,
since all of them were logicians as well as metaphysicians ; but the field on
which their principal battles have been fought, lies beyond the boundaries
of our science.
It can not, indeed, be pretended that logical principles can be altogether
irrelevant to those more abstruse discussions ; nor is it possible but that
the view we are led to take of the problem which logic proposes, must
have a tendency favorable to the adoption of some one opinion, on these
controverted subjects, rather than another. For metaphysics, in endeavor-
ing to solve its own peculiar problem, must employ means, the validity of
which falls under the cognizance of logic. It proceeds, no doubt, as far as
possible, merely by a closer and more attentive interrogation of our con-
sciousness, or more properly speaking, of our memory ; and so far is not
amenable to logic. But wherever this method is insufficient to attain the
end of its inquiries, it must proceed, like other sciences, by means of evi-
dence. Now, the moment this science begins to draw inferences from evi-
dence, logic becomes the sovereign judge whether its inferences are well
grounded, or what other inferences would be so.
This, however, constitutes no nearer or other relation between logic and
metaphysics, than that which exists between logic and every other science.
And I can conscientiously aflSrm that no one proposiiioii laid down in this
work has been adopted for the sake of establishing, or with any reference
to its fitness for being employed in establishing, preconceived opinions in
any department of knowledge or of inquiry on which the speouktive world
is still undecided.*
* The view taken in the text, of the definition and purpose of Logic, stands in marked op-
position to that of the school of philosophy which, in this country, is represented by the writ^
DEFINITION AND PROVINCE OF LOGIC. 25
ings of Sir William Hamilton and of his numerous pupils. Logic, as this school conceives it,
is "the Science of the Formal Laws of Thought;" a definition framed for the express pur-
pose of excluding, as irrelevant to Logic, whatever relates to Belief and Disbelief, or to the
pursuit of truth as such, and restricting the science to that very limited portion of its total
province, which has reference to the conditions, not of Truth, but of Consistency. What I
have thought it useful to say in opposition to this limitation of the field of Logic, has been
said at some length in a separate work, first published in 1865, and entitled "An Examina-
tion of Sir William Hamilton's Philosophy, and of the Principal Philosophical Questions dis-
cussed in his Writings." For the purposes of the present Treatise, I am content that the jus-
tification of the larger extension which I give to the domain of the science, should rest on the
sequel of the Treatise itself. Some remarks on the relation which the Logic of Consistency
bears to the Logic of Truth, and on the place which that particular part occupies in the whole
to which it belongs, will be found in the present volnme (Book II., chap, iii., § 9).
BOOK I.
OF NAMES AND PROPOSITIONS.
"La scolastiqne, qui produisit dans la logique, comme dans la morale, et dans une partie-
de la m^taphysique, une subtilit^, une precision d'id^es, dont I'habitude inconnue aux anciens,
a contribue plus qu'on ne croit au progr^s de la bonne philosophie." — Condokcet, Vie de
Twgot.
"To the schoolmen the vulgar languages are principally indebted for what precision and
analytic subtlety they possess." — Sir W. Hamilton, Discussions in Philosophy.
CHAPTER I.
OF THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF IiANGUAGE.
§ 1. It is SO much the established pi-actice of writers on logic to com-
mence their treatises by a few genei-al observations (in most cases, it is
true, rather meagre) on Terms and their varieties, that it will, perhaps^
scarcely be required from me, in merely following the common usage, to be
as particular in assigning my reasons, as it is usually expected that those-
should be who deviate from it.
The practice, indeed, is recommended by considerations far too obvious
to require a formal justification. Logic is a portion of the Art of Think-
ing : Language is evidently, and by the admission of all philosophers, one
of the principal instruments or helps of thought ; and any imperfection in,
the instrument, or in the mode of employing it, is confessedly liable, still
more than in almost any other art, to confuse and impede the process, and
destroy all ground of confidence in the result. For a mind not previously
versed in the meaning and right use of the various kinds of words, to at-
tempt the study of methods of philosophizing, would be as if some one
should attempt to become an astronomical observer, having never learned to
adjust the focal distance of his optical instruments so as to see distinctly.
Since Reasoning, or Inference, the principal subject of logic, is an opera-
tion which usually takes place by means of words, and in complicated cases
can take place in no other way; those who have not a thorough insight
into the signification and purposes of words, will be under chances, amount-
ing almost to certainty, of reasoning or inferring incorrectly. And logi-
cians have generally felt that unless, in the very first stage, they removed
this source of error ; unless they taught their pupil to put away the glasses
which distort the object, and to use those which are adapted to his pur-
pose in such a manner as to assist, not perplex, his vision ; he would not be-
in a condition to practice the remaining part of their discipline with any
prospect of advantage. Therefore it is that an inquiry into language, so-
far as is needful to guard against the errors to which it gives rise, has St
all times been deemed a necessary preliminary to the study of logic.
NECESSITY OE AN ANALYSIS OF NAMES. 27
But there is another reason, of a still more fundamental nature, why the
import of words should be the earliest subject of the logician's considera-
tion : because without it he can not examine into the import of Proposi-
tions. Now this is a subject which stands on the very threshold of the
science of logic.
The object of logic, as defined in the Introductory Chapter, is to ascer-
tain how we come by that portion of our knowledge (much the greatest
portion) which is not intuitive : and by what criterion we can, in matters
DOt self-evident, distinguish between things proved and things not proved,
between what is. worthy and what is unworthy of belief. Of the various
questions which present themselves to our inqxiiring faculties, some receive
an answer from direct consciousness, others, if resolved at all, can only be
resolved by means of evidence. Logic is concerned with these last. But
before inquiring into the mode of resolving questions, it is necessary to in-
quire what are those which offer themselves; what questions are conceiva-
ble ; what inquiries are there, to which mankind have either obtained, or
been able to imagine it possible that they should obtain, an answer. This
point is best ascertained by a survey and analysis of Propositions.
§ 2. The answer to every question which it is possible to frame, must
be contained in a Proposition, or Assertion. Whatever can be an object
of belief, or even of disbelief, must, when put into words, assume the form
of a proposition. All truth and all error lie in propositions. What, by
a convenient misapplication of an abstract term, we call a Truth, means
simply a True Proposition ; and errors are false propositions. To know
the import of all possible propositions would be to know all questions
which can be raised, all matters which are susceptible of being either be-
lieved or disbelieved. How many kinds of inquiries can be propound-
ed; how many kinds of judgments can be made; and how many kinds
of propositions it is possible to frame with a meaning, are but different
forms of one and the same question. Since, then, the objects of all Be-
lief and of all Inquiry express themselves in propositions, a sufficient scru-
tiny of Propositions and of their varieties will apprise us what questions
mankind have actually asked of themselves, and what, in the nature of an-
swers to those questions, they have actually thought they had grounds to
believe.
Now the first glance at a proposition shows that it is formed by putting
together two names. A proposition, according to the common simple defi-
nition, which is sufficient for our purpose is, discourse, in which something
is affirmed or denied of something. Thus, in the proposition, Gold is yel-
low, the quality yellow is affirmed of the substance gold. In the proposi-
tion, Franklin was not born in England, the fact expressed by the words
horn in England is denied of the man Franklin.
Every proposition consists of three parts : the Subject, the Predicate,
and the Copula. The predicate is the name denoting that which is affirmed
or denied. The subject is the name denoting the person or thing which
something is affirmed or denied of. The copula is the sign denoting that
there is an affirmation or denial, and thereby enabling the hearer or reader
to distinguish a proposition from any other kind of discourse. Thus, in the
proposition, The earth is round, the Predicate is the word roimc?, which de-
notes the quality affirmed, or (as the phrase is) predicated : the earth, words
denoting the object which that quality is affirmed of, compose the Subject ;
the word is, which serves as the connecting mark between the subject and
2g NAMES AND PKOPOSITIONS.
predicate, to show that one of them is affirmed of the other, is called the
Copula.
Dismissing, for the present, the copula, of which more will be said here-
after, every proposition, then, consists of at least two names — brings to-
gether two names, in a particular manner. This is already a first step tofe
ward what we are in quest of. It appears from this, that for an act of be-
Uef, one object is not suflicient ; the simplest act of belief supposes, and has
something to do with, iioo objects — two names, to say the least; and (since
the names must be names of something) two namable things. A large
class of thinkers would cut the matter short by saying, two ideas. They
would say, that the subject and predicate are both of them names of ideas ;
the idea of gold, for instance, and the idea of yellow ; and that what takes
place (or part of what takes place) in the act of belief consists in bring-
ing (as it is often expressed) one of these ideas under the other.. But this
•we are not yet in a condition to say : whether such be the correct mode
of describing the phenomenon, is an after consideration. The result with
which for the present we must be contented, is, that in every act of belief
two objects are in some manner taken cognizance of; that there can be no
belief claimed, or question propounded, which does not embrace two dis-
tinct (either material or intellectual) subjects of thought; each of them
capable, or not, of being conceived by itself, but incapable of being believed
by itself.
I may say, for instance, " the sun." The word has a meaning, and sug-
gests that meaning to the mind of any one who is listening to me. But
suppose I ask him. Whether it is true : whether he believes it ? He can
give no answer. There is as yet nothing to believe, or to disbelieve. Now,
however, let me make, of all possible assertions respecting the sun, the one
■which involves the least of reference to any object besides itself ; let me
say, " the sun exists." Here, at once, is something which a person can say
he believes. But here, instead of only one, we find two distinct objects of
conception: the sun is one object; existence is another. Let it not be said
that this second conception, existence, is involved in the first ; for the sun
may be conceived as no longer existing. "The sun" does not convey all
the meaning that is conveyed by "the sun exists;" "my father" does not
include all the meaning of "my father exists," for he may be dead; "a
round square " does not include the meaning of " a round square exists,"
lov it does not and can not exist. When I say " the sun," " my father," or
a " round square," I do not call upon the hearer for any belief or disbelief,
nor can either the one or the other be afforded me ; but if I say, " the sun
exists," "my father exists," or "a round square exists," I call for belief;
and should, in the first of the three instances, meet with it ; in the second,
with belief or disbelief, as the case might be ; in the third, with disbelief.
§ 3. This first step in the analysis of the object of belief, which, though
so obvious, will be found to be not unimportant, is the only one which we
shall find it practicable to make without a preliminary survey of language.
If we attempt to proceed further in the same path, that is, to analyze any
further the import of Propositions ; we find forced upon us, as a subject of
previous considei'ation, the import of Names. For every proposition con-
sists of two names ; and every proposition affirms or denies one of these
names, of the other. Now what we do, what passes in our mind, when we
affirm or deny two names of one another, must depend on what they are
names of; since it is with reference to that, and not to the mere names
NAMES. 29
themselves, that we make the affirmation or denial. Here, therefore, we
fiiul a new reason why the signification of names, and the relation general-
ly between names and the things signified by them, must occupy the pre^
liminary stage of the inquiry we are engaged in.
It may be objected that the meaning of names can guide us at most only
to the opinions, possibly the foolish and groundless opinions, which man-
kind have formed concerning things, and that as the object of philosophy
is truth, not opinion, the philosopher should dismiss words and look into
things themselves, to ascertain what questions can be asked and answered
in regard to them. This advice (which no one has it in his power to fol-
low) is in reality an exhortation to discard the whole fruits of the labors of
his predecessors, and conduct himself as if he wei'e the first person whd
had ever turned an inquiring eye upon nature. What does any one's per-
sonal knowledge of Things amount to, after subtracting all which he has
acquired by means of the words of other people? Even after he has learn-
ed as much as people usually do learn from others, will the notions of
things contained in his individual mind afford as sufficient a basis for a
catalogue raisonn^ as the notions which are in the minds of all mankind ?
In any enumeration and classification of Things, which does not set out
from their names, no varieties of things will of course be comprehended
but those recognized by the particular inquirer ; and it will still remain to
be established, by a subsequent examination of names, that the enumei-a-
tion has omitted nothing which ought to have been included. But if we
begin with names, and use them as our clue to the things, we bring at once
before us all the distinctions which have been recognized, not by a single
inquii-er, but by all inquirers taken together. It doubtless may, and I be-
liev.e it will, be found, that mankind have multiplied the varieties unneces-
sarily, and have imagined distinctions among things, whei-e there were only
distinctions in the manner of naming them. But we are not entitled to as-
sume this in the commencement. We must begin by recognizing the dis-
tinctions made by ordinary language. If some of these appear, on a close
examination, not to be fundamental, the enumeration of the different kinds
of realities may be abridged accordingly. But to impose upon the facts in
the first instance the yoke of a theory, while the grounds of the theory are
reserved for discussion in a subsequent stage, is not a course which a logi-
cian can reasonably adopt.
CHAPTER II.
OP NAMES.
§ 1. "A NAMB," says Hobbes,* "is a word taken at pleasure to serve for
a mark which may raise in our mind a thought like to some thought we had
before, and which being pronounced to others, may be to them a sign of
what thought the speaker hadf before in his mind." This simple defini-
tion of a name, as a word (or set of words) serving the double purpose of
a mark to recall to ourselves the likeness of a former thought, and a sign
* Computation or Logic, chap. ii.
t In the original "had, or had not." These last words, as involving a suhtlety foreign to
our present purpose, I have forborne to quote.
30 NAMES AND PBOPOSITIONS.
to make it known to others, appears unexceptionable. Names, indeed, do
much more than this ; but whatever else they do, grows out of, and is the'
result of this : as will appear in its proper place.
Are names more properly said to be the names of things, or of our ideas
of things? The first is the expression in common use; the last is that of
some metaphysicians, who conceived that in adoptihg it they were intro-
ducing a highly important distinction. The eminent thinker, just quoted,-
seems to countenance the latter opinion. "But seeing," he continues,
" names ordered in speech (as is defined) are signs of our conceptions, it
is manifest they are not signs of the things themselves ; for that the sound
of this word stx>ne should be the sign of a stone, can not be understood in
any sense but this, that he that hears it collects that he that pronounces it
thinks of a stone."
If it be merely meant that the conception alone, and not the thing itself,
is recalled by the name, or imparted to the hearer, this of course can not
be denied. Nevertheless, there seems ,good reason for adhering to the
common usage, and calling (as indeed Hobbes himself does in other places)
the word sun the name of the sun, and not the name of our idea of the
sun. For names are not intended only to make the hearer conceive what
we conceive, but also to inform him what we believe. Now, when I use a
name for the purpose of expressing a belief, it is a belief concerning the
thing itself, not concerning my idea of it. When t say, "the sun is the
cause of day," I do not mean that my idea of the sun causes or excites in
me the idea of day ; or in other words, that thinking of the sun makes me
think of day. I mean, that a certain physical fact, which is called the sun's
presence (and which, in the ultimate analysis, resolves itself into sensations,
not ideas) causes another physical fact, which is called day. It seems prop-
er to consider a word as the name of that which we intend to be under-
stood by it when we use it ; of that which any fact that we assert of it. is
to be understood of ; that, in short, concerning which, when we employ the
word, we intend to give information. Names, therefore, shall always be
spoken of in this work as the names of things themselves, and not merely
of our ideas of things.
But the question now arises, of what things ? and to answer this it is
necessary to take into consideration the different kinds of names.
§ 2. It is usual, before examining the various classes into which names
are commonly divided, to begin by distinguishing from names of every
description, those words which are not names, but only parts of names.
Among such are reckoned particles, as of, to, truly, often; the inflected
cases of nouns substantive, as me, him, J'ohn's; and even adjectives, as
large, heavy. These words do not express things of which any thing can
be affirmed or denied. We can not say. Heavy fell, or A heavy fell ; Truly,
or A truly, was asserted ; Of, or An of, was in the room. Unless, indeed,
we are speaking of the mere words themselves, as when we sayj' Truly" is
an English word, or, Heavy' is an adjective. In that case they are complete
narnes — viz., names of those particular sounds, or of those particular col-
lections of written characters. This employment of a word to denote the
mere letters and syllables of which it is composed, was termed by the
schoolmen the suppositio materialis of the word. In any other sense we
can not introduce one of these words into the subject of a proposition,
unless in combination with other words ; as, A heavy body fell, A truly
important fact was asserted, A member oi parliament was in the room.
NAMES. 31
An adjective, however, is capable of standing by itself as the predicate
of a proposition; as when we say. Snow is white; and occasionally even
as the subject, foi- we may say, White is an agreeable color. The adjec-
tive is often said to be so used by a grammatical ellipsis : Snow is white,
instead of Snow is a white object ; White is an agreeable color, instead of,
-A white color, or. The color white, is agreeable. The Greeks and Romans
Tvere allowed, by the rules of their language, to employ this ellipsis uni-
-versally in the subject as well as in the predicate of a proposition. In
English this can not, generally speaking, be done. We may say. The earth
is round ; but we can not say. Round is easily moved ; we must say, A
round object. This distinction, however, is rather grammatical than log-
ical. Since there is no difEerence of meaning between round, and a round
object, it is only custom which prescribes that on any given occasion one
shall be used, and not the other. We shall, therefore, without scruple,
-speak of adjectives as names, whether in their own right, or as representa-
tive of the more circuitous forms of expression above exemplified. The
■other classes of subsidiary words have no title whatever to be considered
as names. An adverb, or an accusative case, can not under any circum-
stances (except when their mere letters and syllables are spoken of) figure
■as one of the terms of a proposition.
Words which are not capable of being used as names, but only as parts
■of names, were called by some of the schoolmen Syncategorematic terms :
from avv, with, and Karriyopiw, to predicate, because it was only with some
other word that they could be predicated. A word which could be used
■either as the subject or predicate of a proposition without being accom-
panied by any other word, was termed by the same authorities a Cate-
gorematic term. A combination of one or more Categorematic, and one
or more Syncategorematic words, as A heavy body, or A court of justice,
they sometimes called a mixed term ; but this seems a needless multiplica-
tion of technical expressions. A mixed terra is, in the only useful sense of
the word, Categorematic. It belongs to the class of what have been called
many-worded names.
For, as one word is frequently not a name, but only part of a name, so
a number of words often compose one single name, and no more. These ^
words, " The place which the wisdom or policy of antiquity had destined i
for the residence of the Abyssinian princes," form in the estimation of the \
logician only one name ; one Categorematic term. A mode of determining '
whether any set of words makes only one name, or more than one, is by
predicating something of it, and observing whether, by this predication, we
make only one assertion or several. Thus, when we say, John Nokes, who
was the mayor of the town, died yesterday — by this predication we make
but one assertion ; whence it appears that " John Nokes, who was the
mayor of the town," is no more than one name. It is true that in thi#
proposition, besides the assertion that John Nokes died yesterday, there
is included another assertion, namely, that John Nokes was mayor of the
town. But this last assertion was already made : we did not make it by
adding the predicate, " died yesterday." Suppose, however, that the words
lad been, John Nokes and the mayor of the town, they would have formed
two names instead of one. For when we say, John Nokes and the mayor
of the town died yesterday, we make two assertions : one, that John Nokes
died yesterday ; the other, that the mayor of the town died yesterday.
It being needless to illustrate at any greater length the subject of many-
worded names, we proceed to the distinctions which have been established
32 NAMES AND PROPOSITIONS.
among names, not according to the words they are composed of, but ac-
cording to their signification.
§ 3. All names are names of something, real or imaginary ; but all things
haw not names appropriated to them individually. For some individual
objects we require, and consequently have, separate distinguishing names ;
there is a name for every person, and for every remarkable place. Other
objects, of which we have not occasion to speak so frequently, we do not
designate by a name of their own ; but when the necessity arises for nam-
ing them, we do so by putting together several words, each of which, by
itself, might be and is used for an indefinite number of other objects ; as
when I say, this stone : " this " and " stone " being, each of them, names
that may be used of many other objects besides the particular one meant,
though the only object of which they can both be used at the given mo-
ment, consistently with their signification, may be the one of which I wish
to speak.
Were this the sole purpose for which names, that are common to more
things than one, could be employed ; if they only served, by mutually lim-
iting each other, to afford a designation for such individual objects as have
no names of their own : they could only be ranked among contrivances for
economizing the use of language. But it is evident that this is not their
sole function. It is by their means that we are enabled to assert general
propositions ; to affirm or deny any predicate of an indefinite number of
things at once. The distinction, therefore, between general names, and in-
dividual or singular names, is fundamental; and may be considered as the
first grand division of names.
A general name is familiarly defined, a name which is capable of being
truly affirmed, in the same sense, of each of an indefinite number of things.
_,^n individual or singular name is a name which is only capable of being
truly affirmed, in the same sense, of one thing.
Thus, man is capable of being truly aflnrmed of John, George, Mary, and
other persons without assignable limit ; and it is affirmed of all of them in
the same sense ; for the word man expresses certain qualities, and when we
predicate it of those persons, we assert that they all possess those qualities.
But J'ohn is only capable of being truly affirmed of one single person, at
least in the same sense. For, though there are many persons who bear
that name, it is not conferi'ed upon them to indicate any qualities, or any
thing which belongs to them in common ; and can not be said to be affirm-
-^ ed of them in any sense at all, consequently not in the same sense. " The
king who succeeded William the Conqueror," is also an individual name.
For, that there can not be more than one person of whom it can be truly
affirmed, is implied in the meaning of the words. Even " the king," when
' the occasion or the context defines the individual of whom it is to be un-
derstood, may justly be regarded as an individual name.
It is not unusual, by way of explaining what is meant by a general name,
to say that it is the name of a class. But this, though a convenient mode
of expression for some purposes, is objectionable as a definition, since it
explains the clearer of two things by the more obscure. It would be more
logical to reverse the proposition, and turn it into a definition of the word
class: "A class is the indefinite multitude of individuals denoted by a gen-
eral name."
It is necessary to distinguish general from collective names. A general
name is one which can be predicated of each individual of a multitude • a
NAMES. 33
collective name can not be predicated of each separately, but only of all
taken together. « The YCth regiment of foot in the British army," which
is a collective name, is not a general but an individual name ; for though it
can be predicated of a multitude of individual soldiers taken jointly, it can
not be predicated of them severally. We may say, Jones is a soldier, and
Thompson is a soldier, and Smith is a soldier, but we can not say, Jones is
the 76th regiment, and Thompson is the I6ih regiment, and Smith is the
'zeth regiment. We can only say, Jones, and Thompson, and Smith, and
Brown, and so forth (enumerating all the soldiers), are the V6th regiment.
"The 76th regiment" is a collective name, but not a general one : " a
regiment" is both a collective and a general name. General with respect
to all individual regiments, of each of which separately it can be affirmed :
collective with respect to the individual soldiers of whom any regiment is
composed.
§ 4. The second general division of names is into concrete and abstract.
A concrete name is a name which stands for a thing; an abstract name is
a name which stands for an attribute of a thing. Thus John, the sea, this
table, are names of things. White, also, is a name of a thing, or rather of
things. Whiteness, again, is the name of a quality or attribute of those
things. Man is a nanie of many things; humanity is a name of an attri-
bute of those things. Old is a name of things : old age is a name of one
of their attributes.
I have used the words concrete and abstract in the sense annexed to
them by the schoolmen, who, notwithstanding the imperfections of their
philosophy, were unrivaled in the construction of technical language, and
whose definitions, in logic at least, though they never went more than a lit-
tle way into the subject, have seldom, I think, been altered but to be spoil-
ed. A practice, however, has grown up in more modern times, which, if
not introduced by Locke, has gained currency chiefly from his example, of
applying the expression "abstract name" to all names which are the result
of abstraction or generalization, and consequently to all general names, in-
stead of confining it to the names of attributes. The metaphysicians of the
Condillac school — whose admiration of Locke, passing over the profound-
est speculations of that truly original genius, usually fastens with peculiar
eagerness upon his weakest points — ^have gone on imitating him in this
abuse of language, until there is now some difficulty in restoring the word
to its original signification. A more wanton alteration in the meaning of a
word is rarely to be met with ; for the expression general name, the exact
equivalent of which exists in all languages I am acquainted with, was al-
ready available for the purpose to which abstract has been misappropri-
ated, while the misappropriation leaves that important class of words, the
names of attributes, without any compact distinctive appellation. The old
acceptation, however, has not gone so completely out of use as to deprive
those who still adhere to it of all chance of being understood. By abstract,
then, I shall always, in Logic proper, mean the opposite of concrete; by an
abstract name, the name of an attribute ; by a concrete name, the name of
an object.
Do abstract names belong to the class of general, or to that of singular
names? Some of them are certainly general. I mean those which are
names not of one single and definite attribute, but of a class of attributes.
Such is the word color, which is a name common to whiteness, redness,
etc. Such is even the word whiteness, in respect of the different shades of
3
54 NAMES AND PROPOSITIONS.
whiteness to which it is applied in common : the word magnitude, in re-
spect of the various degrees of magnitude and the various dimensions o%
space ; the word weight, in respect of the various degrees of weight. Such
also is the word attribute itself, the common name of all particular attri-
butes. But when only one attribute, neither variable in degree nor in-
kind, is designated by the name; as visibleuess; tangibleness ; equality;
squareness; milk-whiteness ; then the name can hardly be considered gen- .
eral; for though it denotes an attribute of many different objects, the at-
tribute itself is always conceived as one, not many.* To avoid needless lo-
gomachies, the best course would probably be to consider these names as
neither general nor individual, and to place them in a class apart.
It may be objected to our definition of an abstract name, that not only
the names which we have called abstract, but adjectives, which we have
placed in the concrete class, are names of attributes; that white, for exam-
ple, is as much the name of the color as whiteness is. But (as before re-
marked) a word ought to be considered as the name of that which we intend
to be understood by it when we put it to its principal use, that is, when we
employ it in predication. When we say snow is white, milk is white, linen
is white, we do not mean it to be understood that snow, or linen, or milk,
is a color. We mean that they are things having the color. The reverse
is the case with the word whiteness ; what we affirm to be whiteness is not
snow, but the color of snow. Whiteness, therefore, is the name of the col-
or exclusively : white is a name of all things whatever having the color ; a
name, not of the quality whiteness, but of every white object. It is true,
this name was given to all those various objects on account of the quality;
and we may therefore say, without impropriety, that the quality forms part
of its signification; but a name can only be said to stand for, or to be a,
name of, the things of which it can be predicated. We shall presently see
that all names which can be said to have any signification, all names by ap-
plying which to an individual we give any information respecting that in-
dividual, may be said to imply an attribute of some sort ; but they are not
names of the attribute ; it has its own proper abstract name.
§ 5. This leads to the consideration of a third great division of names,
into connotative and non-connotative, the latter sometimes, but improperly,
called absolute. This is one of the most important distinctions which we
shall have occasion to point out, and one of those which go deepest into
the nature of language.
A non-connotative term is one which signifies a subject only, or an attri-
bute only. A connotative term is one which denotes a subject, and implies
an attribute. By a subject is here meant any thing which possesses attri-
butes. Thus John, or London, or England, are names which signify a sub-
ject only. Whiteness, length, virtue, signify an attribute only. None of
these names, therefore, are connotative. But white, long, virtuous, are con-
notative. The word white, denotes all white things, as snow, paper, the
ioam of the sea, etc., and implies, or in the language of the schoolmen, corir
notes,^ the attribute whiteness. The word white is not predicated of the
attribute, but of the subjects, snow, etc. ; but when we predicate it of
them, we convey the meaning that the attribute whiteness belongs to them.
The same may be said of the other words above cited. Virtuous, for ex-
* Vide infra, note at the end of § 3, book ii., chap. ii.
t Notare, to mark ; connotate, to mark along with ; to mark one thing with or in addition
to another.
NAMES. 35
ample, is the name of a class, which includes Socrates, Howard, the Man of
"Ross, and an undefinable number of other individuals, past, present, and to
«ome. These individuals, collectively and severally, can alone be said with
propriety to be denoted by the word : of them alone can it properly be said
to be a name. But it is a name applied to all of them in consequence of
an attribute which they are supposed to possess in common, the attribute
which has received the name of virtue. It is applied to all beings that are
•considered to possess this attribute; and to none which are not so con-
sidered.
All concrete general names are connotative. The word man, for exam-
ple, denotes Peter, Jane, John, and an indefinite number of other individu-
\a,l8, of whom, taken as a class, it is the name. But it is applied to them,
because they possess, and to signify that they possess, certain attributes.
These seem to be, corporeity, animal life, rationality, and a certain exter-
nal form, which for distinction we call the human. Every existing thing,
which possessed all these atti'ibutes, would be called a man ; and any thing
■which possessed none of them, or only one, or two, or even three of them
-without the fourth, would not be so called. For example, if in the interior
-of Africa there were to be discovered a race of animals possessing reason
•equal to that of human beings, but with the form of an elephant, they
would not be called men. Swift's Houyhnhnms would not be so called.
•Or if such newly-discovered beings possessed the form of man without any
vestige of reason, it is probable that some other name than that of man
would be found for them. How it happens that there can be any doubt
•about the matter, will appear hereafter. The word man, therefore, signi-
:fies all these attributes, and all subjects which possess these attributes..
But it can be predicated only of the subjects. What we call men, are the
subjects, the individual Stiles and Nokes ; not the qualities by which their
humanity is constituted. The name, therefore, is said to signify the sub-
jects directly, the attributes indirectly ; it denotes the s.ubject8, and im-
plies, or involves, or indicates, or as we shall say henceforth connotes, the
attributes. It is a connotative name.
Connotative names have hence been also called denominative, because
the subject which they denote is denominated by, or receives a name from
the attribute which they connote. Snow, and other objects, receive the
name white, because they possess the attribute which is called whiteness ;
Peter, James, and others receive the name man because they possess the
attributes which are considered to constitute humanity. The attribute, or
attributes, may therefore be said to denominate those objects, or to give
them a common name.*
It has been seen that all concrete general names are connotative. Even
abstract names, though the names only of attributes, may in some instances
be justly considered as connotative; for attributes themselves may have
attributes ascribed to them ; and a word which denotes attributes may con-
note an attribute of those attributes. Of this description, for example, is
such a word as fault; equivalent to had or hurtful quality. This word is
a name common to many attributes, and connotes hurtfulness, an attribute
* Archbishop Whately, who, in the later editions of his Elements of Logic, aided in reviving
the important distinction treated of in the text, proposes the term "Attributive" as a substi-
tute for "Connotative" Cp. 22, 9th edit.). The expression is, in itself, appropriate; but as
it has not the advantage of being connected with any verb, of so markedly distinctive a char-
acter as " to connote," it is not, I think, fitted to supply the place of the word Connotative in
scientific use.
36 NAMES AND PROPOSITIONS.
of those various attributes. When, for example, we say that slowness, la
a horse, is a fault, we do not mean that the slow movement, the actual|i
change of place of the slow horse, is a bad thing, but that the property or
peculiarity of the horse, from which it derives that name, the quality of be-
ing a slow mover, is an undesirable peculiarity.
In regard to those concrete names which are not general but individual,
a distinction must be made.
Proper names are not connotative : they denote the individuals who are
called by them ; but they do not indicate or imply any attributes as belong-
ing to those individuals. When we name a child by the name Paul, or a
dog by the name Cajsar, these names are simply marks used to enable those
individuals to be made subjects of discourse. It may be said, indeed, that
we must have had some reason for giving them those names rather than
any others ; and this is true ; but the name, once given, is independent
of the reason. A man may have been named John, because that wasthe
name of his father ; a town may have been named Dartmouth, because it is
situated at the mouth of the Dart. But it is no part of the signification of
the word John, that the father of the person so called bore the same name;
nor even of the word Dartmouth, to be situated at the mouth of the Dart.
If sand should choke up the mouth of the river, or an earthquake change
its course, and remove it to a distance from the town, the name of the
town would not necessarily be changed. That fact, therefore, can form no
part of the signification of the word; for otherwise, when the fact confess-
edly ceased to be true, no one would any longer think of applying the
name. Proper names are attached to the objects themselves, and are not
dependent on the continuance of any attribute of the object.
But there is another kind of names, which, although they are individual
names — that is, predicable only of one object — are really connotative. For,
though we may give to an individual a name utterly unmeaning, which we
call a proper name — a word which answers the purpose of showing what
thing it is we are talking about, but not of telling any thing about it ; yet
a name peculiar to an individual is not necessarily of this description. It
may be significant of some attribute, or some union of attributes, which,
being possessed by no object but one, determines the name exclusively to
that individual. "The sun" is a name of this description; "God," when
used by a monotheist, is another. These, however, are scarcely examples
of what we are now attempting to illustrate, being, in strictness of lan-
guage, general, not individual names : for, however they may be in fact
predicable only of one object, there is nothing in the meaning of the words
themselves which implies this : and, accordingly, when we are imagining
and not affirming, we may speak of many suns ; and the majority of man-
kind have believed, and still believe, that there are many gods. But it is
easy to produce words which are real instances of connotative individual
names. It may be part of the meaning of the connotative name itself, that
there can exist but .one individual possessing the attribute which it con-
notes : as, for instance, " the only son of John Stiles ;" " the Jirst emperoi-
of Rome." Or the attribute connoted may be a connection with some de-
terminate event, and the connection may be of such a kind as only one in-
dividual could have; or may at least be such as only one individual actually
had ; and this may be implied in the form of the expression. " The father
of Socrates" is an example of the one kind (since Socrates could not have
had two fathers) ; " the author of the Iliad," " the murderer of Henri Qua-
tre," of the second. For, though it is conceivable that more persons thaa
NAMES. 37
one might have participated in the authorship of the Iliad, or in the mur-
kier of Henri Quatre, the employment of the article the implies thatj in
fact, this was not the case. -What is here done by the word the, is done
in other cases by the context: thus, "Caesar's army" is an individual
name, if it appears from the context that the araiy meant is that which
Csesar commanded in a particular battle. The still more general expres-
sions, "the Roman army," or "the Christian army," may be individual-
ized in a similar manner. Another case of frequent occurrence has already
Tseen noticed; it is the following: The name, being a many-worded one,
may consist, in the first place, of a general name, capable therefore in it-
self of being affirmed of more things than one, but which is, in the second
place, so limited by other words joined with it, that the entire expression
can only be predicated of one object, consistently with the meaning of
the general terni. This is exemplified in such an instance as the follow-
ing: "the present prime minister of England." Prime Minister of Eng-
land is a general name ; the attributes which it connotes may be possessed
by an indefinite number of persons: in succession, however, not simulta-
neously; since the meaning of the name itself imports (among other
things) that there can be only one such person at a time. This being
the case, and the application of the name being afterward limited by the
article and the warA. present, to such individuals as possess the attributes
at one indivisible point of time, it becomes applicable only to one indi-
vidual. And as this appears from the meaning of the name, without any
extrinsic proof, it is strictly an individual name.
From the preceding observations it will easily be collected, that when-
ever the names given to objects convey any information — that is, when-
ever they have properly any meaning — the meaning resides not in what
they denote, but in what they connote. The only names of objects which
■connote nothing are proper names; and these have, strictly speaking, no
signification.*
If, like the robber in the Arabian Nights, we make a mark with chalk on
a house to enable us to know it again, the mark has a purpose, but it has
not properly any meaning. The chalk does not declare any thing about
the house ; it does not mean. This is such a person's house, or This is a
house which contains booty. The object of making the mark is merely
■distinction. I s.ay to myself, All these houses are so nearly ahke that if I
lose sight of them I shall not again be able to distinguish that which I am
now looking at, from any of the others ; I must therefore contrive to make
the appearance of this one house unlike that of the others, that I may here-
after know when I see the mark — not indeed any attribute of the house —
but simply that it is the same house which I am now looking at. Mor-
giana chalked all the other houses in a similar niannei', and defeated the
scheme: how? simply by obliterating the difference of appearance between
that house and the others. The chalk was still there, but it no longer
served the purpose of a distinctive mark.
*,A writer who entitles his book Philosophy ; or, the Science of Truth, charges me in his
Tery first page (referring pt the foot of it to this passage) with asserting that general names
have properly no signification. And he repeats this statement many times in the course of
his volume, with comments, not at all flattering, thereon. It is well to be now and then re-
minded to how great ? length perverse misquotation (for, strange as it appears, I do not be-
lieve that the writer is dishonest) can sometimes go. It is a warning to readers when they
see an author accused, with volume and page referred to, and the apparent guarantee of invert-
ed commas, of maintaining something more' than commonly absurd, not to give implicit cre-
dence to the assertion without verifying the reference.
38 NAMES AND PROPOSITIONS.
When we impose a proper name, we perform an operation in some de-
gree analogous to what the robber intended in chalking the house. We
put a mark, not indeed upon the object itself, but, so to speak, upon the-
idea of the object. A proper name is but an unmeaning mark which we-
connect in our minds with the idea of the object, in order that whenever
the mark meets our eyes or occurs to our thoughts, we may think ot that
individual object. Not being attached to the thing itself, it does not, like-
the chalk, enable us to distinguish the object when we see it; but it ena-
bles us to distinguish it when it is spoken of, either in the records of our
own experience, or in the discourse of others ; to know that what we hnd
asserted in any proposition of which it is the subject, is asserted of the in-
dividual thing with which we were previously acquainted.
When we predicate of any thing its proper name ; when we say, point-
ing to a man, this is Brown or Smith, or pointing to a city, that it is York,
we do not, merely by so doing, convey to the reader any information about
them, except that those are their names. By enabling him to identify the-
individuals, we may connect them with information previously possessed.
by him ; by saying, This is York, we may tell him that it contains the Min-
ster. But this is in virtue of what he has previously heard concerning
York; not by any thing implied in the name. It is otherwise when ob-
jects are spoken of by connotative names. When we say, The town i»
built of marble, we give the hearer what may be entirely new information,
and this merely by the signification of the many-worded connotative name,
" built of marble." Such names are not signs of the mere objects, invented
because we have occasion to think and speak of those objects individually;
but signs which accompany an attribute; a kind of livery in which the
attribute clothes all objects which are recognized as possessing it. They
are not mere marks, but more, that is to say, significant marks ; and the
connotation is what constitutes their significance.
As a proper name is said to be the name of the one individual which it
is predicated of, so (as well from the importance of adhering to analogy, as
for the other reasons formerly assigned) a connotative name ought to be
considered a name of all the various individuals which it is predicable of,
or in other words denotes, and not of what it connotes. But by learning
what things it is a name of, we do not learn the meaning of the name : for
to the same thing we may, with equal propriety, apply many names, not
equivalent in meaning. Thus, I call a certain man by the name Sophronis-.
cus : I call him by another name. The father of Socrates. Both these are
names of the same individual, but their meaning is altogether different;,
they are applied to that individual for two different purposes: the one,
merely to distinguish him from other persons who are spoken of ; the other
to indicate a fact relating to him, the fact that Socrates was his son. I
further apply to him these other expressions : a man, a Greek, an Athenian,
a sculptor, an old man, an honest man, a brave man. All these are, or may
be, names of Sophroniscus, not indeed of him alone, but of him and each
of an indefinite number of other human beings. Each of these names is
applied to Sophroniscus for a different reason, and by each whoever under-
stands its meaning is apprised of a distinct fact or number of facts con-
cerning him ; but those who knew nothing about the names except that
they were applicable to Sophroniscus, would be altogether ignorant of their
meaning. It is even possible that I might know every single individual of
whom a given name could be with ti-uth affirmed, and yet could not be said
to know the meaning of the name. A child knows who are its brothers-
NAMES. 3»
and sisters, long before it has any definite conception of the nature of the
facts wliich are involved in tlie signification of those words.
In some cases it is not easy to decide precisely how much a particular
word does or does not connote ; that is, we do not exactly know (the case
not having arisen) what degree of difference in the object would occasion
a difference in the name. Thus, it is clear that the word tnan, besides
animal life and rationality, connotes also a certain external form ; but it
would be impossible to say precisely what form ; that is, to decide how
great a deviation from the form ordinarily found in the beings whom we are
accustomed to call men, would suffice in a newly-discovered race to make
us refuse them the name of man. Rationality, also, being a quality which
admits of degrees, it has never been settled what is the lowest degree of
that quality which would entitle any creature to be considered a human
being. In all such cases, the meaning of the general name is so far un-
settled and vague; mankind have not come to any positive agreement-
about the matter. When we come to treat of Classification, we shall have
occasion to show under what conditions this vagueness may exist without-
practical inconvenience; and cases will appear in which the ends of lan-
guage are better promoted by it than by complete precision ; in order that,
in natural history for instance, individuals or species of no very marked
character may be ranged with those more strongly characterized individuals
or species to which, in all their properties taken together, they bear the
nearest resemblance.
But this partial uncertainty in the connotaition of names can only be
free from mischief when guarded by strict precautions. One of the chief
sources, indeed, of lax habits of thought, is the custom of using connotative
terms without a distinctly ascertained connotation, and with no more pre-
cise notion of their meaning than can be loosely collected from observing
what objects they are used to denote. It is in this manner that we all ac-
quire, and inevitably so, our first knowledge of our vernacular language.
A child learns the meaning of the words man, or white, by hearing them
applied to a variety of individual objects, and finding out, by a process of
generalization and analysis which he could not himself describe, what those-
different objects have in common. In the case of these two words the
process is so easy as to require no assistance from culture; the objects
called human beings, and the objects called white, differing from all others-
by qualities of a peculiarly definite and obvious character. But in many
other cases, objects bear a general resemblance to one another, which leads
to their being familiarly classed together under a common name, while,,
without more analytic habits than the generality of mankind possess, it is
not immediately apparent what are the particular attributes, upon the pos-
session of which in common by them all, their general resemblance depends.
When this is the case, people use the name without any recognized con-
notation, that is, without any precise meaning ; they talk, and consequently
think, vaguely, and remain contented to attach only the same degree of
significance to their own words, which a child three years old attaches to
the words brother and sister. The child at least is seldom puzzled by the
starting up of new individuals, on whom he is ignorant whether or not to-
confer the title ; because there is usually an authority close at hand com-
petent to solve all doubts. But a similar resoui-ce does not exist in the
generality of cases ; and new objects are continually presenting themselves-
to men, women, and children, which they are called upon to class proprio
motu. They, accordingly, do this on no other principle than that of super-
40 NAMES AND PEOPOSITIONS.
ficial similarity, giving to each new object the name of that familiar object,
the i(iea of which it most readily recalls, or which, on a cursory inspection,
it seems to them most to resemble : as an unknown substance found in the
grounii will be called, according to its texture, earth, sand, or a stone. In
this manner, names creep on from subject to subject, until all traces of
■a common meaning sometimes disappear, and the word comes to denote
a number of things not only independently of any common attribute,
but which have actually no attribute in common; or none but what is
shared by other things to which the name is capriciously refused.* Even
scientific writers have aided in this perversion of general language from
its purpose; sometimes because, like the vulgar, they knew no better;
and sometimes in deference to that aversion to admit new words, which
induces mankind, on all subjects not considered technical, to attempt to
make the original stock of names serve with but little augmentation. to
«xpress a constantly increasing number of objects and distinctions, and,
■consequently, to express them in a manner progressively more and more
imperfect.
To what a degree this loose mode of classing and denominating objects
has rendered the vocabulary of mental and moral philosophy unfit for the
purposes of accurate thinking, is best known to whoever has most medi-
tated on the present condition of those branches of knowledge. Since,
however, the introduction of a new technical language as the vehicle of
speculations on subjects belonging to the domain of daily discussion, is ex-
tremely difficult to effect, and would not be free from inconvenience even
if effected, the problem for the philosopher, and one of the most difficult
which he has to resolve, is, in retaining the existing phraseology, how-best
to alleviate its imperfections. This can only be accomplished by giving to
•every genei-al concrete name which there is frequent occasion to predicate,
a definite and fixed connotation ; in order that it may be known what attri-
l)utes, when we call an object by that name, we really mean to predicate of
the object. And the question of most nicety is, how to give this fixed con-
notation to a name, with the least possible change in the objects which the
name is habitually employed to denote ; with the least possible disarrange-
ment, either by adding or subtraction, of the group of objects which, in
however imperfect a manner, it serves to circumscribe and hold together;
and with the least vitiation of the truth of any propositions which are com-
monly received as true.
This desirable purpose, of giving a fixed connotation where it is want-
ing, is the end aimed at whenever any one attempts to give a definition of
a general name already in use ; every definition of a connotative name be-
ing an attempt either merely to declare, or to declare and analyze, the con-
notation of the name. And the fact, that no questions which have arisen
in the moral sciences have been subjects of keener controversy than the
* "Take the familiar term Stone. It is applied to mineral and rocky materials, to the
.kernels of fruit, to the accumulations in the gall-bladder and in the kidney ; while it is re-
fused to polished minerals (called gems), to rocks that have the cleavage suited for roofing
{slates), and to baked clay (bricks). It occurs in the designation of the magnetic oxide of
iron (loadstone), and not in speaking of other metallic ores. Such a term is wholly unfit for
accurate reasoning, unless hedged round on every occasion by other phrases; as building
stone, precious stone, gall-stone, etc. Moreover, the methods of definition are baffled for
want of sufficient community to ground upon. There is no qualitv uniformly present in the
cases where it is ap]jliod, and uniformly absent where it is not applied ; hence the definer
■would have to emplov largely the license of striking off existing applications, and taking in
new ones." — Bain, Logic, ii., 172.
NAMES. 41
definitions of almost all the leading expressions, is a proof how great an
extent the evil to which we have adverted has attained.
Names with indeterminate connotation are not to be confounded with
names which have more than one connotation, that is to say, ambiguous
words. A word may have several meanings, but all of them fixed and rec-
ognized ones ; as the word post, for example, or the word box, the various
senses of which it would be endless to enumerate. And the paucity of ex-
isting names, in comparison with the demand for them, may often render
it advisable and even necessary to retain a name in this multiplicity of ac-
ceptations, distinguishing these so clearly as to prevent their being con-
founded with one another. Such a word may be considered as two or
more names, accidentally written and spoken alike.*
§ 6. The fourth principal division of names, is into positive and neffo-
tive. Positive, as man, tree, good; negative, as not-mati, not-tree, not-good.
To every positive concrete name, a corresponding negative one might be
framed. After giving a name to any one thing, or to any plurality of
things, we might create a second name which should be a name of all things
whatever, except that particular thing or things. These negative names
are employed whenevei" we have occasion to speak collectively of all things
other than some thing or class of things. When the positive name is con-
notative, the corresponding negative name is connotative likewise; but in a
* Before quitting the subject of connotative names, it is proper to observe, that tlie first
writer vvho, in our times, has adopted from the schoolmen the word to connote, Mr. Jamea
Mill, in his Analysis of the Phenomena of the Human Mind, employs it in u signification dif-
ferent from that in which it is here used. He uses the word in a sense co-extensive with its
etymology, applying it to every case in which a name, while pointing directly to one thing^
(which is consequently termed its signification), includes also a tacit reference to some other
thing. In the case considered in the text, that of concrete general names, his language and
mine are the converse of one another. Considering (very justly) the signification of the name
to lie in the attribute, he speaks of the word as noting the attribute, and connoting the things
possessing the attribute. And he describes abstract names as being properly concrete names
with their connotation dropped ; whereas, in my view, it is the cfenotation which would be
said to bedropped, what was previously connoted becoming the whole signification.
In adopting a phraseology at variance with that which so high an authoiity, and one which
I am less likely than any other person to undervalue, has deliberately sanctioned, I have been
influenced by the urgent necessity for a term exclusively appropriated to express the manner
in which a concrete general name serves to mark the attributes which are involved in its signi-
fication. This necessity can scarcely be felt in its full force by any one who has not found by
experience how vain is the attempt to communicate clear ideas on the philosophy of language
without such a word. It is hardly an exaggeration to say, that some of the most prevalent of
the en'ors with which logic has been infected, and a large part of the cloudiness and confusion
of ideas which have enveloped it, would, in all probability, have been avoided, if a term had
been in common use to express exactly what I have signified by the term to connote. And
the schoolmen, to whom we are indebted for the greater part of our logical language, gave us
this also, and in this very sense. For though some of their general expressions countenance
the use of the word in the more extensive and vague acceptation in which it is taken by Mr.
Mill, yet when they had to define it specifically as a technical tenn, and to fix its meaning as
such, with that admirable precision which always characterizes their definitions, they clearly
explained that nothing was said to be connoted except /onn«, which word may generally, in
their writings, be understood as synonymous with attributes.
Now, if the word to connote, so well suited to the purpose to which they applied it, be di-
verted from that purpose by being taken to fulfill another, for which it does not seem to me to
be at all required ; I am nnable to find any expression to replace it, but such as are commonly
employed in a sense so much more general, that it would be useless attempting to associate-
them peculiarly with this precise idea. Such are the words, to involve, to imply, etc. By
employing these, I should fail of attaining the object for which alone the name is needed,
namely, to distinguish this particular kind of involving and implying from all other kinds, and
to assure to it the degree of habitual attention which its importance demands.
42 NAMES AND PROPOSITIONS.
peculiar way, connoting not the presence but the absence of an attribute.
Thus, not-white denotes all things whatever except white things ; and con-
notes the attribute of not possessing whiteness. For the non-possession of
any given attribute is also an attribute, and may i-eceive a name as such ;
and thus negative concrete names may obtain negative abstract names to
•correspond to them.*
Names which are positive in form are often negative in reality, and oth.
ers are really positive though their form is negative. The word inconven-
ient, for example, does not express the mere absence of convenience ; it ex-
presses a positive attribute — that of being the cause of discomfort or an-
noyance. So the word unpleasant, notwithstanding its negative form, does
not connote the mere absence of pleasantness, but a less degree of what ia
signified by the word painful, which, it is hardly necessary to say, is posi-
tive. Idle, on the other hand, is a word which, though positive in form,
expresses nothing but what would be signified either by the phrase not
working, or by the phrase not disposed to work/ and sober, either by not
■drunk or by not drunken.
There is a class of names called privative. A pi'ivative name is equiva-
lent in its signification to a positive and a negative name taken together;
being the name of something which has once had a particular attribute, or
for some other reason might have been expected to have it, but which has
it not. Such is the word blind, which is not equivalent to not seeing, or to
not capable of seeing, for it would not, except by a poetical or rhetorical
"figure, be applied to stocks and stones. A thing is not usually said to be
blind, utiless the class to which it is most familiarly referred, or to which
it is referred on the particular occasion, be chiefly composed of things
■which can see, as in the case of a blind man, or a blind horse ; or unless it
is supposed for any reason that it ought to see ; as in saying of a man, that
he rushed blindly into an abyss, or of philosophers or the clergy that the
greater part of them are blind guides. The names called privative, there-
foi'e, connote two things ; the absence of certain attributes, and the pres-
■ence of others, from which the presence also of the former might naturally
have been expected.
§ 7. The fifth leading division of names is into relative and absolute, or
let us rather say, relative and non-relative/ for the word absolute is put
upon much too hard duty in metaphysics, not to be willingly spared wbea
its services can be dispensed with. It resembles the word civil in the lan-
.guage of jurisprudence, which stands for the opposite of criminal, the op-
posite of ecclesiastical, the opposite of military, the opposite of political—
in short, the opposite of any positive word which wants a negative.
Relative names are such as father, son ; ruler, subject ; like ; equal ; un-
like; unequal; longer, shorter; cause, effect. Their characteristic property
is, that they are always given in pairs. Every relative name which is pred-
icated of an object, supposes another object (or objects), of which we may
predicate either that same name or another relative name which is said to
be the correlative of the former. Thus, when we call any person a son, we
* Professor Bain (Logic, i., 66) thinks that negative names are not names of all things
whatever except those denoted by the correlative positive name, but only for all things of some
particular class : not-white, for instance, he deems not to be a name for every thing in nature
except white things, but only for every colored thing other than white. In this case, however,
-as in all others, the test of what a name denotes is what it can be predicated of: and we can
■certainly predicate of a sound, or a smell, that it is not white. The affirmation and the nega-
tion of the same attribute can not but divide the whole field of predication between them.
NAMES. 43
suppose other persons who must be called parents. When we call any event
a cause, we suppose another event which is an effect. When we say of
any distance that it is longer, we suppose another distance which is shorter.
When we say of any object that it is like, we mean that it is like some
other object, which is also said to be like the first. In this last case both
•objects receive the same name ; the relative term is its own correlative.
It is evident that these words, when concrete, are, like other concrete
general names, connotative; they denote a subject, and connote an attri-
bute ; and each of them has, or might have, a corresponding abstract name,
to denote the attribute connoted by the concrete. Thus the concrete like
has its abstract likeness; the concretes, father and son, have, or might have,
the abstracts, paternity, and filiety, or sonship. The concrete name con-
notes an attribute, and the abstract name which answers to it denotes that
attribute. But of what nature is the attribute? Wherein consists the
peculiarity in the connotation of a relative name ?
The attribute signified by a relative name, say some, is a relation ; and
this they give, if not as a sufficient explanation, at least as the only one at-
tainable. If they are asked. What then is a relation ? they do not profess
to be able to tell. It is generally regarded as something peculiarly recondite
and mysterious. I can not, however, perceive in what respect it is more
80 than any other attribute ; indeed, it appears to me to be so in a some-
what less degree. I conceive rather, that it is by examining into the sig-
nification of relative names, or, in other words, into the nature of the at-
tribute which they connote, that a clear insight may best be obtained into
the nature of all attributes : of all that is meant by an attribute.
It is obvious, in fact, that if we take any two correlative names, father
and son for instance, though the objects (denoted by the names are differ-
€nt, they both, in a certain sense, connote the same thing. They can not,
indeed, be said to connote the same attribute: to be a father, is not the
same thing as to be a son. But when we call one man a father, another a
son, what we mean to affirm is a set of facts, which are exactly the same in
both cases. To predicate of A that he is the father of B, and of B that he
is the son of A, is to assert one and the same fact in different words. The
two propositions are exactly equivalent: neither of them asserts more or
asserts less than the other. The paternity of A and the filiety of B are
not two facts, but two modes of expressing the same fact. That fact, when
analysed, consists of a series of physical events or phenomena, in which
both A and B are parties concerned, and from which they both derive
names. What those names really connote, is this series of events : that is
the meaning, and the whole meaning, which either of them is intended to
convey. The series of events may be said to constitute the relation ; the
schoolmen called it the foundation of the relation, fundamentum relationis.
In this manner any fact, or series of facts, in which two different objects
are implicated, and which is therefore predicable of both of them, may be
either considered as constituting an attribute of the one, or an attribute of
the other. According as we consider it in the former, or in the latter as-
pect, it is connoted by the one or the other of the two correlative names.
Father connotes the fact, r^egarded as constituting an attribute of A ; son
■connotes the same fact, as constituting an attribute of B. It may evident-
ly be regarded with equal propriety in either light. And all that appears
necessary to account for the existence of relative names, is, that whenever
there is a fact in which two individuals are concerned, an attribute ground-
ed on that fact may be ascribed to either of these individuals.
44 NAMES AND PROPOSITIONS.
A name, therefore, is said to be relative, when, over and above the object
which it denotes, it implies in its signification the existence of another ob-
ject, also deriving a denomination from the same fact which is the gi-ound
of the first name. Or (to express the same meaning in other words) a
name is relative, when, being the name of one thing, its signification can
not be explained but by mentioning another. Or we may state it thus —
when the name can not be employed in discourse so as to have a meaning,
unless the name of some other thing than what it is itself the name of, be
either expressed or understood. These definitions are all, at bottom, equivar
lent, being modes of variously expressing this one distinctive circumstance
— that every other attribute of an object might, without any contradiction,
be conceived still to exist if no object besides that one had ever existed;*
but those of its attributes which are expressed by relative names, would on
that supposition be swept away.
§ 8. Names have been further distinguished into univocal and oequivocod:
these, however, are not two kinds of names, but two different modes of
employing names. A name is univocal, or applied univocally, with respect
to all things of which it can be pi-edicated in the same sense ; it is sequiv-
ocal, or applied sequivocally, as respects those things of which it is predi-
cated in different senses. It is scarcely necessary to give instances of a
fact so familiar as the double meaning of a word. In reality, as has been
already observed, an sequivocal or ambiguous word is not one name, but
two names, accidentally coinciding in sound. File meaning a steel instru-
ment, and file meaning a line of soldiers, have no more title to be consid-
ed one word, because written alike, than grease and Greece have, because
they are pronounced alike. They are one sound, appropriated to form two
different words.
An intermediate case is that of a name used analogically or metaphor-
ically; that is, a name which is predicated of two things, not univocally,
or exactly in the same signification, but in significations somewhat similar,
and which being derived one- from the other, one of them may be consid-
ered the primary, and the other a secondary signification. As when we
speak of a brilliant light and a brilliant achievement. The word is not
applied in the same sense to the light and to the achievement ; but having
been applied to the light in its original sense, that of brightness to the eye,
it is transferred to the achievement in a dei'ivative signification, supposed
to be somewhat like the primitive one. The word, however, is just as
properly two names instead of one, in this case, as in that of the most per-
fect ambiguity. And one of the commonest forms of fallacious reasoning
arising from ambiguity, is that of arguing from a metapliorical expression
as if it were literal ; that is, as if a word, .when applied metaphorically,
were the same name as when taken in its original sense: which will he
seen more particularly in its place.
* Or rather, all objects except itself and the percipient mind ; for, as we shall see hereafter,
to ascribe any attribute to an object, necessarily implies a mind to perceive it.
The simple and clear explanation given in the text, of relation and relative names, a subject
so long the opprobrium of metaphysics, was given (as far as I know) for the first time, by Mr.
James Mill, in his Analysis of the Phenomena of the Human Mind.
THINGS DENOTED BY NAMES. 45
CHAPTER III.
OF THE THINGS DENOTED BY NAMES.
§ 1. Looking back now to the commencement of our inquiry, let us at-
tempt to measure how far it has advanced. Logic, we found, is the Theory
■of Proof. But proof supposes something provable, which must be a Prop-
osition or Assertion ; since nothing but a Proposition can be an object of
belief, or therefore of proof. A Proposition is, discourse which affirms or
denies something of some other thing. This is one step : there must, it
seems, be two things concerned in every act of belief. But what are these
Things? They can be no other than those signified by the two names,
which being joined together by a copula constitute the Proposition. If,
therefore, we knew what all names signify, we should know every thing
which, in the existing state of human knowledge, is capable either of being
made a subject of affirmation or denial, or of being itself affirmed or de-
nied of a subject. We have accordingly, in the preceding chapter, re-
viewed the various kinds of Names, in order to ascertain what is signified
by each of them. And we have now carried this survey far enough to be
able to take an account of its results, and to exhibit an enumeration of all
kinds of Things which are capable of being made predicates, or of having
any thing predicated of them : after which to determine the import of
Predication, that is, of Propositions, can be no arduous task.
The necessity of an enumeration of Existences, as the basis of Logic, did
not escape the attention of the schoolmen, and of their master Aristotle,
the most comprehensive, if not also the most sagacious, of the ancient phi-
losophers. The Categories, or Predicaments — the former a Greek word,
the latter its literal translation in the Latin language — were believed to be
an enumeration of all things capable of being named ; an enumeration by
the summa genera, i. e., the most extensive classes into which things could
be distributed ; which, therefore, were so many highest Predicates, one or
other of which was supposed capable of being affirmed with truth of every
namable thing whatsoever. The following are the classes into which, ac-
cording to this school of philosophy, Things in general might be reduced :
Ovaia, Substantia.
Iloffdv, Qnantitas.
Jloidv, Qaalitas.
11/0(5? Ti, Belatio.
Hoiclv, Actio.
Udaxetv, Passio.
Ilojj, Ubi.
Tl&re, Quando.
KeiaSai, Situs.
"Exeiv, Habitus.
The imperfections of this classification are too obvious to require, and
its merits are not sufficient to reward, a minute examination. It is a mere
catalogue of the distinctions rudely marked out by the language of familiar
life, with little or no attempt to penetrate, by philosophic analysis, to the
rationale even of those common distinctions. Such an analysis, however
46 NAMES AND PROPOSITIONS.
superficially conducted, would have shown the enumeration to be both re.
dundant and defective. Some objects are omitted, and others repeated!
several times under different heads. It is like a division of animals intO'
men, quadrupeds, horses, asses, and ponies. That, for instance, could not
be a very comprehensive view of the nature of Relation which could ex.
elude action, passivity, and local situation from that category. The same
observation applies to the categories Quando (or position in time), and Ubi
(or position in space) ; while the distinction between the latter and Situs
is merely verbal. The incongruity of erecting into a summum genus the
class which forms the tenth category is manifest. On the other hand, the
enumeration takes no notice of any thing besides substances and attributes.
In what category are we to place sensations, or any other feelings and
states of mind; as hope, joy, fear; sound, smell, taste; pain, pleasure;,
thought, judgment, conception, and the like? Probably all these would
have been placed by the Aristotelian school in the categories of actio and
passio; and the relation of such of them as are active, to their objects, and
of such of them as are passive, to their causes, would rightly be so placed;
but the things themselves, the feelings or states of mind, wrongly. Feel-
ings, or states of consciousness, are assuredly to be accounted among reali-
ties, but they can not be reckoned either among substances or attributes.*
§ 2. Before recommencing, under better auspices, the attempt made with
such imperfect success by the early logicians, we must take notice of an
unfortunate ambiguity in all the concrete names which correspond to the
most general of all abstract terms, the word Existence. When we have
occasion for a name which shall be capable of denoting whatever exists,
as contradistinguished from non-entity or Nothing, there is hardly a word
applicable to the purpose which is not also, and even more familiai'ly, taken
in a sense in which it denotes only substances. But substances are not all
that exists ; attributes, if such things are to be spoken of, must be said to
exist ; feelings certainly exist. Yet when we speak of an object, or of a
* On the preceding passage Professor Bain remarks (Logic, i., 265) : " The Categories do not
seem to have been intended as a classification of Namable Things, in the sense of ' an enu-
meration of all kinds of Things which are capable of being made predicates, or of having any
thing predicated of them.' They seem to have been rather intended as a generalization
oi predicates ; an analysis of the final import of predication. Viewed in this light, they
are not open to the objections offered by Mr. Mill. The proper question to ask is not — In
what Category are we to place sensations or other feelings or states of mind? but. Under
what Categories can we predicate regarding states of mind? Take, for example, Hope.
When we say that it is a state of mind, we predicate Substance : we may also describe how
great it is (Quantity), what is the quality of it, pleasurable or painful (Quality), what it has
reference to (Belation). Aristotle seems to have framed the Categories on the plan — Here is
an individual ; what is the final analysis of all that we can predicate about him ?"
This is doubtless a true statement of the leading idea in the classification. The Category
Ovc'ia was certainly understood by Aristotle to be a general name for all possible answers to
the question Quid sit ? when asked respecting a concrete individual ; as the other Categories
are names comprehending all possible answers to the questions Quantum sit ? Quale sit ? etc.
In Aristotle's conception, therefore, the Categories may not have been a classification of
Things ; but they were soon converted into one by his Scholastic followers, who certainly re-
garded and treated them as a classification of Things, and carried them out as such, dividing
down the Ca,tegory Substance as a naturalist might do, into the different classes of physicd
or metaphysical objects as distinguished from attributes, and the other Categories into the
principal varieties of quantity, quality, relation, etc. It is, therefore, a just subject of com-
plaint against them, that they had no Category of Feeling. Feeling is assuredly predicable as
a Bummum genus, of every particular kind of feeling, for instance, as in Mr. Bain's example, of
Hope : but it can not be brought within any of the Categories as interpreted either by AristO'
tie or by his followers.
THINGS DENOTED BY NAMES. 47
thing, we are almost always supposed to mean a substance. There seems
a kind of contradiction in using such an expression as that one thing is
merely an attribute of another thing. And the announcement of a Classi-
fication of Things would, I believe, prepare most readers for an enumera-
tion like those in natural history, beginning with the great divisions of an-
imal, vegetable, and mineral, and subdividing them into classes and orders.
If, rejecting the word Thing, we endeavor to find another of a more general
import, or at least more exclusively confined to that general import, a word
denoting all that exists, and connoting only simple existence ; no word
might be presumed fitter for such a purpose than being: originally the
present participle of a verb which in one of its meanings is exactly equiv-
alent to the verb exists; and therefore suitable, even by its grammatical
formation, to be the concrete of the abstract existence. But this word,
strange as the fact may appear, is stiE more completely spoiled for the
purpose which it seemed expressly made for, than the word Thing. Being
is, by custom, exactly synonymous with substance ; except that it is free
from a slight taint of a second ambiguity; being implied impartially to
matter and to mind, while substance, though originally and in strictness
applicable to both, is apt to suggest in preference the idea of matter. At-
tributes are never called Beings ; nor are feelings. A Being is that which
excites feelings, and which possesses attributes. The soul is called a Be-
ing ; God and angels are called Beings ; but if we were to say, extension,
color, wisdom, virtue, are beings, we should perhaps be suspected of think-
ing with some of the ancients, that the cardinal virtues are animals ; or, at
the least, of holding with the Platonic school the doctrine of self-existent
Ideas, or with the followers of Epicurus that of Sensible Forms, which de-
tach themselves in every direction from bodies, and by coming in contact
with our organs, cause our perceptions. We should be supposed, in short,
to believe that Attributes are Substances.
In consequence of this perversion of the word Being, philosophers look-
ing about for something to supply its place, laid their hands upon the word
Entity, a piece of barbarous Latin, invented by' the schoolmen to be used
as an abstract name, in which class its grammatical form would seem to
place it: but being seized by logicians in distress to stop a leak in their
terminology, it has ever since been used as a Concrete name. The kindred
word essence, born at the same time and of the same parents, scarcely un-
derwent a more complete transformation when, from being the abstract
of the verb to be, it came to denote something sufiiciently concrete to be
inclosed in a glass bottle. The word Entity, since it settled down into a
concrete name, has retained its universality of signification somewhat less
impaired than any of the names before mentioned. Yet the same gradual
decay to which, after a certain age, all the language of psychology seems
liable, has been at work even here. If you call virtue an entity, you are
indeed somewhat less strongly suspected of believing it to be a substance
than if you called it a being; but you are by no means free from the sus-
picion. Every word which was originally intended to connote mere ex-
istence, seems, after a time, to enlarge its connotation to separate existence,
or existence freed from the condition of belonging to a substance ; which
condition being precisely what constitutes an attribute, attributes are grad-
ually shut out ; and along with them feelings, which in ninety-nine cases
out of a hundred have no other name than that of the attribute which is
grounded on them. Strange that when the greatest embarrassment felt by
all who have any considerable number of thoughts to express, is to find a
48 NAMES AND PEOPOSITIONS.
sufficient variety of precise words fitted to express them, there should be
no practice to which even scientific thinkers are more addicted than that
of taking valuable words to express ideas which are sufficiently expressed
by other words already appropriated to them.
When it is impossible to obtain good tools, the next best thing is to un-
derstand thoroughly the defects of those we have. I have therefore warn-
ed the reader of the ambiguity of the names which, for want of better, I
am necessitated to employ. It must now be the writer's endeavor so to
employ them as in no case to leave the meaning doubtful or obscure. No
one of the above terras being altogether unambiguous, I shall not confine
myself to any one, but shall employ on each occasion the word which seems
least likely in the particular case to lead to misunderstanding; nor do I
pretend to use either these or any other words with a rigorous adherence
to one single sense. To do so would often leave us without a word to ex-
press what is signified by a known word in some one or other of its senses :
unless authors had au unlimited license to coin new words, together with
(what it would be more difficult to assume) unlimited power of making
readers understand them. Nor would it be wise in a writer, on a subject
involving so much of abstraction, to deny himself the advantage derived
from even an improper use of a term, when, by means of it, some familiar
association is called up which brings the meaning home to the mind, as it
were by a flash.
The difficulty both to the writer and reader, of the attempt which must
be made to use vague words so as to convey a precise meaning, is not
wholly a matter of regret. It is not unfitting that logical treatises should
afford an example of that, to facilitate which is among the most important
uses of logic. Philosophical language will for a long time, and popular
language still longer, retain so much of vagueness and ambiguity, that logic
would be of little value if it did not, among its other advantages, exercise
the understanding in doing its work neatly and correctly with these im-
perfect tools.
After this preamble it is time to proceed t^ our enumeration. We shall
commence with Feelings, the simplest class of namable things; the term
Feeling being of course understood in its most enlarged sense.
I. Feelings, ok States or Consciousness.
§ 3. A Feeling and a State of consciousness are, in the language of phi-
losophy, equivalent expressions : every thing is a feeling of which the mind
18 conscious ; every thing which it feels, or, in other words, which forms a
part of its own sentient existence. In popular language Feeling is not al-
ways synonymous with State of Consciousness; being often taken more
peculiarly for those states which are conceived as belonging to the sensi-
tive, or to the emotional, phasis of onr nature, and sometimes, with a still
narrower restriction, to the emotional alone, as distinguished from what
are conceived as belonging to the percipient or to the intellectual phasis.
But this IS an admitted departure from correctness of language; just as,
by a popular perversion the exact converse of this, the word Mind is with-
drawn from its rightful generality of signification, and restricted to the
intellect. The still greater perversion by which Feeling is sometimes con-
lined not only to bodily sensations, but to the sensations of a single sense
that of touch, needs not be more particularly adverted to. '
Feeling, in the proper sense of the term, is a genus, of which Sensation,
Jimotion, and Thought, are subordinate species. Under the word Thought
THINGS DENOTED BY NAMES. 49
is here to be included whatever we are internally conscious of when we are
said to think ; from the consciousness we have when we think of a red col-
or without having it before our eyes, to the most recondite thoughts of a
philosopher or poet. Be it remembered, however, that by a thought is to
be understood what passes in the mind itself, and not any object external
to the mind, which the person is commonly said to be thinking of. He may
be thinking of the sun, or of God, but the sun and God are not thoughts ;
his mental image, however, of the sun, and his idea of God, are thoughts;
states of his mind, not of the objects themselves ; and so also is his belief
of the existence of the sun, or of God ; or his disbelief, if the case be so.
Even imaginary objects (which are said to exist only in our ideas) are to be
distinguished from our ideas of them. I may think of a hobgoblin, as I may
think ot the loaf which was eaten yesterday, or of the flower which will
bloom to-morrow. But the hobgoblin which never existed is not the same
thing with my idea of a hobgoblin, any more than the loaf which once ex-
isted is the same thing with my idea of a loaf, or the flower which does not
yet exist, but which will exist, is the same with my idea of a flower. They
are all, not thoughts, but objects of thought ; though at the present time all
the objects are alike non-existent.
In like manner, a Sensation is to be carefully distinguished from the ob-
ject which causes the sensation; our sensation of white from a white object:
nor is it less to be distinguished from the attribute whiteness, which we
ascribe to the object in consequence of its exciting the sensation. Unfor-
tunately for clearness and due discrimination in considering these subjects,
our sensations seldom receive separate names. We have a name for the
objects which produce in us a certain sensation : the word white. We
have a name for the quality in those objects, to which we ascribe the sen-
sation : the name whiteness. But when we speak of the sensation itself
(as we have not occasion to do this often except in our scientific specula-
tions), language, which adapts itself for the most part only to the common
uses of life, has provided us with no single-worded or immediate defigna-
tion; we must employ a circumlocution, and say. The sensation of white,
or The sensation of whiteness; we must denominate the sensation either
from the object, or from the attribute, by which it is excited. Yet the
sensation, though it never does, might very well be conceived to exist, with-
out any thing whatever to excite it. We can conceive it as arising spon-
taneously in the mind. But if it so arose, we should have no name to de-
note it which would not be a misnomer. In the case of our sensations of
hearing we are better provided ; we have the word Sound, and a whole
vocabulary of words to denote the various kinds of sounds. For as we
are often conscious of these sensations in the absence of any perceptible
object, we can more easily conceive having them in the absence of any
object whatever. We need only shut our eyes and listen to music, to have
a conception of a universe with nothing in it except sounds, and ourselves
hearing them : and what is easily conceived separately, easily obtains a
separate name. But in general our names of sensations denote indiscrim-
inately the sensation and the attribute. Thus, color stands for the sensa-
tions of white, red, etc., but also for the quality in the colored object. We
talk of the colors of things as among th&iv properties.
§ 4. In the case of sensations, another distinction has also to be kept in
view, which is often confounded, and never without mischievous conse-
quences. This is, the distinction between the sensation itself, and the state
50 NAMES AND PROPOSITIONS.
of the bodily organs which pi-ecedes the sensation, and which constitutes
the physical agency by which it is produced. One of the sources of con-
fusion on this subject is the division commonly made of feelings into Bodily
and Mental. Philosophically speaking, there is no foundation at all for this,
distinction : even sensations are states of the sentient mind, not states of
the body, as distinguished from it. What I am conscious of when I se&
the color blue, is a feeling of blue color, which is one thing ; the picture on
my retina, or the phenomenon of hitherto mysterious nature which takes^
place in my optic nerve or in my brain, is another thing, of which I am
not at all conscious, and which scientific investigation alone could have ap-
prised me of. These are states of my body; but the sensation of blue,
which is the consequence of these states of body, is not a state of body :
that which perceives and is conscious is called Mind. When sensations.
are called bodily feelings, it is only as being the class of feelings which are
immediately occasioned by bodily states ; whereas the other kinds of feel-
ings, thoughts, for instance, or emotions, are immediately excited not by
any thing acting upon the bodily organs, bat by sensations, or by previous
thoughts. This, however, is a distinction not in our feelings, but in the
agency which produces our feelings : all of them when actually produced
are states of mind.
Besides the affection of our bodily organs from without, and the sensa-
tion thereby produced in our minds, many writers admit a third link in the
chain of phenomena, which they call a Pei"ception, and which consists iu
the i-ecognition of an external object as the exciting cause of the sensation.
This perception, they say, is an act of the mind, proceeding from its owa
spontaneous activity ; while in a sensation the mind is passive, being mere-
ly acted upon by the outward object. And according to some metaphysi
cians, it is by an act of the mind, similar to perception, except in not being
preceded by any sensation, that the existence of God, the soul, and other
hyperphysical objects, is recognized.
These acts of what is termed perception, whatever be the conclusion ul-
timately come to respecting their nature, must, I conceive, take their place
among the varieties of feelings or states of mind. In so classing them,
I have not the smallest intention of declaring or insinuating any theory
as to the law of mind in which these mental processes may be supposed
to originate, or the conditions under which they may be legitimate or the
reverse. Far less do I mean (as Dr. Whewell seems to suppose must be
meant in an analogous case*) to indicate that as they are " merely states of
mind," it is superfluous to inquire into their distinguishing peculiaritieSr
I abstain from the inquiry as irrelevant to the science of logic. In these '
so-called perceptions, or direct recognitions by the mind, of objects, wheth-
er physical or spiritual, which are external to itself, I can see only cases of
belief ; but of belief which claims to be intuitive, or independent of exter-
nal evidence. When a stone lies before me, I am conscious of certain sen-
sations which I receive from it ; but if I say that these sensations come to-
me from an external object which I perceive, the meaning of these words
is, that receiving the sensations, I intuitively believe that an external cause
of those sensations exists. The laws of intuitive belief, and the conditions
under which it is legitimate, are a subject which, as we have already so
often remarked, belongs not to logic, but to the science of the ultimate laws,
of the human mind.
* Philosophy of the Inductive Sciences, vol. i., p. 40.
THINGS DENOTED BY NAMES. 51
To the same region of speculation belongs all that can be said respecting
the distinction which the German metaphysicians and their French and
English followers so elaborately draw between the acts of the mind and its
merely passive states; between what it receives from, and what it gives to,
the crude materials of its experience. I am aware that with reference to
the view which those writers take of the primary elements of thought and
knowledge, this distinction is fundamental. But for the present purpose,
which is to examine, not the original groundwork of our knowledge, but
how we come by that portion of it which is not original ; the difference be-
tween active and passive states of mind is of secondary importance. For
us, they all are states of mind, they all are feelings ; by which, let it be
said once more, I mean to imply nothing of passivity, but simply that they
are psychological facts, facts which take place in the mind, and are to be
carefully distinguished from the external or physical facts with which they
may be connected either as effects or as causes.
§ 5. Among active states of mind, there is, however, one species which
merits particular attention, because it forms a principal part of the conno-
tation of some important classes of names. I mean volitions, or acts of
the will. When we speak of sentient beings by relative names, a large
portion of the connotation of the name usually consists of the actions of
those beings; actions past, present, and possible or probable future. Take,
for instance, the words Sovereign and Subject. What meaning do these
words convey, but that of innumerable actions, done or to be done by the
sovereign and the subjects, to or in regard to one another reciprocally ?
So with the words physician and patient, leader and follower, tutor and
pupil. In many cases the words also connote actions which would be
done under certain contingencies by persons other than those denoted : as
the words mortgagor and mortgagee, obligor and obligee, and many other
words expressive of legal relation, which connote what a court of justice
would do to enforce the legal obligation if not fulfilled. There are also
words which connote actions previously done by persons other than those
denoted either by the name itself or by its correlative ; as the word brother.
From these instances, it may be seen how large a portion of the connota-
tion of names consists of actions. Now what is an action ? Not one thing,
but a series of two things : the state of mind called a volition, followed by
an effect. The volition or intention to produce the effect, is one thing;
the effect produced in consequence of the intention, is another thing ; the
two together constitute the action. I form the purpose of instantly mov-
ing my arm; that is a state of my mind: my arm (not being tied or par-
alytic)' moves in obedience to my purpose ; that is a physical fact, conse-
quent on a state of mind. The intention, followed by the fact, or (if we
prefer the expression) the fact when preceded and caused by the intention,
is called the action of moving my arm.
§ 6. Of the first leading division of namable things, viz.. Feelings or
States of Consciousness, we began by recognizing three subdivisions ; Sen-
sations, Thoughts, and Emotions. The first two of these we have illustrated
at considerable length ; the third. Emotions, not being perplexed by similar
ambiguities, does not require similar exemplification. And, finally, we have
found it necessary to add to these three a fourth species, commonly known
by the name "Volitions. We shall now proceed to the two remaining class-
es of namable things; all things which are regarded as external to the
52 NAMES AND PROPOSITIONS.
mind being considered as belonging either to the class of Substances or to
that of Attributes.
II. Substances.
Logicians have endeavored to define Substance and Attribute ; but their
definitions are not so much attempts to draw a distinction between the
things themselves, as instructions what difference it is customary to make
in the grammatical structure of the sentence, according as we are speak-
ing of substances or of attributes. Such definitions are rather lessons of
English, or of Greek, Latin, or German, than of mental philosophy. An
attribute, say the school logicians, must be the attribute of something;
color, for example, must be the color of something ; goodness must be the
goodness of something; and if this something should cease to exist, or
should cease to be connected with the attribute, the existence of the attri-
bute would be at an end. A substance, on the contrary, is self-existent ; in
speaking about it, we need not put of after its name. A stone is not the
stone of any thing ; the moon is not the moon of any thing, but simply the
moon. Unless, indeed, the name which we choose to give to the substance
be a relative name ; if so, it must be followed either by of, or by some
other particle, implying, sis that preposition does, a reference to something
else: but then the other characteristic peculiarity of an attribute would
fail ; the something might be destroyed, and the substance might still sub-
sist. Thus, a father must be the father of something, and so far resembles
an attribute, in being referred to something besides himself : if there were
no child, there would be no father : but this, when we look into the matter,
only means that we should not call him father. The man called father
might still exist though there were no child, as he existed before there was
a child; and there would be no contradiction in supposing him to exist,
though the whole universe except himself were destroyed. But destroy
all white substances, and where would be the attribute whiteness ? White-
ness, without any white thing, is a contradiction in terms.
This is the nearest approach to a solution of the difficulty, that will be
found in the common treatises on logic. It will scarcely be thought to be
a satisfactory one. If an attribute is distinguished from a substance by
being the attribute of something, it seems highly necessary to understand
what is meant by of; a particle which needs explanation too much itself,
to be placed in front of the explanation of any thing else. And as for the
self-existence of substance, it is very true that a substance may be con-
ceived to exist without any other substance, but so also may an attribute
without any other attribute: and we can no more imagine a substance
without attributes than we can imagine attributes without a substance.
Metaphysicians, however, have probed the question deeper, and given an
account of Substance considerably more satisfactory than this. Substances
are usually distinguished as Bodies or Minds. Of each of these, philoso-
phers have at length provided us with a definition which seems unexcep-
tionable.
§ 7. A body, according to the received doctrine of modern metaphysi-
cians, may be defined, the external cause to which we ascribe our sensa-
tions. When I see and touch a piece of gold, I am conscious of a sensar
tion of yellow color, and sensations of hardness and weight ; and by vary-
ing the mode of handling, I may add to these sensations many others com-
pletely distinct from them. The sensations are all of which I am directly
THINGS DENOTED BY NAMES. 53
conscious ; but I consider them as produced by something not only exist-
ing independently of my will, but external to my bodily organs and to my
mind. This external something I call a body.
It may be asked, how come we to ascribe our sensations to any exter-
nal cause ? And is there sufficient ground for so ascribing them ? It is
known, that there are metaphysicians who have raised a controversy on
the point; maintaining that we are not warranted in referring our sensa-
tions to a cause such as we understand by the word Body, or to any ex-
ternal cause whatever. Though we haive no concern here with this con-
troversy, nor with the metaphysical niceties on which it turns, one of the
best ways of showing what is meant by Substance is, to consider what po-
sition it is necessary to take up, in order to maintain its existence against
opponents.
It is certain, then, that a part of our notion of a body consists of the
notion of a number of sensations of our own, or of other sentient beings,
habitually occurring simultaneously. My conception of the table at which
I am writing is compounded of its visible form and size, which are com-
plex sensations of sight; its tangible form and size, which are complex
sensations of our organs of touch and of our muscles; its weight, which
is also a sensation of touch and of the muscles ; its color, which is a sensa-
tion of sight; its hardness, which is a sensation of the muscles; its com-
position, which is another word for all the varieties of sensation which we
receive under various circumstances from the wood of which it is made,
and so forth. All or most of these various sensations fi'equently are, and,
as we learn by experience, always might be, experienced simultaneously, or
in many different orders of succession at our own choice : and hence the
thought of any one of them makes us think of the others, and the whole
becomes mentally amalgamated into one mixed state of consciousness,
which, in the language of the school of Locke and Hartley, is termed a
Complex Idea.
Now, there are philosophers who have argued as follows : If we con-
ceive an orange to be divested of its natural color without acquiring any
new one; to lose its softness without becoming hard, its roundness without
becoming square or pentagonal, or of any other regular or irregular figure
whatever ; to be deprived of size", of weight, of taste, of smell ; to lose all
its mechanical and all its chemical properties, and acquire no new ones ; to
become, in short, invisible, intangible, imperceptible not only by all our
senses, but by the senses of all other sentient beings, real or possible ;
nothing, say these thinkers, would remain. For of what nature, they ask,
could be the residuum? and by what token could it manifest its presence?
To the unreflecting its existence seems to rest on the evidence of the senses.
But to the senses nothing is apparent except the sensations. We know,
indeed, that these sensations are bound together by some law ; they do not
come together at random, but according to a systematic order, which is
part of the order established in the universe. When we experience one of
these sensations, we usually experience the others also, or know that we
have it in our power to experience them. But a fixed law of connection,
making the sensations occur together, does not, say these philosophers,
necessarily require what is called a substratum to support them. The con-
ception of a substratum is but one of many possible forms in which that
connection presents itself to our imagination ; a mode of, as it were, real-
izing the idea. If there be such a substratum, suppose it at this instant
miraculously annihilated, and let the sensations continue to occur in the
64 NAMES AND PROPOSITIONS.
same order, and how would the substratum be missed? By what signs
should we be able to discover that its existence had terminated ? Should
we not have as much reason to believe that it still existed as we now have?
And if we should not then be warranted in believing it, how can we be so
now? A body, therefore, according to these metaphysicians, is not any
thing intrinsically different from the sensations which the body is said to
produce in us ; it is, in short, a set of sensaaons, or rather, of possibilities
of sensation, joined together according to a fixed law.
The controversies to which these speculations have given rise, and the
doctrines which have been developed in the attempt to find a conclusive
answer to them, have been fruitful of important consequences to the Science
of Mind. The sensations (it was answered) which we are conscious of, and
which we receive, not at random, but joined together in a certain uniform
manner, imply not only a law or laws of connection, but a cause external to
our mind, which cause, by its own laws, determines the laws according to
which the sensations are connected and experienced. The schoolmen used
to call this external cause by the name we have already employed, a,~sub-
stratum/ and its attributes (as they expressed themselves) inhered, literally
stuck, in it. To this substratum the name Matter is usually given in phil-
osophical discussions. It was soon, however, acknowledged by all who re-
flected on the subject, that the existence of matter can not be proved by ex-
trinsic evidence. The answer, therefore, now usually made to Berkeley and
his followers, is, that the belief is intuitive ; that mankind, in all ages, have
felt themselves compelled, by a necessity of their nature, to refer their sen-
sations to an external cause : that even those who deny it in theory, yield
to the necessity in practice, and both in speech, thought, and feeling, do,
equally with the vulgar, acknowledge their sensations to be the effects of
something external to them: this knowledge, therefore, it is affirmed, is as
evidently intuitive as our knowledge of our sensations themselves is intui-
tive. And here the question merges in the fundamental problem of meta-
physics pi-operly so called: to which science we leave it.
But although the extreme doctrine of the Idealist metaphysicians, that
objects are nothing but our sensations and the laws which connect them,
has not been generally adopted by subsequent thinkers ; the point of most
real importance is one on which those m'etaphysicians are now very gen-
erallyconsidered to have made out their case : viz., that all we /mow of ob-
jects is the sensations which they give us, and the order of the occurrence
of those sensations. Kant himself, on this point, is as explicit as Berke-
ley or Locke. However firmly convinced that there exists a universe of
" Things in themselves," totally distinct from the universe of phenomena,
or of things as they appear to our senses ; and even when bringing into
use a technical expression (JVoumenon) to denote what the thing is in it-
self, as contrasted with the representation of it in our minds ; he allows
that this representation (the matter of which, he says, consists of our sen-
sations, though the form is given by the laws of the mind itself) is all we
know of the object: and that the real nature of the Thing is, and by the
constitution of our faculties ever must remain, at least in the present state
of existence, an impenetrable mystery to us. " Of things absolutely or in
themselves," says Sir William Hamilton,* « be they external, be they in-
ternal, we know nothing, or know them only as incognizable; and become
aware of their incomprehensible existence, only as this is indirectly and
* Discussions on Philosophy, etc. Appendix I., pp. 643, 644.
THINGS DENOTED BY NAMES. 55
accidentally revealed to us, through certain qualities related to our faculties
-of knowledge, and which qualities, again, we can not think as uncondition-
al, irrelative, existent in and of ourselves. All that we know is therefore
phenomenal — phenomenal of the unknown."* The same doctrine is laid
down in the clearest and strongest terras by M. Cousin, whose observations
on the subject are the more worthy of attention, as, in consequence of the
nltra-German and ontological character of his philosophy in other respects,
they may be regarded as the admissions of an opponent.f
There is not the slightest reason for believing that what we call the sen-
sible qualities of the object are a type of any thing inherent in itself, or
tear any affinity to its own natu)-e. A cause does not, as such, resemble
its effects ; an east wind is not like the feeling of cold, nor heat like the
isteam of boiling water. Why then should matter resemble our sensations ?
AVhy should the inmost nature of fire or water resemble the impressions
made by those objects upon our senses ?| Or on what principle are we
* It is to be regretted that Sir William Hamilton, though he often strenuously insists on
this doctrine, and though, in the passage quoted, he states it with a comprehensiveness and
force which leave nothing to be desii-ed, did not consistently adhere to his own doctrine, but
maintained along with it opinions with which it is utterly irreconcilable. See the third and
•other chapters of -4b Examination of Sir William Hamilton's Philosophy.
t "Nous Savons qu'il existe quelque chose hors de nous, parceque nous ne pouvons expli-
quer nos perceptions sans les rattacher a des causes distinctes de nous memes ; nous savons
<de plus que ces causes, dent nous ne connaissons pas d'ailleurs I'essence, produisent les effets
les plus variables, les plus divers, et mSme les plus contraires, selon qu'elles rencontrent telle
nature ou telle disposition du sujet. Mais savons-nous quelque chose de plus ? et mdme, vu
le caractere indetermine des causes que nous concevons dans les corps, y a-t-il quelque chose
■de pins k savoir ? Y a-t-il lieu de nous enquerir si nous percevons les choses telles qu'elles
sont ? Non evidemment Je ne dis pas que le probleme est insoluble, je dis
■^u'il est absurde et enferme une contradiction. Nous ne savons pas ce que ces causes sont en
elles-memes, et la raison nous defend de chercher k le connaitre : mais il est bien evident a
priori, qvCell.es ne sont pas en elles-memes ce qu'elles sont par rapport a nous, puisqne la pre-
sence dn sujet modifie necessairement leur action. Sapprimez tout sujet sentant, il est certain
que ces causes agiraient encore puisqu'elles continueraient d'exister ; mais elles agiraient au-
trement ; elles seraient encore des qualites et des proprietes, mais qui ne ressembleraient k
rien de ce que nous connaissons. Le feu ne manifestevait plus aucune des proprietfe que nous
lui connaissons : que serait-il ? C'est ce que nous ne saurons jamais. Cist d'ailleurs peut-
tctre un probleme qui ne repugne pas seulement a la nature de notre esprit, mais a I'essence meme
des choses. Quand meme en eifet on supprimerait par le pensee tous les sujets sentants, il
faudrait encore admettre que nul corps ne manifesterait ses proprietes autrement qn'en rela-
1;ion avec un sujet quelconque, et dans ce cas ses propriMs ne seraient encore que relatives:
•en sorte qu'il me paralt fort raisonnable d'admettre que les propriete's determin^es des corps
n'existent pas independamment d'un sujet quelconque, et que quand on demande si les pro-
prietes de la matiere sont telles que nous les percevons, il faudrait voir auparavant si elles sont
•«n tant que determinees, et dans quel sens il est vrai de dire qu'elles sont." — Conrs d'JBistoire
'de la Philosojihie Morale au 18me siecle, 8me Ie9on.
t An attempt, indeed, has been made by Eeid and others, to establish that although some
-of the properties we ascribe to objects exist only in our sensations, othei-s exist in the things
themselves, being such as can not possibly be copies of any impression upon the senses ; and
they ask, from what sensations our notions of extension and figure have been derived ? The
gauntlet thrown down by Keid was taken up by Brown, who, applying greater powers of anal-
ysis than had previously been applied to the notions of extension and figure, pointed out that
the sensations from which those notions are derived, are sensations of touch, combined with
sensations of a class previously too little adverted to by metaphysicians, those which have their
seat in our muscular frame. His analysis, which was adopted and followed up by James Mill,
has been further and greatly improved upon in Professor Bain's profound work, The Senses
and the Intellect, and in the chapters on ' ' Perception " of a work of eminent analytic power,
Mr. Herbert Spencer's Principles of Psychology.
On this point M. Cousin may again be cited in favor of the better doctrine. M. Cousin
recognizes, in opposition to Beid, the essential subjectivity of our conceptions of what are called
the primary qualities of matter, as extension, solidity, etc., equally with those of color, heat,
.and the remainder of the so-called secondary qualities. — Cours, ut supra, 9me lefon.
56 NAMES AND PROPOSITIONS.
authorized to deduce from the effects, any thing concerning the cause, ex-
cept that it is a cause adequate to produce those effects ? It may, there-
fore, safely be laid down as a truth both obvious in itself, and admitted by
all whom it is at present necessary to take into consideration, that, of the
outward world, we know and can know absolutely nothing, except the sen-
sations which we experience from it.*
§ 8. Body having now been defined the external cause, and (according
to the more reasonable opinion) the unknown external cause, to which we
refer our sensations ; it remains to frame a definition of Mind. Nor, after
the preceding observations, will this be difficult. For, as our conception
of a body is that of an unknown exciting cause of sensations, so our con-
ception of a mind is that of an unknown recipient or percipient, of them ;
and not of them alone, but of all our other feelings. As body is under-
stood to be the mysterious something which excites the mind to feel, so
mind is the mysterious something which feels and thinks. It is unneces-
sary to give in the case of mind, as we gaye in the case of matter, a par-
ticular statement of the skeptical system by which its existence as a Thing
in itself, distinct from the series of what are denominated its states, is call-
ed in question. But it is necessary to remark, that on the inmost nature
(whatever be meant by inmost nature) of the thinking principle, as well
as on the inmost nature of matter, we are, and with our faculties must al-
ways remain, entirely in the dark. All which we are aware of, even in our
own minds, is (in the words of James Mill) a certain "thread of conscious-
ness ;" a series of feelings, that is, of sensations, thoughts, emotions, and
volitions, more or less numerous and complicated. There is a something
I call Myself, or, by another form of expression, my mind, which I consider
as distinct from these sensations, thoughts, etc. ; a something which I con-
ceive to be not the thoughts, but the being that has the thoughts, and
* This doctrine, which is the most complete form of the philosophical theory known as the
Eelativity of Human Knowledge, has, since the recenLrevival in this country of an active in-
terest in metaphysical speculation, been the subject of a greatly increased amount of discussion
and controversy ; and dissentients have manifested themselves in considerably greater number
than I had any knowledge of when the passage in the text was written. The doctrine has
been attacked from two sides. Some thinkers, among whom are the late Professor Penier,
in his Institutes of Metaphysic, and Professor John Grote, in his Exploratio Philosophica, ap-
pear to deny altogether the reality of Noumena, or Things in themselves — of an unknowable
substratum or support for the sensations which we experience, and which, according to the
theory, constitute all our knowledge of an external world. It seems to me, however, that in
Professor Grote's case at least, the denial of Noumena is only apparent, and that he does not
essentially differ from the other class of objectors, including Mr. Bailey in his valuable Let-
ters on the Philosophy of the Human Mind, and (in spite of the striking passage quoted in
the text) also Sir William Hamilton, who contend for a direct knowledge by the human mind
of more than the sensations — of certain attributes or properties as they exist not in iis, but
in the Things themselves.
With the first of these opinions, that which denies Noumena, I have, as a metaphysician,
no quarrel ; but, whether it be true or false, it is irrelevant to Logic. And since all the forms
of language are in contradiction to it, nothing but confusion could result from its unnecessary
introduction into a treatise, every essential doctrine of which could stand equally well with
tbe opposite and accredited opinion. The other and rival doctrine, that of a direct perception
or intuitive knowledge of the outward object as it is in itself, considered as distinct from the
sensations we receive from it, is of far greater practical moment. But even this question,
depending on the nature and laws of Intuitive Knowledge, is not within the province of Logic.
For the grounds of my own opinion concerning it, I must content myself with referring to a
work already mentioned — An Examination of Sir William Hamilton's Philosophy ; several
chapters of which are devoted to a full discussion of the questions and theories relating to
the supposed diiect perception of external objects.
THINGS DENOTED BY NAMES. 57
■which I can conceive as existing forever in a state of quiescence, without
any thoughts at all. But what this being is, though it is myself, I have no
knowledge, other than the series of its states of consciousness. As bodies
manifest themselves to me only through the sensations of which I regard
them as the causes, so the thinking principle, or mind, in my own nature,
makes itself known to me only by the feelings of which it is conscious. I
know nothing about myself, save my capacities of feeling or being con-
scious (including, of course, thinking and willing) : and were I to learn
any thing new concerning my own nature, I can not with my present facul-
ties conceive this new information to be any thing else, than that I have
some additional capacities, as yet unknown to me, of feeling, thinking, or
willing.
Thus, then, as body is the unsentient cause to which we are naturally
prompted to refer a certain portion of our feelings, so mind may be de-
scribed as the sentient subject (in the scholastic sense of the term) of all
feelings ; that which has or feels them. But of the nature of either body
or iuind, further than the feelings which the former excites, and which the
latter experiences, we do not, according to the best existing doctrine, know
any thing ; and if any thing, logic has nothing to do with it, or with the
manner in which the knowledge is acquired. With this result we may
conclude this portion of our subject, and pass to the third and only remain-
ing class or division of Namable Things.
III. Attributes : and, first, Qualities.
§ 9. From what has already been said of Substance, what is to be said
of Attribute is easily deducible. For if we know not, and can not know,
any thing of bodies but the sensations which they excite in us or in others,
those sensations must be all that we can, at bottom, mean by their attri-
butes ; and the distinction which we verbally make between the properties
of things and the sensations we receive from them, must originate in the
convenience of discourse rather than in the nature of what is signified by
the terms.
Attributes are usually distributed under the three heads of Quality,
Quantity, and Relation. We shall come to the two latter presently: in the
first place we shall confine ourselves to the former.
Let us take, then, as our example, one of what are termed the sensible
qualities of objects, and let that example be whiteness. When we ascribe
whiteness to any substance, as, for instance, snow ; when we say that snow
has the quality whiteness, what do we really assert ? Simply, that when
snow is present to our organs, we have a particular sensation, which we
are accustomed to call the sensation of white. But how do I know that
snow is present ? Obviously by the sensations which I derive from it, and
not otherwise. I infer that the object is present, because it gives me a
certain assemblage or series of sensations. And when I ascribe to it the
attribute whiteness, my meaning is only, that, of the sensations composing
this group or series, that which I call the sensation of white color is pue.
This is one view which may be taken of the subject. But there is also
another and a different view. It may be said, that it is true we know noth-
ing of sensible objects, except the sensations they excite in us; that the
fact of our receiving from snow the particular sensation which is called a
sensation of Vvhite, is the ground on which we ascribe to that substance the
quality whiteness ; the sole proof of its possessing that quality. But be-
cause one thing may be the sole evidence of the existence of another thing;
58 NAMES AKD PKOPOSITIONS.
it does not follow that the two are one and the same. The attribute white-
ness (it may be said) is not the fact of receiving the sensation, but some-
thing in the object itself; a power inherent in it; something in virtue of
which the object produces the sensation. And when we affirm that snow
possesses the attribute whiteness, we do not merely assert that the pres-
ence of snow produces in us that sensation, but that it does so through,
and by reason of, that power or quality. , . , x ,
For the purposes of logic it is not of material importance which of these
opinions we adopt. The full discussion of the subject belongs to the other
department of scientific inquiry, so often alluded to under the name of met-
aphysics ; but it may be said here, that for the doctrine of the existence of
a peculiar species of entities called qualities, I can see no foundation ex-
cept in a tendency of the human mind which is the cause of many delu-
sions. I mean, the disposition, wherever we meet with two names which
are not precisely synonymous, to suppose that they must be the names of
two different things ; whereas in reality they may be names of the same-
thing viewed in two different lights, or under different suppositions as to-
surrounding circumstances. Because quality and sensation can not be put
indiscriminately one for the other, it is supposed that they can not both
signify the same thing, namely, the impression or feeling with which we
are affected through our senses by the presence of an object; though there
is at least no absurdity in supposing that this identical impression or feel-
ing may be called a sensation when considered merely in itself, and a quali-
ty when looked at in relation to any one of the numerous objects, the pres-
ence of which to our organs excites in our minds that among various other
sensations or feelings. And if this be admissible as a supposition, it rests
with those who contend for an entity per se called a quality, to show that
their opinion is preferable, or is any thing in fact but a lingering remnant
of the old doctrine of occult causes ; the very absurdity which Molidre so-
happily ridiculed when he made one of his pedantic physicians account for.
the fact that opium produces sleep by the maxim. Because it has a soporific-
virtue.
It is evident that when the physician stated that opium has a soporific:
virtue, he did not account for, but merely asserted over again, the fact that
it produces sleep. In like manner, when we say that snow is white because'
it has the quality of whiteness, we, are only re-asserting in more technical
language the fact that it excites in us the sensation of white. If it be said
that the sensation must have some cause, I answer, its cause is the presence
of the assemblage of phenomena which is termed the object. When we
have asserted that as often as the object is present, and our organs in their
normal state, the sensation takes place, we have stated all that we know
about the matter. There is no need, after assigning a certain and intelli-
gible cause, to suppose an occult cause besides, for the purpose of enabling
the real cause to produce its effect. If I am asked, why does the presence-
of the object cause this sensation in me, I can not tell: I can only say that
such is ray nature, and the nature of the object ; that the fact forms a part
of the constitution of things. And to this we must at last come, even after
interpolating the imaginary entity. Whatever number of links the chain
of causes and effects may consist of, how any one link produces the one
which is next to it, remains equally inexplicable to us. It is as easy to-
comprehend that the object should produce the sensation directly and at
once, as that it should produce the same sensation by the aid of something;
else called the power of producing it.
THINGS DENOTED BY NAMES. 59
But, as the difficulties which may be felt in adopting this view of the
subject can not be removed without discussions transcending the bounds
of our science, I content myself with a passing indication, and shall, for the
purposes of logic, adopt a language compatible with either view of the na-
ture of qualities. I shall say — what at least admits of no dispute— that
the quality of whiteness ascribed to the object snow, is grounded on its
exciting in us the sensation of white ; and adopting the language already
used by the school logicians in the case of the kind of attributes called
Relations, I shall term the sensation of white ^^ foundation of the quality
whiteness. For logical purposes the sensation is the only essential part of
what is meant by the word ; the only part which we ever can be concerned
in proving. When that is proved, the quality is proved ; if an object ex-
cites a sensation, it has, of course, the power of exciting it.
IV. Relations.
§ 10. The qualUies of a body, we have said, are the attributes grounded
on the sensations which the presence of that particular body to our organs
excites in our minds. But when we ascribe to any object the kind of at-
tribute called a Relation, the foundation of the attribute must be some-
thing in which other objects are concerned besides itself and the percipient.
As there may with propriety be said to be a relation between any two
things to which two correlative names are or may be given, we may ex-
pect to discover what constitutes a relation in general, if we enumerate the
principal cases in which mankind have imposed correlative names, and ob-
serve what these cases have in common.
What, then, is the character which is possessed in common by states of
circumstances so heterogeneous and discordant as these: one thing like
another; one thing unlike another; one thing near another; one thing
far from another; one thing before, after, along with another; one thing
greater, equal, less, than another; one thing the cause of another, the effect
of another ; one person the master, servant, child, parent, debtor, creditor,
sovereign, subject, attorney, client, of another, and so on ?
Omitting, for the present, the case of Resemblance, (a relation which re-
quires to be considered separately,) there seems to be one thing common
to all these cases, and only one ; that in each of them there exists or occurs,
or has existed or occurred, or may be expected to exist or occur, some fact
or phenomenon, into which the two things which are said to be related to
each other, both enter as parties concerned. This fact, or phenomenon, is
what the Aristotelian logicians called the fundamentum relationis. Thus
in the relation of greater and less between two magnitudes, the /Mw<?amew-
tum relationis is the fact that one of the two magnitudes could, under cer-
tain conditions, be included in, without entirely filling, the space occupied
by the other magnitude. In the relation of master and servant, the fun-
dam.entum relationis is the fact that the one has undertaken, or is com-
pelled, to perform certain services for the benefit and at the bidding of the
other. Examples might be indefinitely multiplied ; but it is already obvi-
ous that whenever two things are said to be related, there is some fact, or
series of facts, into which they both enter ; and that whenever any two
things are involved in some one fact, or series of facts, we may ascribe to
those two things a mutual relation grounded on the fact. Even if they
have nothing in common but what is common to all things, that they are
members of the universe, we call that a relation, and denominate them
fellow-creatures, fellow-beings, or fellow-denizens of the universe. But in
60 NAMES AND PROPOSITIONS.
proportion as the fact into which the two objects enter as parts is of a
more special and peculiar, or of a more complicated nature, so also is the
relation grounded upon it. And there are as many conceivable relations
as there are conceivable kinds of fact in which two things can be jointly
concerned.
In the same manner, therefore, as a quality is an attribute grounded on
the fact that a certain sensation or sensations are produced in us by the
object, so an attribute grounded on some fact into which the object enters
jointly with another object, is a relation between it and that other object
But the fact in the latter case consists of the very same kind of elements
as the fact in the former; namely, states of consciousness. In the case,
*for example, of any legal relation, as debtor and creditor, principal and
agent, guardian and ward, the fundamentum relationis consists entirely of
thoughts, feelings, and volitions (actual or contingent), either of the persons
themselves or of other persons concerned in the same series of transactions ;
as, for instance, the intentions which would be formed by a judge, in case
a complaint were made to his tribunal of the infringement of any of the
legal obligations imposed by the relation; and the acts which the judge
would perform in consequence; acts being (as we have already seen) an-
other word for intentions followed by an effect, and that effect being but
another word for sensations, or some other feelings, occasioned either to
the agent himself or to somebody else. There is no part of what the names
expressive of the relation imply, that is not resolvable into states of con-
sciousness ; outward objects being, no doubt, supposed throughout as the
causes by which some of those states of consciousness are excited, and
minds as the subjects by which all of them are experienced, but neither
the external objects nor the minds making their existence known other-
wise than by the states of consciousness.
Cases of relation are not always so complicated as those to which we
last alluded. The simplest of all cases of relation are those expressed by
the words antecedent and consequent, and by the word simultaneous. If
we say, for instance, that dawn preceded sunrise, the fact in which the two
things, dawn and sunrise, were jointly concerned, consisted only of the two
things themselves; no third thing entered into the fact or phenomenon at
all. Unless, indeed, we choose to call the succession of the two objects a
third thing; but their succession is not something added to the things
themselves ; it is something involved in them. Dawn and sunrise announce
themselves to our consciousness by two successive sensations. Our con-
sciousness of the succession of these sensations is not a third sensation or
feeling added to them ; we have not first the two feelings, and then a feel-
ing of their succession. To have two feelings at all, implies having them
either successively, or else simultaneously. Sensations, or other feelings,
bemg given, succession and simultaneousness are the two conditions, to the
alternative of which they are subjected by the nature of our faculties ; and
no one has been able, or needs expect, to analyze the matter any further.
§ n. In a somewhat similar position are two other sorts of relations,
Likeness and Unlikeness. I have two sensations ; we will suppose them
to be simple ones ; two sensations of white, or one sensation of white and
another of black. I call the first two sensations like; the last two unlike.
What IS the fact or phenomenon constituting the fundamentum of this
relation t Ihe two sensations first, and then what we call a feeling of re-
semblance, or of want of resemblance. Let us confine ourselves to the fcr-
THINGS DENOTED BY NAMES. 61
mer case. Resemblance is evidently a feeling; a state of the consciousness
of the observer. Whether the feeling of the resemblance of the two colors
be a third state of consciousness, which I have after having the two sensa-
tions of color, or whether (like the feeling of their succession) it is involved
in the sensations themselves, may be a matter of discussion. But in either
case, these feelings of resemblance, and of its opposite dissimilarity, are
parts of our nature ; and parts so far from being capable of analysis, that
they are presupposed in every attempt to analyze any of our other feelings.
Likeness and uiilikeness, therefore, as well as antecedence, sequence, and
simultaneousness, must stand apart among relations, as things sui generis.
They are attributes grounded on facts, that is, on states of consciousness,
but on states which are peculiar, unresolvable, and inexplicable.
But, though likeness or unlikeness can not be resolved into any thing
else, complex cases of likeness or unlikeness can be resolved into simpler
ones. When we say of two things which consist of parts, that they are
like one another, the likeness of the wholes does admit of analysis ; it is
compounded of likenesses between the various parts . respectively, and of
likeness in their arrangement. Of how vast a variety of resemblances of
parts must that resemblance be composed, which induces us to say that a
porti'ait, or a landscape, is like its original. If one person mimics another
with any success, of how many simple likenesses must the general or com-
plex likeness be compounded : likeness in a succession of bodily postures ;
likeness in voice, or in the accents and intonations of the voice ; likeness
in the choice of words, and in the thoughts or sentiments expressed, wheth-
er by word, countenance, or gesture.
All likeness and unlikeness of which we have any cognizance, resolve
themselves into likeness and unlikeness between states of our own, or some
other, mind. When we say that one body is like another, (since we know
nothing of bodies but the sensations which they excite,) we mean really
that there is a resemblance between the sensations excited by the two
bodies, or between some portions at least of those sensations. If we say
that two attributes are like one another (since we know nothing of attri-
butes except the sensations or states of feeling on which they are ground-
ed), we mean really that those sensations, or states of feeling, resemble each
other. We may also say that two relations are alike. The fact of resem-
blance between relations is sometimes called analogy, forming one of the
numerous meanings of that word. The relation in which Priam stood to
Hector, namely, that of father and son, resembles the relation in which
Philip stood to Alexander ; resembles it so closely that they are called the
same relation. The relation in which Cromwell stood to England resem-
bles the relation in which Napoleon stood to France, though not so closely
as to be called the same relation. The meaning in both these instances
must be, that a resemblance existed between the facts which constituted
the fundamentum relationis.
This resemblance may exist in all conceivable gradations, from perfect
nndistinguishableness to something extremely slight. When we say, that
a thought suggested to the mind of a person of genius is like a seed cast
into the ground, because the former produces a multitude of other thoughts,
and the latter a multitude of other seeds, this is saying that between the
relation of an inventive mind to a thought contained in it, and the relation
of a fertile soil to a seed contained in it, there exists a resemblance : the
real resemblance being in the two fundamenta relationis, in each of which
there occurs a germ, producing by its development a multitude of other
62 NAMES AND PKOPOSITIONS.
things similar to itself. And as, whenever two objects are jointly concern-
ed in a phenomenon, this constitutes a relation between those objects, so,
if we suppose a second pair of objects concerned in a second phenomenon,
the slightest resemblance between the two phenomena is sufficient to ad-
mit of its being said that the two relations resemble; provided, of course,
the points of resemblance are found in those portions of the two phenom-
ena respectively which are connoted by the relative names.
While speaking of resemblance, it is necessary to take notice of an am-
biguity of language, against which scarcely any one is sufficiently on his
guard. Resemblance, when it exists in the highest degree of all, amount-
ing to undistinguishableness, is often called identity, and the two similar
things are said to be the same. I say often, not always ; for we do not say
that two visible objects, two persons, for instance, are the same, because
they are so much alike that one might be mistaken for the other : but we
•constantly use this mode of expression when speaking of feelings ; as when
I say that the sight of any object gives me the same sensation or emotion
to-day that it did yesterday, or the same which it gives to some other per-
son. This is evidently an incorrect application of the word sam,e; for the
feeling which I had yesterday is gone, never to return ; what I have to-
day is another feeling, exactly like the f ormei-, perhaps, but distinct from it ;
and it is evident that two different persons can not be experiencing the
same feeling, in the sense in which we say that they are both sitting at the
same table. By a similar ambiguity we say, that two persons are ill of the
same disease ; that two persons hold the sam,e office ; not in the sense in
which we say that they are engaged in the same adventure, or sailing in
the same ship, but in the sense that they fill offices exactly similar, though,
perhaps, in distant places. Great confusion of ideas is often produced, and
many fallacies engendered, in otherwise enlightened understandings, by
not being sufficiently alive to the fact (in itself not always to be avoided),
that they use the same name to express ideas so different as those of iden-
tity and undistinguishable resemblance. Among modern writers. Arch-
bishop Whately stands almost alone in having drawn attention to this dis-
tinction, and to the ambiguity connected with it.
Several relations, generally called by other names, are really cases of
resemblance. As, for example, equality ; which is but another word for
the exact resemblance commonly called identity, considered as subsisting
between things in respect of their quantity. And this example forms a
suitable transition to the third and last of the three heads under which, as
already remarked, Attributes are commonly arranged.
V. Quantity.
§ 12. Let us imagine two things, between which there is no difference
(that is, no dissimilarity), except in quantity alone; for instance, a gallon
of water, and more than a gallon of water. A gallon of water, like any
other external object, makes its presence known to us by a set of sensa-
tions which it excites. Ten gallons of water are also an external object,
makmg its presence known to us in a similar manner ; and as we do not
mistake ten gallons of water for a gallon of water, it is plain that the set
of sensations is more or less different in the two cases. In like manner
a gallon of water, and a gallon of wine, are two external objects, making
their presence known by two sets of sensations, which sensations are A\t
ferent from each other. In the first case, however, we say that the differ-
ence is in quantity ; in the last there is a difference in quality while the
THINGS DENOTED BY NAMES. 63
«[nantity of the water and of the wine is the same. What is the real dis-
tinction between the two cases ? It is not within the province of Logic to
analyze it ; nor to decide whether it is susceptible of analysis or not. For
us the following considerations ai-e sufficient: It is evident that the sen-
sations I receive from the gallon of water, and those I receive from the
gallon of wine, are not the same, that is, not precisely alike ; neither are
they altogether unlike : they are partly similar, partly dissimilar ; and that
in which they resemble is precisely that in which alone the gallon of wa-
ter and the ten gallons do not resemble. That in which the gallon of wa-
ter and the gallon of wine are like each other, and in which the gallon
and the ten gallons of water are unlike each other, is called their quan-
tity. This likeness and unlikeness I do not pretend to explain, no more
than any other kind of likeness or unlikeness. But my object is to show,
that when we say of two things that they differ in quantity, just as when
we say that they differ in quality, the assertion is always grounded on a
•difference in the sensations which they excite. Xobody, I presume, will
«ay, that to see, or to lift, or to drink, ten gallons of water, does not include
in itself a different set of sensations from those of seeing, lifting, or drink-
ing one gallon ; or that to see or handle a foot-rule, and to see or handle a
yard-measure made exactly like it, are the same sensations. I do not un-
■dertake to say what the difference in the sensations is. Every body knows,
and nobody can tell ; no more than any one could tell what white is to a
person who had never had the sensation. But the difference, so far as
•cognizable by our faculties, lies in the sensations. Whatever difference
we say there is in the things themselves, is, in this as in all other cases,
grounded, and grounded exclusively, on a difference in the sensations ex
«ited by them.
VI. Attributes Concluded.
§ 13. Thus, then, all the attributes of bodies which are classed under
■Quality or Quantity, are grounded on the sensations which we receive from
those bodies, and may be defined, the powers which the bodies have of ex-
citing those sensations. And the same general explanation has been found
to apply to most of the attributes usually classed under the head of Rela-
tion. They, too, are grounded on some fact or phenomenon into which the
related objects enter as parts ; that fact or phenomenon having no mean-
ing and no existence to us, except the series of sensations or other states
•of consciousness by which it makes itself known ; and the relation being
simply the power or capacity which the object possesses of taking pai't
along with the correlated object in the production of that series of sensa-
tions or states of consciousness. We have been obliged, indeed, to recog-
nize a somewhat different character in certain peculiar relations, those of
succession and simultaneity, of likeness and unlikeness. These, not being
grounded on any fact or phenomenon distinct from the related objects
themselves, do not admit of the same kind of analysis. But these relations,
though not, like other relations, grounded on states of consciousness, are
themselves states of consciousness : resemblance is nothing but our feeling
of resemblance ; succession is nothing but our feeling of succession. Or,
if this be disputed (and we can not, without transgressing the bounds of
our science, discuss it here), at least our knowledge of these relations, and
even onr possibility of knowledge, is confined to those which subsist be-
tween sensations, or other states of consciousness ; for, though we ascribe
resemblance, or succession, or simultaneity, to objects and to attributes, it
64 NAMES AND PEOPOSITIONS.
is always in virtue of resemblance or succession or simultaneity in the sen-
sations or states of consciousness which those objects excite, and on which
those attributes are grounded,
§ 14. In the preceding investigation we have, for the sake of simplicity,
considered bodies only, and omitted minds. But what we have said, is ap-
plicable, mutatis mutandis, to the latter. The attributes of minds, as well
as those of bodies, are grounded on states of feeling or consciousness. But
in the case of a mind, we have to consider its own states, as well as those
which it produces in other minds. Every attribute of a mind consists either
in being itself affected in a certain way, or affecting other minds in a certain
way. Considered in itself, we can predicate nothing of it but the series
of its own feelings. When we say of any mind, that it is devout, or super-
stitious, or medttative, or cheerful, we mean that the ideas, emotions, or
volitions implied in those words, form a frequently recurring part of the
series of feelings, or states of consciousness, which fill up the sentient ex-
istence of that. mind.
In addition, however, to those attributes of a mind which are grounded
on its own states of feeling, attributes may also be ascribed to it, in the
same manner as to a body, grounded on the feelings which it excites in
other minds. A mind does not, indeed, like a body, excite sensations, but.
it may excite thoughts or emotions. The most important example of attri-
butes ascribed on this ground, is the employment of terras expressive of
approbation or -blame. When, for example, we say of any character, or (in
other words) of any mind, that it is admirable, we mean that the contem-
plation of it excites the sentiment of admiration ; and indeed somewhat
more, for the word implies that we not only feel admiration, but approve
that sentiment in ourselves. In some cases, under the semblance of a sin-
gle attribute, two are really predicated : one of them, a state of the mind
-itself; the other, a state with which other minds are affected by thinking
of it. As when we say of any one that he is generous. The word gene-
rosity expresses a certain state of mind, but being a term of praise, it also
expresses that this state of mind excites in us another mental state, called
approbation. The assertion made, therefore, is twofold, and of the follow-
ing purport: Certain feelings form habitually a part of this person's sen-
tient existence ; and the idea of those feelings of his, excites the sentiment
of approbation in ourselves oi' others.
As we thus ascribe attributes to minds on the ground of ideas and emo-
tions, so may we to bodies on similar grounds, and not solely on the ground
of sensations : as in speaking of the beauty of a statue ; since this attribute
is grounded on the peculiar feeling of pleasure which the statue produces
in our minds ; which is not a sensation, but an emotion.
VII. General Results.
§ 15. Our survey of the varieties of Things which have been, or which
are capable of being, named — which have been, or are capable of being,
either predicated of other Things, or themselves made the subject of predi-
cations— is now concluded.
Our enumeration commenced with Peelings. These we scrupulously dis-
tinguished from the objects which excite them, and from the organs by
which they are, or may be supposed to be, conveyed. Feelings are of four
sorts : Sensations, Thoughts, Emotions, and Volitions. What are called
Perceptions are merely a particular case of Belief, and Belief is a kind of
thought. Actions are merely volitions followed by an effect.
THINGS DENOTED BY NAMES. 65
After Feelings we proceeded to Substances. These are either Bodies or
Minds. Without entering into the grounds of the metaphysical doubts
which have been raised concerning the existence of Matter and Mind as ob-
jective realities, we stated as sufficient for us the conclusion in which the
best thinkers are now for the most part agreed, that all we can know of
Matter is the sensations which it gives us, and the order of occurrence of
those sensations ; and that while the substance Body is the unknown cause
of our sensations, the substance Mind ia the unknown recipient.
The only remaining class of Namable Things is Attributes; and these
are of three kinds, Quality, Relation, and Quantity. Qualities, like sub-
stances, are known to us no otherwise than by the sensations or other
states of consciousness which they excite : and while, in compliance with
common usage, we have continued to speak of them as a distinct class of
Things, we showed that in predicating them no one means to predicate any
thing but those sensations or states of consciousness, on which they may be
said to be grounded, and by which alone they can be defined or described.
Relations, except the simple cases of likeness and unlikeness, succession
and simultaneity, are similarly grounded on some fact or phenomenon, that
is, on some series of sensations or states of consciousness, more or less
complicated. The third species of Attribute, Quantity, is also manifestly
grounded on something in our sensations or states of feeling, since there is
an indubitable difference in the sensations excited by a larger and a smaller
bulk, or by a greater or a less degree of intensity, in any object of sense or
of consciousness. All attributes, therefore, are to us nothing but either
our sensations and other states of feeling, or something inextricably in-
volved therein; and to this even the peculiar and simple relations just ad-
verted to are not exceptions. Those peculiar relations, however, are so im-
portant, and, even if they might in strictness be classed among states of
consciousness, are so fundamentally distinct from any other of those states,
that it would be a vain subtlety to bring them under that common descrip-
tion, and it is necessary that they should be classed apart.*
As the result, therefore, of our analysis, we obtain the following as an
enumeration and classification of all Namable Things :
1st. Feelings, or States of Consciousness.
2d. The Minds which experience those feelings.
3d. The Bodies, or external objects which excite certain of those feelings,
together with the powers or properties whereby they excite them ; these
latter (at least) being included rather in compliance with common opinion,
and because their existence is taken for granted in the common language
from which I can not prudently deviate, than because the recognition of
such powers or properties as real existences appears to be warranted by a
sound philosophy.
4th, and last. The Successions and Co-existences, the Likenesses and Un-
likenesses, between feelings or states of consciousness. Those relations,
when considered as subsisting between other things, exist in reality only
between the states of consciousness which those things, if bodies, excite, if
minds, either excite or experience.
* Professor Bain {Logic, i., 49) defines attributes as "points of community among classes."
This definition expresses well one point of view, but is liable to the objection that it applies
only to the attributes of classes ; though an object, unique in its kind, may be said to have at-
tributes. Moreover, the definition is not ultimate, since the points of community themselves
admit of, and require, further analysis ; and Mr. Bain does analyze them into resemblances in
the sensations, or other states of consciousness excited by the object.
66 NAMES AND PROPOSITIONS.
This, until a better can be suggested, may serve as a substitute for the
Categories of Aristotle considered as a classification of Existences. The
practical application of it will appear when we commence the inquiry into
the Import of Propositions ; in other words, when we inquire what it is
which the mind actually believes, when it gives what is called its assent to
a proposition.
These four classes comprising, if the classification be correct, all Namable
Things, these or some of them must of course compose the signification of
all names : and of these, or some of them, is made up whatever we call a
fact.
For distinction's sake, every fact which is solely composed of feelings or
states of consciousness considered as such, is often called a Psychological
or Subjective fact ; while every fact which is composed, either wholly or in
part, of something different from these, that is, of substances and attri-
butes, is called an Objective fact. We may say, then, that every objective
fact is grounded on a corresponding subjective one ; and has no meaning
to us (apart from the subjective fact which corresponds to it), except as a
name for the unknown and inscrutable process by which that subjective or
psychological fact is brought to pass.
CHAPTER IV.
OF PEOPOSITIONS.
§ 1. Ik treating of Propositions, as already in treating of Names, some
considerations of a comparatively elementary nature respecting their form
and varieties must be premised, before entering upon that analysis of the
import conveyed by them, which is the real subject and purpose of this
preliminary book.
A proposition, we have before said, is a portion of discourse in which a
predicate is affirmed or denied of a subject. 'A predicate and a subject are
all that is necessarily required to make up a proposition : but as we can not
conclude from merely seeing two names put together, that they are a predi-
cate and a subject, that is, that one of them is intended to be affirmed or
denied of the other, it is necessary that there should be some mode or form
of indicating that such is the intention ; some sign to distinguish a predi-
cation from any other kind of discourse. This is sometimes done by a
slight alteration of one of the words, called an inflection; as when we say,
Fire burns ; the change of the second word from burn to burns showing
that we mean to affirm the predicate burn of the subject fire. But this
function is more commonly fulfilled by the word is, when an affirmation is
intended, is not, when a negation ; or by some other part of the verb to be.
The word which thus serves the purpose of a sign of predication is called,
as we formerly observed, the copula. It is important that there should be
no indistinctness in our conception of the nature and office of the copula ;
for confused notions respecting it are among the causes which have spread
myHticism over the field of logic, and perverted its speculations into logoma-
chies.
It is apt to be supposed that the copula is something more than a mere
sign of predication ; that it also signifies existence. In the proposition,
Socrates is just, it may seem to be implied not only that the quality Just
can be affirmed of Socrates, but moreover that Socrates is, that is to say.
PROPOSITIONS. 67
-exists. This, however, only shows that there is an ambiguity in the word
is; a word which not only performs the function of the copula in aflSrma-
"tions, but has also a meaning of its own, in virtue of which it may itself be
made the predicate of a proposition. That the employment of it as a cop-
ula does not necessarily include the affirmation of existence, appears from
such a proposition as this, A centaur is a fiction of the poets ; where it can
not possibly be implied that a centaur exists, since the proposition itself ex-
pressly asserts that the thing has no real existence.
Many volumes might be filled with the frivolous speculations conceniing
the nature of Being (to ov, ovaia. Ens, Entitas, Essentia, and the like), which
have arisen from overlooking this double meaning of the word to he; from
-supposing that when it signifies to exist, and when it signifies to he some
specified thing, as to he a man, to he Socrates, to he seen or spoken of, to he
s( phantom, even to he a nonentity, it must still, at bottom, answer to the
«ame idea ; and that a meaning must be found for it which shall suit all
these cases. The fog which rose from this narrow spot diffused itself at
an early period over the whole surface of metaphysics. Yet it becomes
us not to triumph over the great intellects of Plato and Aristotle because
we ai-e now able to preserve ourselves from many errors into which they,
perhaps inevitably, fell. The fire-teazer of a modern steam-engine produces
by his exertions far greater effects than Milo of Crotona could, but he is
not therefore a stronger man. The Greeks seldom knew any language but
their own. This rendered it far more difi[icult for them than it is for us, to
acquire a readiness in detecting ambiguities. One of the advantages of
having accurately studied a plurality of languages, especially of those lan-
guages which eminent thinkers have used as the vehicle of their thoughts,-^
is the practical lesson we learn respecting the ambiguities of words, by find-
ing that the same word in one language corresponds, on different occasions,
to different words in another. When not thus exercised, even the strong-
est understandings find it difficult to believe that things which have a com-
mon name, have not in some respect or other a common nature ; and often
expend much labor very unprofitably (as was frequently done by the two
philosophers just mentioned) in vain attempts to discover in what this com-
mon nature consists. But, the habit once formed, intellects much inferior
are capable of detecting even ambiguities which are common to many lan-
guages : and it is surprising that the one now under consideration, though
it exists in the modern languages as well as in the ancient, should have
been overlooked by almost all authors. The quantity of futile speculation
which had been caused by a misapprehension of the nature of the copula,
was hinted at by Hobbes ; but Mr. James Mill* was, I believe, the first who
distinctly characterized the ambiguity, and pointed out how many errors in
the received systems of philosophy it has had to answer for. It has, indeed,
misled the moderns scarcely less than the ancients, though their mistakes,
because our understandings are not yet so completely emancipated from
their influence, do not appear equally irrational.
We shall now briefly review the principal distinctions which exist among
propositions, and the technical terms most commonly in use to express
those distinctions.
§ 2. A proposition being a portion of discourse in which something is
affirmed or denied of something, the first division of propositions is into
* Analysis of the Human Mind, i., 126 et se(i.
68 NAMES AND PROPOSITIONS.
affirmative and negative. An affirmative proposition is that in which the-
predicate is affirmed oi the subject; as, Cassar is dead. Anegative prop-
osition is that in which the predicate is denied oi the subject; as, C^sar
is not dead. The copula, in this last species of proposition, consists of
the words is not, which are the sign of negation ; is being the sign of
affirmation.
Some logicians, among whom may be mentioned Hobbes, state this dis-
tinction differently ; they recognize only one form of copula, is, and attach
the negative sign to the predicate. " CiBsar is dead," and " Caesar is not
dead," according to these writers, are propositions agreeing not in the sub-
ject and predicate, but in the subject only. They do not consider " dead,'^
but " not dead," to be the predicate of the second proposition, and they ac-
cordingly define a negative proposition to be one in which the predicate is
a negative name. The point, though not of much practical moment, d^
serves notice as an example (not nnfrequent in logic) where by means of
an apparent simplification, but which is merely verbal, matters are made
more complex than before. The notion of these writers was, that they
could get rid of the distinction between affirming and denying, by treating-
every case of denying as the affirming of a negative name. But what is
meant by a negative name? A name expressive of the absence of an attri-
bute. So that when we affirm a negative name, what we are really predi-
cating is absence and not presence ; we are asserting not that any thing is,
but that something is not; to express which operation no word seems so-
proper as the word denying. The fundamental distinction is between a
fact and the non-existence of that fact; between seeing something and
not seeing it, between Caesar's being dead and his not being dead ; and if
this were a merely verbal distinction, the generalization which brings both
within the same form of assertion would be a real simplification : the dis-
tinction, however, being real, and in the facts, it is the generalization con-
founding the distinction that is merely verbal ; and tends to obscure the-
subject, by treating the difference between two kinds of truths as if it were
only a difference between two kinds of words. To put things together,
and to put them or keep them asunder, will remain different operations,,
whatever tricks we may play with language.
A remark of a similar nature may be applied to most of those distinc-
tions among propositions which are said to have reference to their modali-
ty; as, difference of tense or time; the sun did rise, the sun is rising, the
sun will rise. These differences, like that between affirmation and nega-
tion, might be glossed over by considering the incident of tifne as a mere
modification of the predicate : thus. The sun is an object having risen, The
sun is an object now rising, The sun is an object to rise hereafter. But the
simplification would be merely verbal. Past, present, and future, do not
constitute so many different kinds of rising ; they are designations belong-
ing to the event asserted, to the suit's rising to-day. They affect, not the
predicate, but the applicability of the predicate to the particular subject.
That which wo affirm to be past, present, or future, is not what the subject
signifies, nor what the predicate signifies, but specifically and expressly
what the predication signifies ; what is expressed only by the propositioni
as such, and not by either or both of the terms. Therefore the circum-
stance of time is properly considered as attaching to the copula, which is
the sign of predication, and not to the predicate. If the same can not be
said of such modifications as these, Caesar may be dead ; Caesar is perhaps
dead ; it is possible that Caesar is dead ; it is only because these fall alto-
PROPOSITIONS. 69
-gether under anothei- head, being properly assertions not of any thing re-
lating to the fact itself, but of the state of our own mind in regard to it ;
namely, our absence of disbelief of it. Thus " Caesar may be dead" means
*' I am not sure that Caesar is alive."
§ 3. The next division of propositions is into Simple and Complex ; more
aptly (by Professor Bain*) termed Compound. A simple proposition is
that in which one predicate is aflBrmed or denied of one subject. A com-
pound proposition is that in which there is more than one predicate, or
more than one subject, or both.
At first sight this division has the air of an absurdity ; a solemn distinc-
tion of things into one and more than one ; as if we were to divide horses
into single horses and teams of horses. And it is true that what is called
a complex (or compound) proposition is often not a proposition at all, but
several propositions, held together by a conjunction. Such, for example, is
this : Caesar is dead, and Brutus is alive : or even this, Caesar is dead, but
Brutus is alive. There are here two distinct assertions ; and we might as
well call a street a complex house, as these two propositions a complex
proposition. It is true that the syncategorematic words a7id and but have
a, meaning ; but that meaning is so far from making the two pi-opositions
one, that it adds a third proposition to them. All particles are abbrevia-
tions, and generally abbreviations of propositions ; a kjnd of short-hand, •
whereby something which, to be expressed fully, would have required a
proposition or a series of propositions, is suggested to the mind at once.
Thus the words, Caesar is dead and Brutus is alive, are equivalent to these :
■Caesar is dead ; Brutus is alive ; it is desired that the two preceding prop-
ositions should be thought of together. If the words were, Caesar is dead,
hut Brutus is alive, the sense would be equivalent to the same three propo-
sitions together with a fourth ; " between the two preceding propositions
there exists a contrast :" viz., either between the two facts themselves, or
between the feelings with which it is desired that they should be regarded.
In the instances cited the two propositions are kept visibly distinct, each
subject having its separate predicate, and each predicate its separate sub-
ject. For brevity, however, and to avo^d repetition, the propositions are
often blended together: as in this, "Peter and James preached at Jerusa-
lem and in Galilee," which contains four propositions : Peter preached at
Jerusalem, Peter preached in Galilee, James preached at Jerusalem, James
preached in Galilee.
We have seen that when the two or more propositions comprised in
■what is called a complex proposition are stated absolutely, and not under
any condition or proviso, it is not a proposition at all, but a plurality of
propositions ; since .what it expresses is not a single assertion, but several
assertions, which, if true when joined, are true also when separated. But
there is a kind of proposition which, though it contains a plurality of sub-
jects and of predicates, and may be said in one sense of the word to con-
sist of several propositions, contains but one assertion ; and its truth does
not at all imply that of the simple propositions which compose it. An ex-
ample of this is, when the simple propositions are connected by the parti-
ble or; as, either A is B or C is D ; or by the particle if; as, A is B if C
is D. In the former case, the proposition is called disjunctive, in the lat-
ter, conditional: the name hypothetical was originally common to both.
Logic, i., 85.
>J0 NAMES AND PROPOSITIONS.
As has been well remarked by Archbishop Whately and others, the dis-
junctive form is resolvable into the conditional; every disjunctive proposi-
tion being equivalent to two or more conditional ones. " Either A is B or
C is D," means, " if A is not B, C is D ; and if C is not D, A is B." All
hypothetical propositions, therefore, though disjunctive in form, are condi-
tional in meaning; and the words hypothetical and conditional may be, as
indeed they generally are, used synonymously. Propositions in which the
assertion is not dependent on a condition, ai"e said, in the language of logi-
cians, to be categorical.
A hypothetical proposition is not, like the pretended complex proposi..
tions which we previously considered, a mere aggregation of simple propo-
sitions. The simple propositions which form part of the words in which
it is couched, form no part of the assertion which it conveys. When we
say. If the Koran comes from God, Mohammed is the prophet of God, we
do not intend to affirm either that the Koran does come from God, or that
Mohammed is really his prophet. Neither of these simple propositions may-
be true, and yet the truth of the hypothetical proposition may be indis-
putable. What is asserted is not the truth of either of the propositions,
but the inferribility of the one from the other. What, then, is the subject,
and what the predicate of the hypothetical proposition? "The Koran"
is not the subject of it, nor is " Mohammed :" for nothing is affirmed or de-
nied either of the Koran or of Mohammed. The real subject of the pred-
ication is the entire proposition, "Mohammed is the prophet of God;" and
the affirmation is, that this is a legitimate inference from the proposi-
tion, " The Koran comes from God." The subject and predicate, therefore,
of a hypothetical proposition are names of propositions. The subject is-
some one proposition. The predicate is a general relative name applicable
to propositions ; of this form — " an inference from so and so." A fresh
instance is here afforded of the remark, that particles are abbreviations;
since "J^ A is B, G is D," is found to be an abbreviation of the follow-
ing : " The proposition C is D, is a legitimate inference from the proposi-
tion A is B."
The distinction, therefore, between hypothetical and categorical proposi-
tions is not so great as it at first appeal's. In the conditional, as well as in
the categorical form, one predicate is affirmed of one subject, and no more:
but a conditional proposition is a proposition concerning a proposition;
the subject of the assertion is itself an assertion. Nor is this a property
peculiar to hypothetical propositions. There are other classes of assertions
concerning propositions. Like other things, a proposition has attributes
which may be predicated of it. The atti-ibute predicated of it in a hypo-
thetical proposition, is that of being an inference from a certain other prop-
osition. But this is only one of many attributes that plight be predicated.
We may say, That the whole is greater than its part, is an axiom in math-
ematics : That the Holy Ghost proceeds from the Father alone, is a tenet
of the Greek Church : The doctrine of the divine right of kings was re-
nounced by Parliament at the Revolution: The infallibility of the Pope
has no countenance from Scripture. In all these cases the subject of the
predication is an entire proposition. That which these different predicates-
are affirmed of, is the proposition," the whole is greater than its part;" tli£
proposition, " the Holy Ghost proceeds from the Father alone ;" the propo-
sition, " kings have a divine right ;" the proposition, " the Pope is infallible."'
Seeing, then, that there is much less difference between hypothetical
propositions and any others, than one might be led to imagine from their
PROPOSITIONS. 71
form, we should be at a loss to account for the conspicuous position which
they have been selected to fill in treatises on logic, if we did not remem-
ber that what they predicate of a proposition, namely, its being an inference
from something else, is precisely that one of its attributes with which most
of all a logician is concerned.
§ 4. The next of the common divisions of Propositions is into Universal,
Particular, Indefinite, and Singular : a distinction founded on the degree
of generality in which the name, which is the subject of the proposition,,
is to be understood. The following are examples :
All men are mortal — Universal.
Some men are mortal — Particular.
Man is mortal — Indefinite.
Julius Ccesar is mortal — Singular.
The proposition is Singular, when the subject is an individual name.
The individual name needs not be a proper name. "The Founder of
Christianity was crucified," is as much a singular proposition as " Christ
was crucified."
When the name which is the subject of the proposition is a general
name, .we may intend to aflirm or deny the predicate, either of all the
things that the subject denotes, or only of some. When the predicate is
affirmed or denied of all and each of the things denoted by the subject,,
the proposition is universal ; when of some undefined portion of them only,
it is particular. Thus, All men are mortal ; Every man is mortal ; are uni-
versal propositions. No man is immortal, is also a universal proposition,
since the predicate, immortal, is denied of each and every individual de-
noted by the term man ; the negative proposition being exactly equivalent
to the following. Every man is not-immortal. But " some men are wise,"
" some men are not wise," are particular propositions ; the predicate wise
being in the one case affirmed and in the other denied not of each and ev-
ery, individual denoted by the term man, but only of each and every one
of some portion of those individuals, without specifying what portion ; for
if this were specified, the proposition would be changed either into a singu-
lar proposition, or into a universal proposition with a different subject ;
as, for instance, " all properly instructed men are wise." There are other
forms of particular propositions ; as, "Most men are imperfectly educated :"
it being immaterial how large a portion of the subject the predicate is as-
serted of, as long as it is left uncertain how that portion is to be distin-
guished from the rest.*
When the form of the expression does not clearly show whether the-
general name which is the subject of the proposition is meant to stand for
all the individuals denoted by it, or only for some of them, the proposition
is, by some logicians, called Indefinite ; but this, as Archbishop Whately ob-
* Instead of Universal and Particular as applied to propositions, Professor Bain proposes
(Logic, i., 81) the terras Total and Partial; reserving the former pair of terms for their in-
ductive meaning, "the contrast between a general proposition and the particulars or individ-
uals that we derive it from." This change in nomenclature would be attended with the further
advantage, that Singular propositions, which in the Syllogism follow the same rules as Univer-
sal, would be included along with them in the same class, that of Total predications. It is not
the Subject's denoting many things or only one, that is of importance in reasoning, it is that
the assertion is made of the whole or a part only of what the Subject denotes. The words
Universal and Particular, however, are so familiar and so well understood in both the senses-
mentioned by Mr. Bain, that the double meaning does not produce any material inconvenience.
72 NAMES AND PROPOSITIONS.
serves, is a solecism, of the same nature as that committed by some gram,
marians when in their list of genders they enumerate the doubtful gender.
The speaker must mean to assert the proposition either as a universal or
as a particular proposition, though he has failed to declare which : and it
often happens that though the words do not show which of the two he in-
tends, the context, or the custom of speech, supplies the deficiency. Thus,
when it is affirmed that " Man is mortal," nobody doubts that the asser-
tion is intended of all human beings ; and the word indicative of universal-
ity is commonly omitted, only because the meaning is evident without it.
In the proposition, " Wine is good," it is understood with equal readiness,
though for somewhat different reasons, that the assertion is not intended
, to be universal, but particulai-.* As is observed by Professor Bain,f the
«hief examples of Indefinite propositions occur " with names of material,
which are the subjects sometimes of universal, and at other times of partic-
ular predication. 'Food is chemically constituted by carbon, oxygen, etc.,'
is a proposition of universal quantity ; the meaning is all food — all kinds
of food. 'Food is necessary to animal life' is a case of particular quan-
tity; the meaning is some sort of food, not necessarily all sorts. 'Metal
is requisite in order to strength ' does not mean all kinds of metal. ' Gold
■will make a way,' means a portion of gold."
When a general name stands for each and every individual which it is a
name of, or in other words, which it denotes, it is said by logicians to be
distributed, or taken distributively. Thus, in the proposition, All men are
mortal, the subject, Man, is distributed, because mortality is affirmed of
«ach and every man. The predicate, Mortal, is not distributed, because
the only mortals who are spoken of in the proposition are those who hap-
pen to be men ; while the word may, for aught that appears, and in fact
does, comprehend within it an indefinite number of objects besides men.
In the proposition. Some men are mortal, both the predicate and the sub-
ject are undistributed. In the following, No men have wings, both the
predicate and the subject are distributed. Not only is the attribute of
having wings denied of the entire class Man, but that class is severed and
oast out from the whole of the class Winged, and not merely from some
part of that class.
This phraseology, which is of great service in stating and demonstrating
the rules of the syllogism, enables us to express very concisely the defini-
tions of a universal and a particular proposition. A universal proposition
is that of which the subject is distributed ; a particular proposition is that
of which the subject is undistributed.
There are many more distinctions among propositions than those we
have here stated, some of them of considerable importance. But, for ex-
plaining and illustrating these, more suitable opportunities will occur in the
■ sequel.
* It may, however, be considered as equivalent to a universal proposition with a different
predicate, viz. : "All wine is good qua wine," or "is good in respect of the qualities which
constitute it wine."
t Logic, i., 82.
IMPORT OF PROPOSITIONS. 73
CHAPTER V.
OF THE IMPORT OF PROPOSITIONS.
§ 1. An inquiry into the nature of propositions must have one of two
objects : to analyze the state of mind called Belief, or to analyze what is
believed. All language recognizes a difference between a doctrine or opin-
ion, and the fact of entertaining the opinion ; between assent, and what is
assented to.
Logic, according to the conception here formed of it, has no concern
with the nature of the act of judging or believing; the consideration of
that act, as a phenomenon of the mind, belongs to another science. Phi-
losophers, however, from Descartes downward, and especially from the era
of Leibnitz and Locke, have by no means observed this distinction ; and
would have treated with great disrespect any attempt to analyze the im-
port of Propositions, unless founded on an analysis of the act of Judgment..
A proposition, they would have said, is but the expression in words of a
Judgment. The thing expressed, not the mere verbal expression, is the
important matter. When the mind assents to a proposition, it judges.
Let us find out what the mind does when it judges, and we shall know
what propositions mean, and not otherwise.
Conformably to these views, almost all the writers on Logic in the last
two centuries, whether English, German, or French, have made their the-
ory of Propositions, from one end to the other, a theory of Judgments.
They considered a Proposition, or a Judgment, for they used the two
words indiscriminately, to consist in affii-ming or denying one idea of an-
other. To judge, was to put two ideas together, or to bring one idea un-
der another, or to compare two ideas, or to perceive the agreement or disa-
greement between two ideas : and the whole doctrine of Propositions, to-
gether with the theory of Reasoning (always necessarily founded on the
theory of Propositions), was stated as if Ideas, or Conceptions, or whatever
other term the writer preferred as a name for mental representations gen-
erally, constituted essentially the subject-matter and substance of those op-
erations.
It is, of course, true, that in any case of judgment, as for instance wheu
we judge that gold is yellow, a process takes place in our minds, of which
some one or other of these theories is a partially correct account. We
must have the idea of gold and the idea of yellow, and these two ideas
must be brought together in our mind. But in the first place, it is evident
that this is only a part of what takes place ; for we may put two ideas to-
gether without any act of belief; as when we merely imagine something,
such as a golden mountain ; or when we actually disbelieve : for in order
even to disbelieve that Mohammed was an apostle of God, we must put the
idea of Mohammed and that of an apostle of God together. To determine
what it is that happens in the case of assent or dissent besides putting two
ideas together, is one of the most intricate of metaphysical problems. But
whatever the solution may be, we may venture to assert that it can have
nothing whatever to do with" the import of propositions; for this reason.
-74 NAMES AND PROPOSITIONS.
that propositions (except sometimes when the mind itself is the subject
treated of) are not assertions respecting our ideas of things, but assertions
respecting the things theaiselves. In order to believe that gold is yellow,
I must, indeed, have the idea of gold, and the idea of yellow, and some-
thing having reference to those ideas must take place in my mind ; but
mv belief has not reference to the ideas, it has reference to the things.
What I believe, is a fact relating to the outward thing, gold, and to the
impression made by that outward thing upon the human organs ; not a
fact relating to my conception of gold, which would be a fact in my mental
history, not a fact of external nature. It is true, that in order to believe
this fact in external nature, another fact must take place in my mind, a
. process must be performed upon my ideas ; but so it must in every thing
«lse that I do. I can not dig the ground unless I have the idea of the
ground, and of a spade, and of all the other things I am operating upon,
and unless I put those ideas together.* But it would be a very ridiculous
•description of digging the ground to say that it is putting one idea into an-
other. Digging is an operation which is performed upon the things them-
selves, though it can not be performed unless I have in my mind the ideas
•of them. And in like manner, believing is an act which has for its subject
the facts themselves, though a previous mental conception of the facts is
an indispensable condition. When I say that fire causes heat, do I mean
that my idea of fire causes my idea of heat? No : I mean that the natural
phenomenon, fire, causes the natural phenomenon, heat. When I mean to
-assert any thing respecting the ideas, I give them their proper name, I
•call them ideas : as when I say, that a child's idea of a battle is unlike the
reality, or that the ideas entertained of the Deity have a great effect on the
characters of mankind.
The notion that what is of primary importance to the logician in a prop-
osition, is the relation between the two ideas corresponding to the subject
-and predicate (instead of the relation between the two phenomena which
they respectively express), seems to me one of the most fatal errors ever
introduced into the philosophy of Logic ; and the principal cause why the
theory of the science has made such inconsiderable progress during the last
two centuries. The treatises on Logic, and on the branches of Mental Phi-
losophy connected with Logic, which have been produced since the intru-
■sion of this cardinal error, though sometimes written by men of extraor-
■dinary abilities and attainments, almost always tacitly imply a theory that
the investigation of truth consists in contemplating and handling our ideas,
or conceptions of things, instead of the things themselves : a doctrine tan-
tamount to the assertion, that the only mode of acquiring knowledge of
nature is to study it at second hand, as represented in our own minds.
Meanwhile, inquiries into every kind of natural phenomena were incessant-
ly establishing great and fruitful truths on most important subjects, by
processes upon which these views of the nature of Judgment and Reason-
ing threw no light, and in which they afforded no assistance whatever. No
wonder that those who knew by practical experience how truths are ar-
rived at, should deem a science futile, which consisted chiefly of such spec-
* Dr. Whewell {Philosophy of Discovery, p. 242) questions this statement, and asks, "Are
we to say that a mole can not dig the ground, except he has an idea of the ground, and of
the snout and paws with which he digs it?" I do not know what passes in a mole's mind,
■nor what amount of mental apprehension may or may not accompany his instinctive actions.
But a human being does not use a spade by instinct ; and he certainly could not use it unless
he had knowledge of a spade, and of the earth which he uses it upon.
IMPORT OF PEOPOSITIONS. 75
Illations. What has been done for the advancement of Logic since these
doctrines came into vogue, has been done not by professed logicians, but
by discoverers in the other sciences; in whose methods of investigation
many principles of logic, not previously thought of, have successively come
forth into light, but who have generally committed the error of supposing
that nothing whatever was known of the art of philosophizing by the old
logicians, because their modern interpreters have written to so little pur-
pose respecting it.
We have to inquire, then, on the present occasion, not into Judgment,
Tjut judgments ; not into the act of believing, but into the thing believed.
What is the immediate object of belief in a Proposition ? What is the
matter of fact signified by it? What is it to which, when I assert the
proposition, I give my assent, and call upon others to give theirs ? What is
that which is expressed by the form of discourse called a Proposition, and
the conformity of which to fact constitutes the truth of the proposition ?
§ 2. One of the clearest and most consecutive thinkers whom this coun-
try or the world has produced, I mean Hobbes, has given the following an-
swer to this question. In every proposition (says he) what is signified is,
the belief of the speaker that the predicate is a name of the same thing of
which the subject is a name ; and if it really is so, the proposition is true.
Thus the proposition. All men are living beings (he would say) is true,
because living being is a name of every thing of which man is a name.
All men are six feet high, is not true, because six feet high is not a name
of every thing (though it is of some things) of which man is a name.
What is stated in this theory as the definition of a true proposition, must
be allowed to be a property which all true propositions possess. The sub-
ject and predicate being both of them names of things, if they were names
of quite different things the one name could not, consistently with its sig-
nification, be predicated of the other. If it be true that some men are cop-
per-colored, it must be true — and the proposition does really assert — that
among the individuMs denoted by the name man, there are some who are
also among those denoted by the name copper-colored. If it be true that
all oxen ruminate, it must be true that all the individuals denoted by the
name ox are also among those denoted by the name ruminating ; and who-
ever asserts that all oxen ruminate, undoubtedly does assert that this rela-
tion subsists between the two names.
The assertion, therefore, which, according to Hobbes, is the only one
made in any proposition, really is made in every proposition : and his anal-
ysis has consequently one of the requisites for being the true one. We
may go a step further ; it is the only analysis that is rigorously true of all
propositions without exception. What he gives as the meaning of propo-
sitions, is part of the meaning of all propositions, and the whole meaning
of some. This, however, only shows what an extremely minute fragment
of meaning it is quite possible to include within the logical formula of a
proposition. It does not show that no proposition means more. To war-
rant us in putting together two words with a copula between them, it is
really enough that the thing or things denoted by one of the names should
be capable, without violation of usage, of being called by the other name also.
If, then, this be all the meaning necessarily implied in the form of discourse
■called a Proposition, why do I object to it as the scientific definition of what
a proposition means ? Because, though the mere collocation which makes
the proposition a proposition, conveys no more than this scanty amount of
76 NAMES AND PROPOSITIONS.
meaning, that same collocation combined with other circumstances, that
form combined with other matter, does convey more, and the proposition,
in those other circumstances does assert more, than merely that relation
between the two names.
The only propositions of which Hobbes's principle is a suiScient account,,
are that limited and unimportant class in which both the predicate and
the subject are proper names. For, as has already been remarked, proper
names have strictly no meaning; they are mere marks for individual ob-
jects : and when a proper name is predicated of another proper name, all
the signification conveyed is, that both the names are marks for the same
object. But this is precisely what Hobbes produces as a theory of predi-
cation in general. His doctrine is" a full explanation of such predications
as these : Hyde was Clarendon, or, TuUy is Cicero. It exhausts the mean-
ing of those propositions. But it is a sadly inadequate theory of any oth-
ers. That it should ever have been thought of as such, can be accounted
for only by the fact, that Hobbes, in common with the other Nominalists,,
bestowed little or no attention upon the connotation of words ; and sought
for their meaning exclusively in what they denote: as if all names had been
(what none but proper names reall)' are) marks put upon individuals ; and
as if there were no difference between a proper and a general name, except
that the first denotes only one individual, and the last a greater number.
It has been seen, however, that the meaning of all names, except proper
names and that portion of the class of abstract names which are not conno-
tative, resides in the connotation. When, therefore, we are analyzing the-
meaning of any proposition in which the predicate and the subject, or
either of them, are oonnotative names, it is to the connotation of those
terms that we must exclusively look, and not to what they denote, or in the-
language of Hobbes (language so far correct) are names of.
In asserting that the truth of a proposition depends on the conformity of
import between its terms, as, for instance, that the proposition, Socrates is
wise, is a true proposition, because Socrates and wise are names applicable-
to, or, as he expresses it, names of, the same person ; it is very remarkable
that so powerful a thinker should not have asked himself the question, But
how came they to be names of the same person ? Surely not because snub
was the intention of those who invented the words. When mankind fixed
the meaning of the word wise, they were not thinking of Socrates, nor,
when his parents gave him the name of Soci-ates, were they thinking of
wisdom. The names happen to fit the same person because of a certain
fact, which fact was not known, nor in being, when the names were in-
vented. If we want to know what the fact is, we shall find the clue to it
in the connotation of the names.
A bird or a stone, a man, or a wise man, means simply, an object having
such and such attributes. The real meaning of the word man, is those at-
tributes, and not Smith, Brown, and the remainder of the individuals. The
word mortal, in like manner connotes a certain attribute or attributes ; and
when we say. All men are mortal, the meaning of the proposition is, that all'
beings which possess the one set of attributes, possess also the other. If,
in our experience, the attributes connoted by man are always accompanied
by the attribute connoted by mortal, it will follow as a consequence, that
the class man will be wholly included in the class mortal, and that.morto?
will be a name of all things of which maw is a name : but why ? Those
objects are brought under the name, by possessing the attributes connoted
by it : but their possession of the attributes is the real condition on which
IMPORT OF PROPOSITIONS. 77
the truth of the proposition depends ; not their being called by. the name.
Oonnotative names do not precede, but follow, the attributes which they
-connote. If one attribute happens to be always found in conjunction with
another attribute, the concrete names which answer to those attributes will
■of course be predicable of the same subjects, and may be said, in Hobbes's
language (in the propriety of which on this occasion I fully concur), to be
two names for the same things. But the possibility of a concurrent appli-
■cation of the two names, is a mere consequence of the conjunction between
the two attributes, and was, in most cases, never thought of when the
names were introduced and their signification fixed. That the diamond is
■combustible, was a proposition certainly not dreamed of when the words
Diamond and Combustible first received their meaning; and could not
have been discovered by the most ingenious and refined analysis of the sig-
rification of those words. It was found out by a very diffei-ent process,
namely, by exerting the senses, and learning from them, that the attribute
■of combustibility existed in the diamonds upon which the experiment was
tried ; the number or character of the experiments being such, that what
was true of those individuals might be concluded to be true of all sub-
stances " called by the name," that is, of all substances possessing the at-
tributes which the name connotes. The assertion, therefore, when ana-
lyzed, is, that wherever we find certain attributes, there will be found a cer-
tain other attribute : which is not a question of the signification of names,
hut of laws of nature ; the order existing among phenomena.
§ 3. Although Hobbes's theory of Predication has not, in the terms in
which he stated it, met with a very favorable reception from subsequent
thinkers, a theory virtually identical with it, and not by any means so per-
spicuously expressed, may almost be said to have taken the rank of an es-
tablished opinion. The most generally received notion of Predication de-
cidedly is that it consists in referring something to a class, i. e., either pla-
cing an individual under a class, or placing one class under another class.
Thus, the proposition, Man is mortal, asserts, according to this view of it,
that the class man is included in the class mortal. "Plato is a philoso-
pher," asserts that the incfividual Plato is one of those who compose the
class philosopher. If the proposition is negative, then instead of placing
something in a class, it is said to exclude something from a class. Thus,
if the following be the proposition, The elephant is not carnivorous ; what
is asserted (according to this theory) is, that the elephant is excluded from
the class carnivorous, or is not numbered among the things comprising that
class. There is no real difference, except in language, between this theory
of Predication and the theory of Hobbes. For a class is absolutely noth-
ing but an indefinite number of individuals denoted by a general name.
The name given to them in common, is what makes them a class. To re-
fer any thing to a class, therefore, is to look upon it as one of the things
which are to be called by that common name. To exclude it from a class,
is to say that the common name is not applicable to it.
How widely these views of predication have prevailed, is evident from
this, that they are the basis of the celebrated dictum de omni et nulla.
When the syllogism is resolved, by all who treat of it, into an inference
that what is true of a class is true of all things whatever that belong to the
class ; and when this is laid down by almost all professed logicians as the
ultimate principle to which all reasoning owes its validity ; it is clear that
in the general estimation of logicians, the propositions of which reasonings
78 NAMES AND PROPOSITIONS.
are composed can be the expression of nothing but the process of dividing-
things into classes, and referring every thing to its proper class.
This theory appears to me a signal example of a logical ei:ror very often
committed in logic, that of voTepov irporipov, or explaining a thing by some-
thing which presupposes it. When I say that snow is white, I may and
ought to be thinking of snow as a class, because I am asserting a proposi-
tion as true of all snow : but I am certainly not thinking of white objects,
as a class ; I am thinking of no white object whatever except snow, but
only of that, and of the sensation of white which it gives me. When, in-
deed, I have judged, or assented to the propositions, that snow is white,
and that several other things are also white, I gradually begin to think of
white objects as a class, including snow and those other things. But this
is a conception which followed, not preceded, those judgments, and there-
fore can not be given as an explanation of them. Instead of explaining the
effect by the cause, this doctrine explains the cause by the effect, and is, I
conceive, founded on a latent misconception of the nature of classification.
There is a sort of language very generally prevalent in these discussions,
which seems to suppose that classification is an arrangement and grouping
of definite and known individuals : that when names were imposed, man-
kind took into consideration all the individual objects in the universe, dis-
tributed them into parcels or lists, and gave to the objects of each list a
common name, repeating this operation toties quoties until they had invent-
ed all the general names of which language consists ; which having been
once done, if a question subsequently arises whether, a certain general
name can be truly predicated of a certain particular object, we have only
(as it were) to read the roll of the objects upon which that name was con-
ferred, and see whether the object about which the question arises is to be
found among them. The framers of language (it would seem to be sup-
posed) have predetermined ajl the objects that are to compose each class,
and we have only to refer to the record of an antecedent decision.
So absurd a doctrine will be owned by nobody when thus nakedly stated;
but if the commonly received explanations of classification and naming do
not imply this theory, it requires to be shown how they admit of being rec-
onciled with any other.
General names are not marks put upon definite objects ; classes are not
made by drawing a line round a given number of assignable individuals.
The objects which compose any given class are perpetually fluctuating.
We may frame a class without knowing the individuals, or even any of the
individuals, of which it may be composed ; we may do so while believing
that no such individuals exist. If by the meaning of a general name are
to be understood the things which it is the name of, no general name, ex-
cept by accident, has a fixed meaning at all, or ever long retains the same
meaning. The only mode in which any general name has a definite mean-
ing, is by being a name of an indefinite variety of things ; namely, of all
things, known or unknown, past, present, or future, which possess certain
definite attributes. When, by studying not the meaning of words, but the
phenomena of nature, we discover that these attributes are possessed by
some object not previously known to possess them (as when chemists
found that the diamond was combustible), we include this new object in
the class ; but it did not already belong to the class. We place the indi-
vidual in the class because the proposition is true; the proposition is not
true because the object is placed in the class.*
* Professor Bain remarks, in qualification of the statement in the text (Logic, i., 50), that
IMPORT OF PROPOSITIONS. 79
It will appear hereafter, in treating of reasoning, bow much the theory
of that intellectual process has been vitiated by the influence of these erro-
neous notions, and by the habit which they exemplify of assimilating all
the operations of the human understanding which have truth for their ob-
ject, to processes of mere classification and naming. Unfortunately, the
minds which have been entangled in this net are precisely those which have
escaped the other cardinal error commented upon in the beginning of the
present chaptei-. Since the revolution which dislodged Aristotle from the
schools, logicians niay almost be divided into those who have looked upon
reasoning as essentially an affair of Ideas, and those who have looked upon
it as essentially an affair of Names.
Although, however, Hobbes's theory of Predication, according to the
well-known remark of Leibnitz, and the avowal of Hobbes himself,* renders
truth and falsity completely arbitrary, with no standard but the will of
men, it must not be concluded that either Hobbes, or any of the other
thinkers who have in the main agreed with him, did in fact consider the
distinction between truth and error as less real, or attached less importance
to it, than other people. To suppose that they did so would argue total
.nnacquaintance with their other speculations. But this shows how little
hold their doctrine possessed over their own minds. No person, at bot-
tom, ever imagined that there was nothing more in truth than propriety of
expression ; than using language in conformity to a previous convention.
When the inquiry was brought down from generals to a particular case, it
has always been acknowledged that there is a distinction between verbal
and real questions ; that some false propositions are uttered from ignorance
of the meaning of words, but that in others the source of the error is a
misapprehension of things ; that a person who has not the use of language
at all may form propositions mentally, and that they may be untrue — that
is, he may believe as matters of fact what are not really so. This last ad-
mission can not be made in stronger terms than it is by Hobbes himself,')
though he will not allow such erroneous belief to be called falsity, but only
error. And he has himself laid down, in other places, doctrines in which
the true theory of predication is by implication contained. He distinctly
the word Class has two meanings; "the class definite, and the class indefinite. The class
definite is an enumeration of actual individuals, as the Peers of the Realm, the oceans of the
globe, the known planets. . . . The class indefinite is unenumerated. Such classes are
stars, planets, gold-bearing rocks, men, poets, virtuous. ... In this last acceptation of the
word, class name and general name are identical. The class name denotes an indefinite num-
ber of individuals, and connotes the points of community or likeness."
The theory controverted in the text, tacitly supposes all classes to be definite. I have as-
sumed them to be indefinite ; because, for the purposes of Logic, definite classes, as such, are
almost useless ; though often serviceable as means of abridged expression. (Vide infra, book
iii., chap, ii.)
* "From hence also this may be deduced, that the first truths were arbitrarily made by
those that first of all imposed names upon things, or received them from the imposition of oth-
ers. For it is true (for example) that man is a living creature, but it is for this reason, that it
pleased men to impose both these names on the same thing." — Computation or Logic, chap,
iii., sect. 8.
t " Men are subject to err not only in afiSrming and denying, but also in perception, and in
silent cogitation. . . . Tacit errors, or the errors of sense and cof^tation, are made by pass-
ing fiom one imagination to the imagination of another diflerent thing ; or by feigning that to
be past, or future, which never was, nor ever shall be ; as when by seeing the image of the
Bun in water, we imagine the sun itself to be there ; or by seeing swords, that there has been,
or shall be,. fighting, because it uses to be so for the most part; or when from promises we
■ feign the mind of the promiser to be such and such ; or, lastly, when from any sign we vainly
imagine something to be signified which is not. And errors of this sort are common to all
things that have sense." — Computation or Logic, chap, v., sect. 1.
so NAMES AND PROPOSITIONS.
says that general names are given to things on account of their attributes,
and that abstract names are the names of those attributes. " Abstract is
that which in any subject denotes the cause of the concrete name
And these causes of names are the same with the causes of our conceptions,
namely, some power of action, or affection, of the thing conceived, which
some call the manner by which any thing works upon our senses, but by
most men they are called accidents."* It is strange that having gone so
far, he should not have gone one step further, and seen that what he calls
the cause of the concrete name, is in reality the meaning of it; and that
when we predicate of any subject a name which is given because of an at-
tribute (or, as he calls it, an accident), our object is not to affirm the name,
but, by means of the name, to affirm the attribute.
§ 4. Let the predicate be, as we have said, a connotative term ; and to
take the simplest case first, let the subject be a proper name: "The sum-
mit of Chimborazo is white." The word white connotes an attribute which
is possessed by the individual object designated by the words " summit of
Chimborazo ;" which attribute consists in the physical fact, of its exciting
in human beings the sensation which we call a sensation of white. It will*
be admitted that, by asserting the proposition, we wish to communicate in-
formation of that physical fact, and are not thinking of the names, except
as the necessary means of making that communication. The meaning of
the proposition, therefore, is, that the individual thing denoted by the sub-
ject, has the attributes connoted by the predicate.
If we now suppose the subject also to be a connotative name, the mean-
ing expressed by the proposition has advanced a step further in complicar
tion. Let us first suppose the proposition to be universal, as well as affirm-
ative: "All men are mortal." In this case, as in the last, what the propo-
sition asserts (or ' expresses a belief of) is, of course, that the objects de-
noted by the subject (man) possess the attributes connoted by the predi-
cate (mortal). But the characteristic of this case is, that the objects are
no longer individually designated. They are pointed out only by some of
their attributes : they are the objects called men, that is, possessing the at-
tributes connoted by the name man ; and the only thing known of them
may be those attributes : indeed, as the proposition is general, and the ob-
jects denoted by the subject are therefore indefinite in number, most of
them are not known individually at all. The assertion, therefore, is not, as
before, that the attributes which the predicate connotes are possessed by
any given individual, or by any number of individuals previously known as
John, Thomas, etc., but that those attributes are possessed by each and ev-
ery individual possessing certain other attributes ; that whatever has the
attributes connoted by the subject, has also those connoted by the predi-
cate ; that the latter set of attributes constantly accompany the former set.
Whatever has the attributes of man has the attribute of mortality ; mortal-
ity constantly accompanies the attributes of man.f
* Chap. iii. , sect. 3.
t To the preceding stattfment it has been objected, that " we naturally construe the subject
of a proposition in its extension, and the predicate (which therefore may be an adjective) in
its intension (connotation) : and that consequently co-existence of attributes does not, any
more than the opposite theory of equation of groups, correspond with the living processes of
thought and language." I acknowledge the distinction here drawn, which, indeed, I had my-
self laid down and exemplified a few pages back (p. 77). But though it is true that we nat-
urally "construe the subject of a proposition in its extension," this extension, or in other
words, the extent of the class denoted by the name, is not apprehended or indicated directly.
IMPORT OF PROPOSITIONS. 81
If it be remembered that every attribute is grounded on some fact or
phenomenon, either of outward sense or of inward consciousness, and that
to possess an attribute is another phrase for being the cause of, or forming
part of, the fact or phenomenon upon which the attribute is grounded ; we
may add one more step to complete the analysis. The proposition which
asserts that one attribute always accompanies another attribute, really as-
serts thereby no other thing than this, that one phenomenon always accom-
panies another phenomenon ; insomuch that where we find the latter, we
have assurance of the existence of the former. Thus, in the proposition.
All men are mortal, the word man connotes the attributes which we ascribe
to a certain kind of living creatures, on the ground of certain phenomena
which they exhibit, and which are partly physical phenomena, namely the
impressions made on our senses by their bodily form and structure, and
partly mental phenomena, namely the sentient and intellectual life which
they have of their own. All this is understood when we utter the word
man, by any one to whom the meaning of the word is known. Now, when
we say, Man is mortal, we mean that wherever these various physical and
mental phenomena are all found, there we have assurance that the other
physical and mental phenomenon, called death, will not fail to take place.
The proposition does not affirm when; for the connotation of the word
mortal goes no further than to the occurrence of the phenomenon at some
time or other, leaving the particular time undecided.
§ 5. We have already proceeded far enough, not only to demonstrate the
error of Hobbes, but to ascertain the real import of by far the most numer-
ous class of propositions. The object of belief in a proposition, when it
asserts any thing more than the meaning of words, is generally, as in the
cases which we have examined, either the co-existence or the sequence of
two phenomena. At the very commencement of our inquiry, we found that
every act of belief implied two Things : we have now ascertained what, in
the most frequent case, these two things are, namely, two Phenomena; in
other words, two states of consciousness ; and what it is which the propo-
sition affirms (or denies) to subsist between them, namely, either succession
or co-existence. And this case includes innumerable instances which no
one, previous to reflection, would think of referring to it. Take the follow-
ing example : A generous person is worthy of honor. Who would expect
to recognize here a case of co-existence between phenomena? But so it is.
The attribute which causes a person to be termed generous, is ascribed to
him on the ground of states of his mind, and particulars of his conduct :
both are phenomena : the former are facts of internal consciousness ; the
latter, so far as distinct from the former, are physical facts, or perceptions
of the senses. Worthy of honor admits of a similar analysis. Honor, as
here used, means a state of approving and admiring emotion, followed on
occasion by corresponding outward acts. " Worthy of honor" connotes all
this, together with our approval of the act of showing honor. All these
are phenomena; states of internal consciousness, accompanied or followed
by physical facts. When we say, A generous person is worthy of honor.
It is both apprehended and indicated solely through the attributes. In the "living processes
of thought and language" the extension, though in this case really thought of (which in the
case of the predicate it is not), is thought of only through the medium of what my acute and
courteous critic terms the "intension."
For further illustrations of this subject, see Examination of Sir William Hamilton's Phi-
losophy, chap. xxii.
82 NAMES AND PROPOSITIONS.
we affirm co-existence between the two complicated phenomena connote(J
by the two terms respectively. We affirm, that wherever and whenever
the inward feelings and outward facts implied in the word generosity-
have place, then and there the existence and manifestation of an inward,
feeling, honor, would be followed in our minds by another inward feeling,,
approval.
After the analysis, in a former chapter, of the import of names, many
examples are not needed to illustrate the import of propositions. Whca
there is any obscurity, or difficulty, it does not lie in the meaning of the
proposition, but in the meaning of the names which compose it; in the
extremely complicated connotation of many words; the immense multitude-
and prolonged series of facts which often constitute the phenomenon con-
noted by a name. But where it is seen what the phenomenon is, there is
seldom any difficulty in seeing that the assertion conveyed by the proposi-.
tion is, the co-existence of one such phenomenon with anothei- ; or the suc-
cession of one such phenomenon to another: so that where the one is found,
we may calculate on finding the other, though perhaps not conversely.
This, however, though the most common, is not the only meaning whiohi
propositions are ever intended to convey. In the first place, sequences and
co-existences are not only asserted respecting Phenomena ; we make propo-
sitions also respecting those hidden causes of phenomena, which are named
substances and attributes. A substance, however, being to us nothing but
either that which causes, or that which is conscious of, phenomena ; and the
same being true, mutatis mutandis, of attributes; no assertion can be made,
at least with a meaning, concerning these unknown and unknowable en-
tities, except in virtue of the Phenomena by which alone they manifest
themselves to our faculties. When we say Socrates was contemporary with
the Peloponnesian war, the foundation of this assertion, as of all assertion*
concerning substances, is an assertion concerning the phenomena which
they exhibit — namely, that the series of facts by which Socrates manifested
himself to mankind, and the series of mental states which constituted hi*
sentient existence, went on simultaneously with the series of facts known
by the name of the Peloponnesian war. Still, the proposition as commonly
understood does not assert that alone; it asserts that the Thing in itself,
the noumenon Socrates, was existing, and doing or experiencing those vari-
ous facts during the same time. Co-existence and sequence, therefore, may
be affirmed or denied not only between phenomena, but between nouraena,
or between a noumenon and phenomena. And both of noumena and of
phenomena we may affirm simple existence. But what is a noumenon?
An unknown cause. In affirming, therefore, the existence of a noumenon,
we affirm causation. Here, therefore, are two additional kinds of fact,
capable of being asserted in a proposition. Besides the propositions which
assert Seijuence or Co-existence, there are some which assert simple Exist-
ence;* and others assert Causation, which, subject to the explanation*
* Professor Bain, ip his Logic (i. , 256), excludes Existence from the list, considering it as a
mere name. All propositions, he says, which predicate mere existence "are more or less ab-
breviated, or elliptical : when fully expressed they fall under either co-existence or succession.
■When we say there exists a conspiracy for a particular purpose, we mean that at the present
time a body of men have formed themselves into a society for a particular object ; which is a
complex affirmation, resolvable into propositions of co-existence and succession (as causation).
The assertion that the dodo does not exist, points to the fact that this animal, once known in
a certain place, has disappeared or become extinct; is no longer associated with the locality:
all which may be better stated without the use of the verb ' exist.' There is a debated ques-
tion—Does an ether exist? but the concrete form would be this— 'Are heat and light auii
IMPORT OF PEOPOSITIONS. 83
which will follow in the Third Book, must be considered provisionally as a
distinct and peculiar kind of assertion.
§ 6. To these four kinds of matter-of-fact or assertion, must be added
a fifth, Resemblance. This was a species of attribute which we found it
impossible to analyze ; for which no fundamentum, distinct from the ob-
jects themselves, could be assigned. Besides propositions which assert a
sequence or co-existence between two phenomena, there are therefore also
propositions which assert resemblance between them ; as. This color is like
that color; The heat of to-day is equal to the heat of yesterday. It i«
true that snch an assertion might with some plausibility be brought within
the description of an affirmation of sequence, by considering it as an asser-
tion that the simultaneous contemplation of the two colors is followed by
a specific feehng termed the feeling of resemblance. But there would be
nothing gained by incumbering ourselves, especially in this place, with a
generalization which may be looked upon as strained. Logic does not un-
dertake to analyze mental facts into their ultimate elements. Resemblance
between two phenomena is more intelligible in itself than any explanation
could make it, and under any classification must remain specifically distinct
from the ordinary cases of sequence and co-existence.
It is sometimes said, that all propositions whatever, of which the pred-
icate is a general name, do, in point of fact, affirm or deny resemblance. All
snch propositions afiirm that a thing belongs to a class ; but things being
classed together according to their resemblance, every thing is of course
classed with the things which it is supposed to resemble most ; and thence,
it may be said, when we affirm that Gold is a metal, or that Socrates is a
man, the affirmation intended is, that gold resembles other metals, and Soc-
other radiant influences propagated by an ethereal medium diffused in space ;' which is a prop-
osition of cansation. In like manner the question of the Existence of a Deity can not be dis-
cussed in that form. It is properly a question as to the First Cause of the Universe, and as to
the continued exertion of that Cause in providential superintendence." (i., 407.)
Mr. Bain thinks it "fictitious and unmeaning language" to carry up the classification of
Nature to one summum germs. Being, or that which Exists ; since nothing can be perceived or
apprehended but by way of contrast with something else (of which important truth, under the
name of Law of Relativity, he has been in our time the principal expounder and champion),
and we have no other class to oppose to Being, or fact to contrast with Existence.
I accept fully Mr. Bain's Law of Relativity, but I do not understand by it that to enable us
to apprehend or be conscious of any fact, it is necessary that we should contrast it with some
other positive fact. The antithesis necessary to consciousness need not, I conceive, be an an-
tithesis between two positives ; it may be between one positive and its negative. Hobbes was
undoubtedly right when he said that a single sensation indefinitely prolonged would cease to be
felt at all ; but simple intermission, without other change, would restore it to consciousness.
In order to be conscious of heat, it is not necessary that we should pass to it from cold ; it
sufiices that we should pass to it from a state of no sensation, or from a sensation of some other
kind. The relative opposite of Being, considered as a summum genus, is Nonentity, or
Nothing ; and we have, now and then, occasion to consider and discuss things merely in con-
trast with Nonentity.
I grant that the decision of questions of Existence usually if not always depends on a pre-
vious question of either Causation or Co-existence. But Existence is nevertheless a diflferent
thing from Causation or Co-existence, and can be predicated apart from them. The meaning
of the abstract name Existence, and the connotation of the concrete name Being, consist, like
the meaning of all other names, in sensations or states of consciousness : their peculiarity is
that to exist, is to excite, or be capable of exciting, any sensations or states of consciousness :
no matter what, but it is indispensable that there should be some. It was from overlooking
this that Hegel, finding that Being is an abstraction reached by thinking away all particular
attributes, anived at the self-contradictory proposition on which he founded all his philosophy,
that Being is the same as Nothing. It is really the name of Something, taken in the most
comprehensive sense of the word.
84 NAMES AND PROPOSITIONS.
rates other men, more nearly than they resemble the objects contained in
any other of the classes co-ordinate with these.
There is some slight degree of foundation for this remark, but no more
than a slight degree. The arrangement of things into classes, such as the
class metal, or the class man, is grounded indeed on a resemblance among
the things which are placed in the same class, but not on a mere general
resemblance : the resemblance it is grounded on consists in the possession
by all those things, of certain common peculiarities ; and those peculiarities
it is which the terms connote, and which the propositions consequently as-
sert ; not the resemblance. For though when I say. Gold is a metal, I say
by implication that if there be any other metals it must resemble them, yet
if there were no other metals I might still assert the proposition with the
same meaning as at present, namely, that gold has the various properties
implied in the Word metal ; just as it might be said. Christians are men,
even if there were no men who were not Christians. Propositions, there-
fore, in which objects are referred to a class because they possess the attri-
butes constituting the class, are so far from asserting nothing but resem-
blance, that they do not, properly speaking, assert resemblance at all.
But we remarked some time ago (and the reasons of the remark will be
more fully entered into in a subsequent Book*) that there is sometimes a
convenience in extending the boundaries of a class so as to include things
which possess in a very inferior degree, if in any, some of the characteris-
tic properties of the class — provided they resemble that class more than
any other, insomuch that the general propositions which are true of the
class, will be nearer to being true of those things than any other equally
general propositions. For instance, there are substances called metals
which have very few of the properties by which metals are commonly rec-
ognized ; and almost every great family of plants or animals has a few anom-
alous genera or species on its borders, which are admitted into it by a sort
of courtesy, and concerning which it has been matter of discussion to what
family they properly belonged. Now when the class-name is predicated of
any object of this desci'iption, we do, by so predicating it, affirm resem-
blance and nothing more. And in order to be scrupulously correct it ought
to be said, that in every case in which we predicate a general name, we af-
firm, not absolutely that the object possesses the properties designated by
the name, but that it either possesses those properties, or if it does not, at
any rate resembles the things which do so, more than it resembles any oth-
er things. In most cases, however, it is unnecessary to suppose any sueh
alternative, the latter of the two grounds being very seldom that on which
the assertion is made : and when it is, there is generally some slight differ-
ence in the form of the expression, as. This species (or genus) is consider-
ed, or m,ay be ranked, as belonging to such and such a family: we should
hardly say positively that it does belong to it, unless it possessed unequiv-
ocally the properties of which the class-name is scientifically significant.
There is still another exceptional case, in which, though the predicate is
the name of a class,, yet in predicating it we affirm nothing but resemblance,
the class being founded not on resemblance in any given particular, but on
general unanalyzable resemblance. The classes in question are those into
which our simple sensations, or other simple feelings, are divided. Sensa-
tions of white, for instance, are classed together, not because we can take
them to pieces, and say they are alike in this, and not alike in that, but be-
* Book iv., ch»p. vil.
IMPORT OF PROPOSITIONS. 85
cause we feel them to be alike altogether, though in different degrees.
When, therefore, I say, The color I saw yesterday was a white color, or.
The sensation I feel is one of tightness, in both cases the attribute I affirm
of the color or of the other sensation is mere resemblance — simple likeness
to sensations which I have had before, and which have had those names be-
stowed upon them. The names of feelings, like other concrete general
names, are connotative; but they connote a mere i-esemblance. When
predicated of any individual feeling, the information they convey is that of
its likeness to the other feelings which we have been accustomed to call by
the same name. Thus much may suffice in illustration of the kind of prop-
ositions in which the matter-of-fact asserted (or denied) is simple Resem-
blance.
Existence, Co-existence, Sequence, Causation, Resemblance : one or other
of these is asserted (or denied) in every proposition which is not merely
verbal. This five-fold division is an exhaustive classification of matters-of-
fact ; of all things that can be believed, or tendered for belief ; of all ques-
tions that can be propounded, and all answers that can be returned to them.
Professor Bain* distinguishes two kinds of Propositions of Co-existence.
"In the one kind, account is taken of Place; they may be described as
propositions of Order in Place." In the other kind, the co-existence which
is predicated is termed by Mr. Bain Co-inherence of Attributes. " This is a
distinct variety of Propositions of Co-existence. Instead of an arrangement
in pFace with numerical intervals, we have the concurrence of two or more
attributes or powers in the same part or locality. A mass of gold contains,
in every atom, the concurring attributes that mark the substance — weight,
hardness, color, lustre, incorrosibility, etc. An animal, besides having parts
situated in place, has co-inhering functions in the same parts, exerted by
the very same masses and molecules of its substance. . . . The Mind,
which affords no Propositions of Order in Place, has co-inhering functions.
We affirm mind to contain Feeling, Will, and Thought, not in local separa^
tion, but in commingling exercise. The concurring properties of minerals,
of plants, and of the bodily and the mental structure of animals, are united
in affirmations of co-inherence."
The distinction is real and important. But, as has been seen, an Attri-
bute, when it is any thing but a simple unanalyzable Resemblance between
the subject and some other things, consists in causing impressigns of some
sort on consciousness. Consequently, the co-inherence of two attributes
is but the co-existence of the two states of consciousness implied in their
meaning : with the difference, however, that this co-existence is sometimes
potential only, the attribute being considered as in existence, though the
fact on which it is grounded may not be actually, but only potentially pres-
ent. Snow, for instance, is, with great convenience, said to be white even
in a state of total darkness, because, though we are not now conscious of
the color, we shall be conscious of it as soon as morning breaks. Co-in-
herence of attributes is therefore still a case, though a complex one, of
co-existence of states of consciousness ; a totally different thing, however,
from Order in Place. Being a part of simultaneity, it belongs not to Place
but to Time.
We may therefore (and we shall sometimes find it a convenience) instead
of Co-existence and Sequence, say, for greater particularity. Order in Place
and Order in Time : Order in Place being a specific mode of co-existence,
* Logic, i., 103-105.
86 NAMES AND PROPOSITIONS.
not necessary to be more particularly analyzed here ; while th3 mere fact of
co-existence, whether between actual sensations, or between the potentiali-
ties of causing them, known by the name of attributes, may be classed, to%
gether with Sequence, under the head of Order in Time.
§ 7. In the foregoing inquiry into the import of propositions, we have
thought it necessary to analyze directly those alone, in which the terms of
the proposition (or the predicate at least) are concrete terms. But, in do-
ing so, we have indirectly analyzed those in which the terras are abstract,
The distinction between an abstract term and its corresponding concrete,
does not turn upon any difference in what they are appointed to signify;
for the real signification of a concrete general name is, as we have so often
said, its connotation ; and what the concrete term connotes, forms the en-
tire meaning of the abstract name. Since there is nothing in the import
of an abstract name which is not in the import of the corresponding con-
crete, it is natural to suppose that neither can there be any thing in the im-
port of a proposition of which the terms are abstract, but what there is in
some proposition which can be framed of concrete terms.
And this presumption a closer examination will confirm. An abstract
name is the name of an attribute, or combination of attributes. The cor-
responding concrete is a name given to things, because of, and in order to
express, their possessing that attribute, or that combination of attributes.
When, therefore, we predicate of any thing a concrete name, the attribute
is what we in reality predicate of it. But it has now been shown that in
all propositions of which the predicate is a concrete name, what is really
predicated is one of five things : Existence, Co-existence, Causation, Se-
quence, or Resemblance. An attribute, therefore, is necessarily either an
existence, a co-existence, a causation, a sequence, or a resemblance. When
a proposition consists of a subject and predicate which are abstract terms,
it consists of terms which must necessarily signify one or other of these
things. When we predicate of any thing an abstract name, we afiirm
of the thing that it is one or other of these five things ; that it is a case of
Existence, or of Co-existence, or of Causation, or of Sequence, or of Ke-
semblance.
It is impossible to imagine any proposition expressed in abstract terras,
which can not be transformed into a precisely equivalent proposition in
which the terms are concrete ; namely, either the concrete names which
connote the attributes themselves, or the names of the fundamenta of those
attributes; the facts or phenomena on which they. are grounded. To il-
lustrate the latter case, let us take this proposition, of which the subject
only is an abstract name, " Thoughtlessness is dangerous." Thoughtless-
ness is an attribute, grounded on the facts which we call thoughtless ac-
tions ; and the proposition is equivalent to this. Thoughtless actions are
dangerous. In the next example the predicate as well as the subject are
abstract names : " Whiteness is a color ;" or " The color of snow is a white-
ness." These attributes being grounded on sensations, the equivalent prop-
ositions in the concrete would be, The sensation of white is one of the sen-
sations called those of color— The sensation of sight, caused by looking at
snow, is one of the sensations called sensations of white. In these proposi-
tions, as we have before seen, the matter-of-fact asserted is a Resemblance.
In the following examples, the concrete terms are those which directly cor-
respond to the abstract names ; connoting the attribute which thes'e de-
note. " Prudence is a virtue :" this may be rendered, « All prudent per-
IMPORT OF PROPOSITIONS. 8T
--sons, in so far as prudent, are virtuous :" " Courage is deserving of hon-
or ;" thus," All courageous persons are deserving of honor in so far as they
are courageous:" which is equivalent to this — "All courageous persons
deserve an addition to the honor, or a diminution of the disgrace, which
would attach to them on other grounds."
In order to throw still further light upon the import of propositions of
which the terms are abstract, we will subject one of the examples given
above to a minuter analysis. The proposition we shall select is the follow-
ing : " Prudence is a virtue." Let us substitute for the word virtue an
equivalent but more definite expression, such as " a mental quality beneficial
to society," or " a mental quality pleasing to God," or whatever else we
adopt as the definition of virtue. What the proposition asserts is a se-
quence, accompanied with causation; namely, that benefit to society, or
that the approval of God, is consequent on, and caused by, prudence. Here
is a sequence ; but between what ? We understand the consequent of the
-sequence, but we have yet to analyze the antecedent. Prudence is an at-
tribute ; and, in connection with it, two things besides itself are to be con-
sidered ; prudent persons, who are the subjects of the attribute, and pru-
dential conduct, which may be called the foundation of it. Now is either
of these the antecedent? and, first, is it meant, that the approval of God,
•or benefit to society, is attendant upon all prudent persons ? No ; except
in so far as they are prudent; for prudent persons who are scoundrels can
seldom, on the whole, be beneficial to society, nor can they be acceptable to
a good being. Is it upon prudential conduct, then, that divine approbation
.and benefit to mankind are supposed to be invariably consequent ? Neither
is this the assertion meant, when it is said that prudence is a virtue ; ex-
cept with the same reservation as before, and for the same reason, namely,
that prudential conduct, although in so far as it is prudential it is benefi-
•cial to society, may yet, by reason of some other of its qualities, be produc-
tive of an injury outweighing the benefit, and deserve a displeasure exceed-
ing the approbation which would be due to the prudence. Neither the
substance, therefore (viz., the person), nor the phenomenon (the conduct),
is an antecedent on which the other terra of the sequence is universally
consequent. But the proposition, "Prudence is a virtue," is a universal
proposition. What is it, then, upon which the proposition afiirms the ef-
fects in question to be universally consequent ? Upon that in the person,
and in the conduct, which causes them to be called prudent, and which is
equally in them when the action, though prudent, is wicked ; namely, a cor-
rect foresight of consequences, a just estimation of their importance to the
■object in view, and repression of any unreflecting impulse at variance with
the deliberate purpose. These, which are states of the person's mind, are
the real antecedent in the sequence, the real cause in the causation, asserted
by the proposition. But these are also the real ground, or foundation, of
the attribute Prudence ; since wherever these states of mind exist we may
predicate prudence, even before we know whether any conduct has fol-
lowed. And in this manner every asseition respecting an attribute, may
be transfoi'med into an assertion exactly equivalent respecting the fact or
phenomenon which is the ground of the attribute. And no case can be
-assigned, where that which is predicated of the fact or phenomenon, does
not belong to one or other of the five species formerly enumerated : it is
-either simple Existence, or it is some Sequence, Co-existence, Causation, or
Jiesemblance.
And as these five are the only things which can be affirmed, so are they
88 NAMES AND PROPOSITIONS.
the only things which can be denied. "No horses are web-footed" denies
that the attributes of a horse ever co-exist with web-feet. It is scarcely
necessary to apply the same analysis to Particular affirmations and nega-
tions. " Some birds are web-footed," affirms that, with the attributes con-
noted by bird, the phenomenon web-feet is sometimes co-existent : " Some
birds are not web-footed," asserts that there are other instances in which
this co-existence does not have place. Any further explanation of a thing
which, if the previous exposition has been assented to, is so obvious, may
here be spared.
CHAPTER VI.
OF PROPOSITIONS MERELY VERBAL.
§ 1. As a preparation for the inquiry which is the proper object of
Logic, namely, in what manner propositions are to be proved, we have
found it necessary to inquire what they contain which requires, or is sus-
ceptible of, proof; or (which is the same thing) what they assert. In the
course of this preliminary investigation into tlie import of Propositions,
we examined the opinion of the Conceptualists, that a proposition is the
expression of a relation between two ideas ; and the doctrine of the ex-
treme Nominalists, that it is the expression of an agreement or disagree-
ment between the meanings of two names. We decided that, as general
theories, both of these are erroneous ; and that, though propositions may
be made both respecting names and respecting ideas, neither the one nor
the other are the subject-matter of Propositions considered generally. We
then examined the different kinds of Propositions, and found that, with the
exception of those which are merely verbal, they assert five different kinds
of matters of fact, namely. Existence, Order in Place, Order in Time, Causa-
tion, and Resemblance; that in every proposition one of these five is either
affirmed, or denied, of some fact or phenomenon, or of some object the un-
known source of a fact or phenomenon.
In distinguishing, however, the different kinds of matters of fact asserted
in propositions, we reserved one class of propositions, which do not relate
to any matter of fact, in the proper sense of the term at all, but to the
meaning of names. Since names and their signification are entirely arbi-
trary, such propositions are not, strictly speaking, susceptible of truth or
falsity, but only of conformity or disconformity to usage or convention;
and all the proof they are capable of, is proof of usage ; proof that the
words have been employed by others in the acceptation in which the speak-
er or writer desires to use them. These propositions occupy, however, a
conspicuous place in philosophy; and their nature and characteristics are
of as much importance in logic, as those of any of the other classes of prop-
ositions previously adverted to.
If all propositions respecting the signification of words were as simple
and unimportant as those which served us for examples when examining
Hobbes's theory of predication, viz., those of which the subject and predi-
cate are proper names, and which assert only that those names have, or
that they have not, been conventionally assigned to the same individual^
there would be little to attract to such propositions the attention of phi»
losophers. But the class of merely verbal propositions embraces not only
much more than these, but much more than any propositions which at first
VERBAL AND REAL PROPOSITIONS. 89
sight present themselves as verbal; comprehending a kind of assertions
which have been regarded not only as relating to things, but as having
actually a more intimate relation with them than any other propositions
whatever. The student in philosophy will perceive that I allude to the
distinction on which so much stress was laid by the schoolmen, and which
has been retained either under the same or under other names by most
metaphysicians to the present day, viz., between what were called essential,
and what were called accidental, propositions, and between essential and
accidental properties or attributes.
§ 2. Almost all metaphysicians prior to Locke, as well as many since his
time, have made a great mystery of Essential Predication, and of predi-
cates which are said to be of the essence of the subject. The essence of a
thing, they said, was that without which the thing could neither be, nor
be conceived to be. Thus, rationality was of the essence of man, because
without rationality, man could not be conceived to exist. The different
attributes which made up the essence of the thing were called its essential
properties ; and a proposition in which any of these were predicated of it
was called an Essential Proposition, and was considered to go deeper into
the nature of the thing, and to convey more important information respect-
ing it, than any other proposition could do. All properties, not of the es-
sence of the thing, were called its accidents ; were supposed to have noth-
ing at all, or nothing comparatively, to do with its inmost nature; and the
propositions in which any of these were predicated of it were called Acci-
dental Propositions. A connection may be traced between this distinction,
which originated with the schoolmen, and the well-known dogmas of sub-
stanticB secundee or general substances, and substantial forms, doctrines
which under varieties of language pervaded alike the Aristotelian and the
Platonic schools, and of which more of the spirit has come down to mod-
ern times than might be conjectured from the disuse of the phraseology.
The false views of the nature of classification and generalization which pre-
vailed among the schoolmen, and of which these dogmas were the technical
expression, afford the only explanation which can be given of their having
misunderstood the real nature of those Essences which held so conspicuous
a place in their philosophy. They said, truly, that ma?i can not be con-
ceived without rationality. Bat though man can not, a being may be con-
ceived exactly like a man in all points except that one quality, and those
others which are the conditions or consequences of it. All, therefore, which
is really true in the assertion that man can not be conceived without ration-
ality, is only, that if he had not rationality, he would not be reputed a man.
There is no impossibility in conceiving the thing, nor, for aught we know,
in its existing : the impossibility is in the conventions of language, which
will not allow the thing, even if it exist, to be called by the name which is
reserved for ratfonal beings. Rationality, in short, is involved in the mean-
ing of the word man : is one of the attributes connoted by the name. The
essence of man, simply means the whole of the attributes connoted by the
word ; and any one of those attributes taken singly, is an essential property
of man.
But these reflections, so easy to us, would have been diiBcult to persons
who thought, as most of the later Aristotelians did, that objects were made
what they were called, that gold (for instance) was made gold, not by the
possession of certain properties to which mankind have chosen to attach
that name, but by participation in the nature of a general substance, called
90 NAMES AND PROPOSITIONS.
gold in general, which substance, together with all the properties that be-
longed to it, inhered in every individual piece of gold.* As they did not
consider these universal sabstances to be attached to all general names, but
only to some, they thought that an object borrowed only a part of its prop-
erties from a universal substance, and that the rest belonged to it individu-
ally : the former they called its essence, and the latter its accidents. The
scholastic doctrine of essences long survived the theory on which it rested,
that of the existence of real entities cori'esponding to general terms ; and it
was reserved for Locke, at the end of the seventeenth century, to convince
philosophers that the supposed essences of classes were merely the signifi-
cation of their names ; nor, among the signal services which his writings,
rendered to philosophy, was there one more needful or more valuable.
Kow, as the most familiar of the general names by which an object is.
designated usually connotes not one only, but several attributes of the ob-
ject, each of which attributes separately forms also the bond of union of
some class, and the meaning of some general name ; we may predicate of a
name which connotes a variety of attributes, another name which connotes,
only one of these attributes, or some smaller number of them than all. In
such cases, the universal affirmative proposition will be true ; since what-
ever possesses the whole of any set of attributes, must posses.3 any part of
that same set. A proposition of this sort, however, conveys no informa-
tion to any one who previously understood the whole meaning of the terms..
The propositions. Every man is a corporeal being. Every man is a living
creature. Every man is rational, convey no knowledge to any one who was^
already aware of the entire meaning of the word man, for the meaning of
the word includes all this : and that every man has the attributes connoted
by all these predicates, is already asserted when he is called a man. Now,.
of this nature are all the propositions which have been called essential.
They are, in fact, identical propositions.
It is true that a proposition which predicates any attribute, even thougK
it be one implied in the name, is in most cases understood to involve a tacit
assertion that there exists a thing corresponding to the name, and possess-
ing the attributes connoted by it ; and this implied assertion may convey
information, even to those who understood the meaning of the name. But
all information of this sort, conveyed by all the essential propositions of
which man can be made the subject, is included in the assertion. Men exist,
And this assumption of real existence is, after all, the result of an imper-
fection of language. It arises from the ambiguity of the copula, which, in.
addition to its proper office of a mark to show that an assertion is made, is
also, as formerly remarked, a concrete word connoting existence. The act-
ual existence of the subject of the proposition is therefore only apparently^
not really, implied in the predication, if an essential one : we may say, A
ghost is a disembodied spirit, without believing in ghosts. But an acci-
dental, or non-essential, affirmation, does imply the real existence of the
subject, because in the case of a non-existent subject there is nothing for
the pi-oposition to assert. Such a proposition as, The ghost of a murdered
person haunts the couch of the murderer, can only have a meaning if un-
derstood as implying a belief in ghosts; for since the signification of the
* The doctrines which prevented the real meaning of Essences from being understood, had
not assumed so settled a shape in the time of Aristotle and his immediate followers, as was
afterward given to them by the Realists of the Middle Ages. Aristotle himself (in his Trea-
tise on the Categories) expressly denies that the deiregai oioLai, or Substantive Secunde, in-
here in a subject. They are only, he says, predicated of it.
VERBAL AND REAL PROPOSITIONS. 91
-word ghost implies nothing of the liind, the speaker either means nothing,
6r means to assert a thing which he wishes to be believed to have really
taken place.
It will be hereafter seen that when any important consequences seem to
follow, as in mathematics, from an essential proposition, or, in other words,
from a proposition involved in the meaning of a name, what they really
flow from is the tacit assumption of the real existence of the objects so
named. Apart from this assumption of real existence, the class of proposi-
tions in which the predicate is of the essence of the subject (that is, in
which the predicate connotes the whole or part of what the subject con-
notes, but nothing besides) answer no purpose but that of unfolding the
whole or some part of the meaning of the name, to those who did not pre-
viously know it. Accordingly, the most useful, and in strictness the only
useful kind of essential propositions, are Definitions: which, to be com-
plete, should unfold the whole of what is involved in the meaning of the
word defined ; that is (when it is a connotative word), the whole of what it
connotes. In defining a name, however, it is not usual to specify its entire
connotation, but so much only as is sufficient to mark out the objects usu-
ally denoted by it from all other known objects. And sometimes a merely
accidental property, not involved in the meaning of the name, answers this
purpose equally well. The various kinds of definition which these distinc-
tions give rise to, and the purposes to which they are respectively subserv-
ient, will be minutely considered in the proper place.
§ 3. According to the above view of essential propositions, no proposi-
tion can be reckoned such which relates to an individual by name, that is,
in which the subject is a proper name. Individuals have no essences.
When the schoolmen talked of the essence of an individual, they did not
mean the properties implied in its name, for the names of individuals imply
no properties. They regarded as of the essence of an individual, whatever
was of the essence of the species in which they were accustomed to place
that individual ; i. e., of the class to which it was most familiarly referred,
and to which, therefore, they conceived that it by nature belonged. Thus,
because the proposition Man is a rational being, was an essential proposi-
tion, they affirmed the same thing of the proposition, Julius CsBsar is a
rational being. This followed very naturally if genera and species were to
be considered as entities, distinct from, but inhering in, the individuals
composing them. If man was a substance inhering in each individual
man, the essence of man (whatever that might mean) was naturally sup-
posed to accompany it ; to inhere in John Thompson, and to form the
common essence of Thompson and Julius Csesar. It might then be fairly
said, that rationality, being of the essence of Man, was of the essence also
of Thompson. But if Man altogether be only the individual men and a
name bestowed upon them in consequence of certain common properties,
what becomes of John Thompson's essence ?
A fundamental error is seldom expelled from philosophy by a single vic-
tory. It retreats slowly, defends every inch of ground, and often, after it
has been driven from the open country, retains a footing in some remote
fastness. The essences of individuals were an unmeaning figment arising
from a misapprehension of the essences of classes, yet even Locke, when he
extirpated the parent error, could not shake himself free from that which
was its fruit. He distinguished two sorts of essences. Real and Nominal.
His nominal essences were the essences of classes, explained nearly as we
92 NAMES AND PROPOSITIONS.
have now explained them. Nor is any thing wanting to vender the third
book of Locke's Essay a nearly unexceptional treatise on the connotatioa
of names, except to free its language from the assumption of what are
called Abstract Ideas, which unfortunately is involved in the phraseology,
though not necessarily connected with the thoughts contained in that im-
mortal Third Book.* But besides nominal essences, he admitted real es-
sences, or essences of individual objects, which he supposed to be the causes
of the sensible properties of those objects. We know not (said he) what
these are (and this acknowledgment rendered the fiction comparatively in-
nocuous) ; but if we did, we could, from them alone, demonstrate the sen-
sible properties of the object, as the properties of the triangle are demon-
strated from the definition of the triangle. I shall have occasion to revert
to this theory in treating of Demonstration, and of the conditions under
■which one property of a thing admits of being demonstrated from another
property. It is enough here to remai-k that, according to this definition,
the real essence of an object has, in the progress of physics, come to be
conceived as nearly equivalent, in the case of bodies, to their corpuscular
structure: what it is now supposed to mean in the case of any other en-
tities, I would not take upon myself to define.
§ 4. An essential proposition, then, is one which is purely verbal ; which
asserts of a thing under a particular name, only what is asserted of it in
the fact of calling it by that name ; and which, therefore, either gives no
information, or gives it respecting the name, not the thing. Non-essential,
or accidental propositions, on the contrary, may be called Real Proposi-
tions, in opposition to Verbal. They predicate of a thing some fact not
involved in the signification of the name by which the proposition speaks'
of it ; some attribute not connoted by that name. Such are all proposi-
tions concerning things individually designated, and all general or partic-
ular propositions in which the predicate connotes any attiibute not con-
noted by the subject. All these, if true, add to our knowledge: they con-
vey information, not already involved in the names employed. When I
am told that all, or even that some objects, which have certain qualities, or
which stand in certain relations, have also certain other qualities, or stand
in certain other relations, I learn from this proposition a new fact; a fact
not included in my knowledge of the meaning of the words, nor even of
the existence of Things answering to the signification of those words. It
is this class of propositions only which are in themselves instructive, or
from which any instructive propositions can be inferred. f
Nothing has probably contributed more to the opinion so long prevalent
of the futility of the school logic, than the circumstance that almost all the
examples used in the common school books to illustrate the doctrine of
* The always acute and often profound author of An Outline of Sematology (Mr. B. H.
Smart) justly says, "Locke will be much more intelligible, if, in the majority of places, we
substitute 'the knowledge of for what he calls 'the Idea of" (p. 10). Among the many
criticisms on Locke's use of the word Idea, this is the one which, as it appears to me, most
nearly hits tlie mark : and I quote it for the additional reason that it precisely expresses the
point of diffei-ence respecting the import of Propositions, between my view and what I have
spoken of as the Conceptualist view of them. Where a Conceptualist says that a name or a
jiroposifion expresses our Idea of a thing, I should generally say (instead of our Idea) our
Knowledge, or Belief, concerning the thing itself.
f This distinction corresponds to that which is drawn by Kant and other metaphysicians
between what they term analytic and synthetic, judgments ; the former being those which can
be evolved from the meaning of the terms used.
VERBAL AND REAL PROPOSITIONS. 93
predication and that of the syllogism, consist of essential propositions.
They wei-e usually taken either from the branches or from the main trunk
of the Predicamental Tree, which included nothing but what was of the es-
sence of the species : Omne corpus est substantia, Omne animal est corpus,
Omnis homo est corpus, Omnis homo est animal, Omnis homo est rationalis,
niid 80 forth. It is far from wonderful that the syllogistic art should have
been thought to be of no use in assisting correct reasoning, when almost
the only propositions which, in the hands of its professed teachers, it was
employed to prove, were such as every one assented to without proof the
moment he comprehended the meaning of the words; and stood exactly
on a level, in point of evidence, with the premises from which they were
drawn. I have, therefore, throughout this work, avoided the employment
of essential propositions as examples, except where the nature of the prin-
ciple to be illustrated specifically required them.
§ 5. With respect to propositions which do convey information — which
assert something of a Thing, under a name that does not already presup-
pose what is about to be asserted ; thei-e are two diflEerent aspects in which
these, or rather such of them as are general propositions, may be consid-
ered: we may either look at them as portions of speculative truth, or as
memoranda for practical use. According as we consider propositions in
one or the other of these lights, their import may be conveniently expressed
in one or in the other of two formulas.
According to the formula which we have hitherto employed, and which
is best adapted to express the import of the proposition as a portion of
our theoretical knowledge. All men are mortal, means that the attributes
of man are always accompanied by the attribute mortality: No men are
gods, means that the attributes of man are never accompanied by the at-
tributes, or at least never by all the attributes, signified by the word god.
But when the proposition is considered as a memorandum for practical use,
we shall find a different mode of expressing the same meaning better adapt-
ed to indicate the ofBce which the proposition performs. The practical use
of a proposition is, to apprise or remind us what we have to expect, in any
individual case which comes within the assertion contained in the proposi-
tion. In reference to this purpose, the proposition. All men are mortal,
means that the attributes of man are evidence of, are a mark of, mortality ;
an indication by which the presence of that attribute is made manifest.
No men are gods, means that the attributes of man are a mark or evidence
that some or all of the attributes understood to belong to a god are not
there ; that where the former are, we need not expect to find the latter.
These two forms of expression are at bottom equivalent; but the one
points the attention more directly to what a proposition means, the latter
to the manner in which it is to be used.
Now it is to be observed that Reasoning (the subject to which we are
next to proceed) is a process into which propositions enter not as ultimate
results, but as means to the establishment of other propositions. We may
expect, therefore, that the mode of exhibiting the import of a general prop-
osition which shows it in its application to practical use, will best express
the function which propositions perform in Reasoning. And accordingly,
in the theory of Reasoning, the mode of viewing the subject which consid-
ei's a Proposition as asserting that one fact or phenomenon is a mark or ev-
idence of another fact or phenomenon, will be found almost indispensable.
For the purposes of that Theory, the best mode of defining the import of
94 NAMES AND PKOPOSITIONS.
a proposition is not the mode which shows most clearly what it is in itself,
but that which most distinctly suggests the manner in which it may be
made available for advancing from it to other propositions.
CHAPTER VII.
OF THE NATUEE OP CLASSIFICATION, AND THE FIVE PEEDICABLES.
§ 1. In examining into the nature of general propositions, we have ad-
verted much less than is usual with logicians to the ideas of a Class, and
Classification ; ideas which, since the Realist doctrine of General Substances
went out of vogue, have formed the basis of almost every attempt at a
philosophical theory of general terms and general propositions. We have
considered general names as having a meaning, quite independently of their
being the names of classes. That circumstance is in truth accidental, it
being wholly immaterial to the signification of the name whether there are
many objects, or only one, to which it happens to be applicable, or whether
there be any at all. God is as much a general term to the Christian or
Jew as to the Polytheist; and dragon, hippogriff, chimera, mermaid, ghost,
are as much so as if real objects existed, corresponding to those names.
Every name the signification of which is constituted by attributes, is po-
tentially a name of an indefinite number of objects ; but it needs not be
actually the name of any ; and if of any, it may be the name of only one.
As soon as we employ a name to connote attributes, the things, be they
more or fewer, which happen to possess those attributes, are constituted
ipso facto a class. But in predicating the name we predicate only the at-
tributes ; and the fact of belonging to a class does not, in many cases, come
into view at all.
Although, howevei'. Predication does not presuppose Classification, and
though the theory of Names and of Propositions is not cleared up, but only
encumbered, by intruding the idea of classification into it, there is never-
theless a close connection between Classification and the employment of
General Names. By every general name which we introduce, we create a
class, if there be any things, real or imaginary, to compose it; that is, any
Things corresponding to the signification of the name. Classes, therefore,
mostly owe their existence to general language. But general language,
also, though that is not the most common case, sometimes owes its exist-
ence to classes. A general, which is as much as to say a significant, name,
is indeed mostly introduced because we have a signification to express by
it ; because we need a word by means of which to predicate the attributes
which it connotes. But it is also true that a name is sometimes introduced
because we have found it convenient to create a class ; because we have
thought it useful for the regulation of our mental operations, that a certain
group of objects should be thought of together. A naturalist, for purposes
connected with his particular science, sees reason to distribute the animal
or vegetable creation into certain groups rather than into any others, and
he requires a name to bind, as it were, each of his groups together. It
must not, however, be supposed that such names, when introduced, differ
in any respect, as to their mode of signification, from other connotative
names. The classes which they denote are, as much as any other classes,
constituted by certain common attributes, and their names are significant
^ of those attributes, and of nothing else. The names of Cuvier's classes and
CLASSIFICATION AND THE PEEDICABLES. 95
•orders, Plantigrades, Digitigrades, etc., are as much the expression of at-
tributes as if those names had preceded, instead of grown out of, his clas-
«ilication of aiiimals. The only peculiarity of the case is, that the conven-
ience of classification was here the primary motive for introducing the
names ; while in other cases the name is introduced as a means of predica-
tion, and the formation of a class denoted by it is only an indirect conse-
quence.
The principles which ought to regulate Classification, as a logical process
subservient to the investigation of truth, can not be discussed to any pur-
pose until a much later stage of our inquiry. But, of Classification as re-
sulting from, and implied in, the fact of employing general language, we
•can not forbear to treat here, without leaving the theory of general names,
and of their employment in predication, mutilated and formless.
§ 2. This portion of the theory of general language is the subject of
what is termed the doctrine of the Predicables ; a set of distinctions hand-
ed down from Aristotle, and his follower Porphyry, many of which have
taken a firm root in scientific, and some of them even in popular, phraseolo-
gy. The predicables are a fivefold division of General Names, not ground-
ed as usual on a difference in their meaning, that is, in the attribute which
they connote, but on a difference in the kind of class which they denota.
We may predicate of a thing five different varieties of class-name :
A genus of the thing
(yevoc).
A species
(eI^oc).
A differentia
(Sia^opa).
A proprium
(.3(01').
An accidens
(avfijiefiriKOQ)
It is to be remarked of these distinctions, tjiat they express, not what the
predicate is in its own meaning, but what relation it bears to the subject
of which it happens on the particular occasion to be predicated. There
are not some names which are exclusively genera, and others which are ex-
clusively species, or differentiae ; but the same name is referred to one or
another predicable, according to the subject of which it is predicated on
the paitieular occasion. Animal, for instance, is a genus with respect to
man, or John ; a species with respect to Substance, or Being. Rectangu-
lar is one of the Differentiae of a geometrical square ; it is merely one of
the Accidentia of the table at which I am writing. The words genus, spe-
cies, etc., are therefore relative terms ; they are names applied to certain
predicates, to express the relation between them and some given subject : a
relation grounded, as we shall see, not on what the predicate connotes, but
on the class which it denotes, and on the place which, in some given classi-
fication, that class occupies relatively to the particular subject.
§ 3. Of these five names, two. Genus and Species, are not only used by
naturalists in a technical acceptation not precisely agreeing with their phil-
osophical meaning, but have also acquired a popular acceptation, much
more general than either. In this popular sense any two classes, one of
which includes the whole of the other and more, may be called a Genua
and a Species. Such, for instance, are Animal and Man ; Man and Mathe-
matician. Animal is a Genus ; Man and Brute are its two species ; or we
may divide it into a greater number of species, as man, horse, dog, etc.
JBiped, or two-footed animal, may also be considered a genus, of which
96 NAMES AND PROPOSITIONS.
man and bird are two species. Taste is a genus, of which sweet taste, sour
taste, salt taste, etc., are species. Virtue is a genus; justice, prudence,
courage, fortitude, generosity, etc., are its species.
The same class which is a genus with reference to the sub-classes or
species included in it, may be itself a species with reference to a more
comprehensive, or, as it is often called, a superior genus. Man is a species,
with reference to animal, but a genus with reference to the species Mathe-
matician. Animal is a genus, divided into two species, man and brute ; but
animal is also a species, which, with another species, vegetable, makes up
the genus, organized being. Biped is a genus "with reference to man and
bird, but a species with respect to the superior genus, animal. Taste is a
genus divided into species, but also a species of the genus sensation. Vir.
tue, a genus with reference to justice, temperance, etc., is one of the species
of the genus, mental quality.
In this popular sense the words Genus and Species have passed into
common -discourse. And it should be observed that in ordinary parlance,
not the name of the class, but the class itself, is said to be the genus or
species; not, of course, the class in the sense of each individual of the
class, but the individuals collectively, considered as an aggregate whole;
the name by which the class is designated being then called not the genus
or species, but the generic or specific name. And this is an admissible
form of expression ; nor is it of any importance which of the two modes
of speaking we adopt, provided the rest of our language is consistent with
it ; but, if we call the class itself the genus, we must not talk of predica-
ting the genus. We predicate of man the name mortal ; and by predica-
ting the name, we may be said, in an intelligible sense, to predicate what
the name expresses, the attribute mortality ; but in no allowable sense of
the word predication do we predicate of man the class mortal. We predi-
cate of him the fact of belonging to the class.
By the Aristotelian logicians, the terms genus and species were used in
a Kiore restricted sense. They did not admit every class which could be
divided into other classes to be a genus, or. every class which could be in^
eluded in a larger class to be a species. Animal was by them considered
a genus ; man and brute co-ordinate species under that genus : biped, how-
ever, would not have been admitted to be a genus with reference to man,
but a proprium or aceidens only. It was requisite, according to their
theory, that genus and species should be of the essence of the subject.
Animal was of the essence of man ; biped was not. And in every classi-
fication they considered some one class as the lowest or ^w/l»^a 'species.
Man, for instance, was a lowest species. Any further divisions into which
the class might be capable of being broken down, as man into white, black,
and red man, or into priest and layman, they did not admit to be species.
It has been seen, however, in the preceding chapter, that the distinction
between the essence of a class, and the attributes or properties which are
not of its essence — a distinction which has given occasion to so much ab-
struse speculation, and to which so mysterious a character was formerly,
and by many writers is still, attached — amounts to nothing more than the
difference between those attributes of the class which are, and those which
are not, involved in the signification of the class-name. As applied to in-
dividuals, the word Essence, we found, has no meaning, except in connec-
tion with the exploded tenets of the Realists; and what the schoolmen
chose to call the essence of an individual, was simply the essence of the
class to which that individual was most familiarly referred.
CLASSIFICATION AND THE PREDICABLES. 97
Is there no difference, then, save this merely verbal one, between the
classes which the schoolmen admitted to be genera or species, and those to
which they refused the title ? Is it an error to regard some of the differ-
ences which exist among objects as differences in kind {genere or specie),
and others only as differences in the accidents ? Were the schoolmen right
or wrong iil^iying to some of the classes into which things may be divided,
the name of kinds, and considering others as secondary divisions, ground-
ed on differences of a comparatively superficial nature ? Examination will
show that the Aristotelians did mean something by this distinction, and
something important ; but which, being but indistinctly conceived, was in-
adequately expressed by the phraseology of essences, and the various other
modes of speech to which they had recourse.
§ 4. It is a fundamental principle in logic, that the power of framing
classes is unlimited, as long as there is any (even the smallest) difference to
found a distinction upon. ■ Take any attribute whatever, and if some things
have it, and others have not, we may ground on the attribute a division of
all things into two classes ; and we actually do so, the moment we create a
name which connotes the attribute. The number of possible classes, there-
fore, is boundless ; and there are as many actual classes (either of real or
of imaginary things) as there are general names, positive and negative to-
gether.
But if we contemplate any one of the classes so formed, such as the class
animal or plant, or the class sulphur or phosphorus, or the class white or
red, and consider in what particulars the individuals included in the class
differ fi om those which do not come within it, we find a very remarkable
diversity in this respect between some classes and others. There are some
classes, the things contained in which differ from other things only in cer-
tain particulars which may be numbered, while others differ in more than
can be numbered, more even than we need ever expect to know. Some
classes have little or nothing in common to characterize them by, except
precisely what is connoted by the name : white things, for example, are not
distinguished by any common properties except whiteness ; or if they are,
it is only by such as are in some way dependent on, or connected with,
whiteness. But a hundred generations have not exhausted the common
properties of animals or of plants, of sulphur or of phosphorus ; nor do we
suppose them to be exhaustible, but proceed to new observations and ex-
periments, in the full confidence of discovering new properties which were
by no means implied in those we previously knew. While, if any one were
to propose for investigation the common properties of all things which are
of the same color, the same shape, or the same specific gravity, the absurd-
ity would be palpable. We have no ground to believe that any such com-
mon properties exist, except such as may be shown to be involved in the
supposition itself, or to be derivable from it by some law of causation. It
appears, therefore, that the properties, on which we ground our classes,
sometimes exhaust all that the class has in common, or contain it all by
some mode of implication ; but in other instances we make a selection of a
few properties from among not only a greater number, but a number inex-
haustible by us, and to which as we know no bounds, they may, so far as
■we are concerned, be regarded as infinite.
There is no impropriety in saying that, of these two classifications, the
one answers to a much more radical distinction in the things themselves,
than the bther does. And if any one even chooses to say that the one clas-
1
©8 NAMES AND PROPOSITIONS.
sification is made by nature, the other by us for our convenience, he will be
Tight; provided he means no more than this: Where a certain apparent
difference between things (though perhaps in itself of little moment) an-
swers to we know not what number of other differences, pervading not
•only their known properties, but properties yet undiscovered, it is not op-
tional but imperative to recognize this difference as the foundation of a
specific distinction ; while, on the contrary, differences that are merely finite
and determinate, like those designated by the words white, black, or red,
may be disregarded if the purpose for which the classification is made does
not require attention to those particular properties. The differences, how-
ever, are made by nature, in both cases ; while the recognition of those dif-
ferences as grounds of classification and of naming, is, equally in both cases,
the act of man : only in the one case, the ends of language and of classifica-
tion would be subverted if no notice were taken of the difference, while in
the other case, the necessity of taking notice of it depends on the impor-
tance or unimportance of the particular qualities in which the difference
happens to consist.
Now, these classes, distinguished by unknown multitudes of properties,
and not solely by a few determinate ones — which are parted off from one
another by an unfathomable chasm, instead of a mere ordinary ditch with
a visible bottom — are the only classes which, by the Aristotelian logicians,
were considered as genera or species. Differences which extended only to
a certain property or properties, and there terminated, they considered as
differences only in the accidents of things ; but where any class differed
from other things by an infinite series of differences, known and unknown,
they considered the distinction as one of kind, and spoke of it as being an
essential difference, which is also one of the current meanings of that vague
expression at the present day.
Conceiving the schoolmen to have been justified in drawing a broad line
of separation between these two kinds of classes and of class-distinctions, I
shall not only retain the division itself, but continue to express it in their
language. According to that language, the proximate (or lowest) Kind to
which any individual is referrible, is called its species. Conformably to
this, Isaac Newton would be said to be of the species man. There are
indeed numerous sub-classes included in the class man, to which Newton
also belongs ; for example. Christian, and Englishman, and Mathematician.
But these, though distinct classes, are not, in our sense of the term, distinct
Kinds of men. A Christian, for example, differs from other human be-
ings ; but he differs only in the attribute which the word expresses, namely,
belief in Christianity, and whatever else that implies, either as involved in
the fact itself, or connected with it through some law of cause and effect.
We should never think of inquiring what properties, unconnected with
Christianity, either as cause or effect, are common to all Christians and pe-
culiar to them; while in regard to all Men, physiologists are perpetually
carrying on such an inquiry ; nor is the answer ever likely to be completed.
Man, therefore, we may call a species ; Christian, or Mathematician, we
can not.
Note here, that it is by no means intended to imply that there may not
be different Kinds, or logical species, of man. The various races and tem-
peraments, the two sexes, and even the various ages, may be differences of
kind, within our meaning of the tej-m. I do not say that they are so. For
in the progress of physiology it may almost be said to be made out, that
the differences which really exist between different races, sexes, etc., follow
CLASSIFICATION AND THE PREDICABLES. 99
--as consequences, under laws of nature, from a small number of primary
•differences which can be precisely determined, and which, as the phrase is,
account for all the rest. If this be so, these are not distinctions in kind ;
no more than Christian, Jew, Mussulman, and Pagan, a_ difference which
i^also carries many consequences along with it. And in this way classes are
often mistaken for real Kinds, which are afterward proved not to be so.
But if it turned out that the differences were not capable of being thus ac-
counted for, then Caucasian, Mongolian, Negro, etc., would be really differ-
-ent Kinds of human beings, and entitled to be ranked as species by the
logician ; though not by the naturalist. For (as already noticed) the word
.species is used in a different signification in logic and in natural history.
By the naturalist, organized beings are not usually said to be of different
.species, if it is supposed that they have descended from the same stock.
That, however, is a sense artificially given to the word, for the technical
purposes of a particular science. To the logician, if a negro and a white
man differ in the same manner (however less in degree) as a horse and a
«amcl do, that is, if their differences are inexhaustible, and not referrible to
any common cause, they are different species, whether they are descended
from common ancestors or not. But if their differences can all be traced
to climate and habits, or to some one or a few special differences in struc-
ture, they are not, in the logician's view, specifically distinct.
When the infima species, or proximate Kind, to which an individual
belongs, has been ascertained, the properties common to that Kind include
necessarily the whole of the common properties of every other real Kind
to which the individual can be referrible. Let the individual, for example,
be Socrates, and the proximate Kind, man. Animal, or living creature, is
also a real kind, and includes Socrates; but, since it likewise includes man,
■or in other words, since all men.are animals, the properties common to ani-
mals form a portion of the common properties of the sub-class, man. And
if there be any class which includes Socrates without including man, that
class is not a real Kind. Let the class, for example, be flat-nosed; that
being a class which includes Socrates, without including all men. To de-
termine whether it is a real Kind, we must ask ourselves this question ;
Have all flat-nosed animals, in addition to whatever is implied in their flat
noses, any common properties, other than those which are common to all
animals whatever ? If they had ; if a flat nose were a mark or index to an
indefinite number of other peculiarities, not deducible from the former by
an ascertainable law, then out of the class man we might cut another class,
flat-nosed man, which, according to our definition, would be a Kind. But
if we could do this, man would not be, as it was assumed to be, the proxi-
mate Kind. Therefore, the properties of the proximate Kind do compre-
hend those (whether known or unknown) of all other Kinds to which the
individual belongs; which was the point we undertook to prove. And
hence, every other Kind which is predicable of the individual, will be to
the proximate Kind in the relation of a genus, according to even the popu-
lar acceptation of the terms genus and species ; that is, it will be a larger
-class, including it and more.
We are now able to fix the logical meaning of these terms. Every class
which is a real Kind, that is, which is distinguished from all other classes
by an indeterminate multitude of properties not derivable from one an-
other, is either a genus or a species. A Kind which is not divisible into
other Kinds, can not be a genus, becaufse it has no species under it; but it
is itself a species, both with reference to the individuals below and to the
100 NAMES AND PROPOSITIONS.
genera above (Species Prsedicabilis and Species Subjicibilis). But every
Kind which admits of division into real Kinds (as animal into mammal,
bird, fish, etc., or bird into various species of birds) is a genus to all below
it, a species to all. genera in which it is itself included. And here we may ,
close this part of" the discussion, and pass to the three remaining predica-
bles, Differentia, Proprium, and Accidens.
§ 5. To begin with Differentia. This word is correlative with the words
genus and species, and as all admit, it signifies the attribute which distin-
guishes a given species from every Other species of the same genus. This
is so far clear : but we may still ask, which of the distinguishing attiibutes
it signifies. For we have seen that every Kind (and a species must be a
Kind) is distinguished from other Kinds, not by any one attribute, but by
an indefinite number. Man, for instance, is a species of the genus animal :.
Rational (or rationality, for it is of no consequence here whether we use
the concrete or the abstract form) is generally assigned by logicians as the
Differentia ; and doubtless this attribute serves the purpose of distinction :
but it has also been remarked of man, that he is a cooking animal ; the
only animal that dresses its food. This, therefore, is another of the at-
tributes by which the species man is distinguished from other species of
the same genus: would this attribute serve equally well for a differentia?
The Aristotelians say No ; having laid it down that the differentia must,
like the genus and species, be of the esseiice of the subject.
And here we lose even that vestige of a meaning grounded in the nature
of the things themselves, which may be supposed to be attached to the
word essence when it is said that genus and species must be of the essence
of the thing. There can be no doubt that when the schoolmen talked of
the essences of things as opposed to their accidents, they had confusedly
in view the distinction between differences of kind, and the differences
which are not of kind ; they meant to intimate that genera and species
must be Kinds. Their notion of the essence of a thing was a vague notion
of a something which makes it what it is, i. e., which makes it the Kind of
thing that it is — which causes it to have all that variety of properties which
distinguish its Kind. But when the matter came to be looked at more
closely, nobody could discover what caused the thing to have all those prop-
erties, nor even that there was any thing which caused it to have them.
Logicians, howevei-, not liking to admit this, and being unable to detect
what made the thing to be what it was, satisfied themselves with what
made it to be what it was called. Of the innumerable properties, known
and unknown, that are common to the class man, a portion only, and of
course a very small portion, are connoted by its name ; these few, however,
will naturally have been thus distinguished from the rest either for their
greater obviousness, or for greater supposed importance. These prop-
erties, then, which were connoted by the name, logicians seized upon, and
called them the essence of the species; and not stopping there, they af-
firmed them, in the case of the infima species, to be the essence of the in-
dividual too ; for it was their. maxim, that the species contained the " whole
essence" of the thing. Metaphysics, that fertile field of delusion propa-
gated by language, does not afford a more signal instance of such delusion.
On this account it was that rationality, being connoted by the name man,
was allowed to be a differentia of the class ; but the peculiarity of cook-
ing their food, not being connoted, was relegated to the class of accidental
properties.
CLASSIFICATION AND THE PREDICABLES. 101
The distinction, therefore, between Differentia, Proprium, and Acoidens,
is not grounded in the nature of things, but in the connotation of names j
and we must seek it there, if we wish to find what it is.
From the fact that the genus includes the species, in other words c?enotes
more than, the species, or is predicable of a greater number of individuals,
it follows that the species must connote more than the genus. It must
•connote all the attributes which the genus connotes, or there would be
nothing to prevent it from denoting individuals not included in the genus.
And it must connote something besides, otherwise it would include the
-whole genus. Animal denotes all the individuals denoted by man, and
many more. Man, therefore, must connote all that animal connotes, other-
wise there might be men who are not animals ; and it must connote some-
thing more than animal connotes, otherwise all animals would be men.
This surplus of connotation — this which the species connotes over and
above the connotation of the genus'— is the Differentia, or specific differ-
«nce; or, to state the same proposition in other words, the Differentia is
that which must be added to the connotation of the genus, to complete the
■connotation of the species.
The word man, for instance, exclusively of what it connotes in common
-with animal, also connotes rationality, and at least some approximation to
that external form which we all know, but which as we have no name for
it considered in itself, we are content to call the human. The Differentia,
-or specific difference, therefore, of man, as referred to the genus animal, is
that outward form and the possession of reason. The Aristotelians said,
the possession of reason, without the outward form. But if they adhered
to this, they would have been obliged to call the Houyhnhnms men. The
•question never arose, and they were never called upon to decide how such
a case would have affected their notion of essentiality. -However this may
be, they were satisfied with taking such a portion of the differentia as suf-
ficed to distinguish the species from all other existing things, though by so
■doing they might not exhaust the connotation of the name.
§ 6. And here, to prevent the notion of differentia from being restricted
within too narrow limits, it is necessary to remark, that a species, even as
referred to the same genus, will not always have the same differentia, but
a different one, according to the principle and pui-pose which preside over
the particular classification. For example, a naturalist surveys the various
kinds of animals, and looks out for the classification of them most in ac-
•cordance with the order in which, for zoological purposes, he considers it
■desirable that we should think of them. With this view he finds it advisa-
l3le that one of his fundamental divisions should be into warm-blooded and
•cold-blooded animals ; or into animals which breathe with lungs and those
which breathe with gills ; or into carnivorous, and frugivorous or graminiv-
orous ; or into those which walk on the flat part and those which walk on
the extremity of the foot, a distinction on which two of Cuvier's families are
founded. In doing this, the naturalist creates as many new classes ; which
are by no means those to which the individual animal is familiarly and spon-
taneously referred ; nor should we ever think of assigning to them so prom-
inent a position in our arrangement of the animal kingdom, unless for a pre-
conceived purpose of scientific convenience. And to the liberty of doing
this there is no limit. In the examples we have given, most of the classes
are real Kinds, since each of the peculiarities is an index to a multitude
<of properties belonging to the class which it characterizes : but even if the
102 NAMES AND PROPOSITIONS.
case were otherwise — if the other properties of those classes could all be-
derived, by any process known to us, from the one peculiarity on which the'
class is founded — even then, if these derivative properties wei-e of piimary
importance for the purposes of the naturalist, he would be warranted in
founding his primary divisions on them.
If, however, practical convenience is a sufficient warrant for making the
main demarkations in our arrangement of objects run in lines not coin-
ciding with any distinction of Kind, and so creating genera and species in
the popular sense which are not genera or species in the rigorous sense at-
all ; d fortiori must we be warranted, when our genera and species are real
genei-a and species, in mai-king the distinction between them by those of
their properties which considerations of practical convenience most strong-
ly recommend. If we cut a species put of a given genus — the species man,^
for instance, out of the genus animal — with an intention on our part that
the peculiarity by which we are to be guided in the application of the
name man should be rationality, then rationality is the differentia of the-
species man. Suppose, however, that being naturalists, we, for the pur-
poses of our particular study, cut out of the genus animal the same species-
man, but with an intention that the distinction between man and all other
species of-animal should be, not rationality, but the possession of " four
incisors in each jaw, tusks solitary, and erect posture." It is evident that
the word man, when used by us as naturalists, no longer connotes rational-
ity, but connotes the three other properties specified; for that which we
have expressly in view when we impose a name, assuredly forms part of
the meaning of that name. We may, therefore, lay it down as a maxim,
that wherever there is a Genus, and a Species marked out from that genus
by an assignable differentia, the name of the species must be connotative,
and must connote the differentia ; but the connotation may be special — not
involved in the signification of the term as ordinarily used, but given to it.
■when employed as a term of art or science. The word Man in common
use, connotes rationality and a certain form, but does not connote the num-
ber or character of the teeth ; in the Linnaean system it connotes the num-
ber of incisor and canine teeth, but does not connote rationality nor any
particular form. The word man has, therefore, two different meanings;
though not commonly considered as ambiguous, because it happens in both
cases to (denote the same individual objects. But a case is conceivable in
•which the ambiguity would become- evident : we have only to imagine that
some new kind of animal were discovered, having LinnsBus's three char-
acteristics of humanity, but not rational, or not of the human form. In
ordinary parlance, these animals would not be called men ; but in natural
history they must still be called so by those, if any there should be, who
adhere to the Linnssan classification ; and the question would arise, whether
the word should continue to be used in two senses, oi- the classification be
given up, and the technical sense of the term be abandoned along with it.
Words not otherwise connotative may, in the mode just adverted to,
acquire a special or technical connotation. Thus the word whiteness, as
we have so often remarked, connotes nothing ; it merely denotes the at-
tribute corresponding to a certain sensation : but if we are making a clas-
sification of colors, and desire to justify, or even merely to point out, the'
particular place assigned to whiteness in our arrangement, we may define
it "the color produced by the mixture of all the simple rays;" and this
fact, though by no means implied in the meaning of the word whitenesis
as ordinarily used, but only known by subsequent scientific investigation.
CLASSIFICATION AND THE PEEDICABLES. lOJ.
is part of its meaning in the particular essay or treatise, and becomes the-
differentia of the species.*
The differentia, therefore, of a species may be defined to be, that part of
the connotation of the specific name, whether ordinary oi- special and tech-
nical, which distinguishes the species in question from all other species of
the genus to which on the particular occasion we are referring it.
§ 7. Having disposed of Genus, Species, and Differentia, we shall not find
much diflSculty in attaining a clear conception of the distinction between
the other two predicables, as well as between them and the first three.
In the Aristotelian phraseology. Genus and Differentia ai-e of the essence
of the subject; by which, as we have seen, is really meant that the proper-
ties signified by the genus and those signified by the differentia, form part
of the connotation of the name denoting the species. Proprium and Ac-
cidens, on the other hand, form no pai't of the essence, but are predicated
of the species only accidentally/. Both are Accidents, in the wider sense in
-which the accidents of a thing are opposed to its essence ; though, in the
doctrine of the Predicables, Accidens is used for one sort of accident only,,
Proprium being another sort. Proprium, continue the schoolmen, is pred-
icated accidentally, indeed, but necessarily; or, as they further explain it,,
signifies an attribute which is nof indeed part of the essence, but which
flows from, or is a consequence of, the essence, and is, therefore, insepai-ably
attached to the species ; e. g., the various properties of a ti-iangle, which,
though no part of its definition, must necessarily be possessed by whatever
comes under that definition. Accidens, on the contrary, has no connection
whatever with the essence, but may come and go, and the species still re-
main what it was before. If a species could exist without its Propria, it
must be capable of existing without that on which its Propria are neces-
sarily consequent, and therefore without its essence, without that which con-
stitutes it a species. But an Accidens, whether separable or inseparable
from the species in actual experience, may be supposed separated, without,
the necessity of supposing any other alteration ; or at least, without sup-
posing any of the essential properties of the species to be altered, since
with them an Accidens has no connection.
A Proprium, therefore, of the species, may be defined, any attribute which
belongs to all the individuals included in the species, and which, though
not connoted by the specific name (either ordinarily if the classification we-
are considering be for ordinary purposes, or specially if it be for a special
purpose), yet follows from some attribute which the name either ordinarily
or specially connotes.
One attribute may follow from another in two ways ; and there are con-
sequently two kinds of Proprium. It may follow as a conclusion follows
premises, or it may follow as an effect follows a cause. Thus, the attribute
of having the opposite sides equal, which is not one of those connoted by
the word Parallelogram, nevertheless follows from those connoted by it,,
namely, from having the opposite sides straight lines and parallel, and the
number of sides four. The attribute, therefore, of having the opposite
sides equal, is a Proprium of the class parallelogram ; and a Propi'ium of
the first kind, which follows from the connoted attributes by way of dem-
* If we allow a diflferentia to what is not really a species. Eor the distinction of Kinds,
in the sense explained by as, not being in any way applicable to attributes, it of course follows,
that although attributes may be put into classes, those classes can be admitted to be genera
or species only by courtesy.
104 NAMES AND PROPOSITIONS.
onstration. The attribute of being capable of understanding language, is
a Proprium of the species man, since without being connoted by the word,
it follows from an attribute which the word does connote, viz., from the
attribute of rationality. But this is a Proprium of the second kind, which
follows by way of causation. How it is that one property of a thing fol-
lows, or can be inferred, from another; under what conditions this is pos-
sible, and what is the exact meaning of the phrase; are among the ques-
tions which will occupy us in the two succeeding Books. At present it
meeds only be said, that whether a Proprium follows by demonstration or
by causation, it follows necessarily; that is to say, its not following would
be inconsistent with some law which we regard as a part of the constitu-
tion either of our thinking faculty or of the universe.
§ 8. Under the remaining predicable, Accidens, are included all attri-
butes of a thing which are neither involved in the signification of the name
(whether ordinarily or as a term of art), nor have, so far as we know,
any necessary connection with attributes which are so involved. They are
commonly divided into Separable and Inseparable Accidents. Inseparable
accidents are those which — although we know of no connection between
them and the attributes constitutive of the species, and although, therefore,
so far as we are aware, they might be absent without making the name in-
applicable and the species a different species — are yet never in fact known
to be absent. A concise mode of expressing the same meaning is, that in-
separable accidents are pi'operties which are universal to the species, but
not necessary to it. Thus, blackness is an attribute of a crow, and, as far
as we know, a universal one. But if we were to discover a I'ace of white
birds, in other respects resembling crows, we should not say. These are
not crows ; we should say. These are white crows. Crow, therefoi-e, does
not connote blackness ; nor, from any of the attributes which it does con-
note, whether as a word in popular use or as a term of art, could blackness
be inferred. Not only, therefore, can we conceive a white crow, but we
know of no reason why such an animal should not exist. Since, how-
ever, none but black crows are known to exist, blackness, in the present
state of our knowledge, ranks as an accident, but an inseparable accident,
of the species crow.
Separable Accidents are those which are found, in point of fact, to be
sometimes absent from the species ; which are not only not necessary, but
not even universal. They are such as do not belong to every individual
of the species, but only to some individuals; or if to all, not at all times.
Thus the color of a European is one of the separable accidents of the spe-
■cies man, because it is not an attribute of all human creatures. Being
boi-n, is also (speaking in the logical sense) a separable accident of the spe-
•cies man, because, though an attribute of all human beings, it is so only at
one particular time. A fortiori those attributes which are not constant
even in the same individual, as, to be in one or in another place, to be hot
or cold, sitting or walking, must be ranked as separable accidents.
DEFINITION. 105
CHAPTER VIII.
OF DEPINITIOlSr.
§ 1. One necessary part of the theory of Names and of Propositions re-
mains to be treated of in this place : the theory of Definitions. As being
the most important of the class of propositions which we have charactei^
ized as purely verbal, they have already received some notice in the chapter
preceding the last. But their fuller treatment was at that time postponed,,
because definition is so closely connected with classification, that, until the
nature of the latter process is in some measure understood, the former can
not be discussed to much purpose.
The simplest aud most correct notion of a Definition is, a pi-oposition
declaratory of the meaning of a word ; namely, either the meaning which
it bears in common acceptation, or that which the speaker or writer, for
the particular purposes of his discourse, intends lo annex to it.
The definition of a word being the proposition which enunciates its
meaning, words which have no meaning are unsusceptible of definition.
Proper names, therefore, can not be defined. A proper name being a mere
mark put upon an individual, and of which it is the characteristic propeity
to be destitute of meaning, its meaning can not of course be declared;
though we may indicate by language, as we might indicate slill more con-
veniently by pointing with the finger, upon what individual that particular
mark has been, or is intended to be, put. It is no definition of " John
Thomson " to say he is " the son of General Thomson ;" for the name John
Thomson does not express this. Neither is it any definition of " John
Thomson " to say he is " the man now crossing the street." These propo-
sitions may serve to make known who is the particular man to whom the
name belongs, but that may be done still more unambiguously by pointing
to him, which, however, has not been esteemed one of the modes of defi-
nition.
In the case of connotative names, the meaning, as has been so often ob-
served, is the connotation ; and the definition of a connotative name, is the
proposition which declares its connotation. This might be done either di-
rectly or indirectly. The direct mode would be by a proposition in this
form: "Man " (or whatsoever the word may be) "is a name connoting such
and such attributes," or " is a name which, when predicated of any thing,,
signifies the possession of such and such attributes by that thing." Or
thus : Man is every thing which possesses such and such attributes : Man
is every thing which possesses corporeity, organization, life, rationality, and
certain peculiarities of external form.
This form of definition is the most precise and least equivocal of any;
but it is not brief enough, and is besides too technical for common discourse.
The more usual mode of declaring the connotation of a name, is to predi-
cate of it another name or names of known signification, which connote the
same aggregation of attributes. This may be done either by pi-edicating
of the name intended to be defined, another connotative name exactly syn-
onymous, as, " Man is a human being," which is not commonly accounted a
106 NAMES AND PROPOSITIONS.
definition at all ; or by predicating two or more connotative names, which
make up among them the whole connotation of the name to be defined. In
this last case, again, we may either compose our definition of as many con-
notative names as there are attributes, each attribute being connoted by
one, as, Man is a corporeal, organized, animated, rational being, shaped so
and so; or we employ names which connote several of the attributes at
once, as, Man is a rational animal, shaped so and so.
The definition of a name, according to this view of it, is the sum total
of all the essential propositions which can be framed with that name for
their subject. All propositions the truth of which is implied in the name,
all those which we are made aware of by merely hearing the name, are in-
cluded in the definition, if complete, and may be evolved from it without
the aid of any other premises ; whether the definition expresses them in
two or three words, or in a larger number. It is, therefore, not without
reason that Condillac and other writers have affirmed a definition to be an
analysis. To resolve any complex whole into the elements of which it is
compounded, is the meaning of analysis : and this we do when we replace
one word which connotes a set of attributes collectively, by two or more
which connote the same attributes singly, or in smaller groups.
§ 2. From this, however, the question naturally arises, in what manner
are we to define a name which connotes only a single attribute: for in-
stance, " white," which connotes nothing but whiteness ; " rational," which
•connotes nothing but the possession of reason. It might seem that the
meaning of such names could only be declared in two ways ; by a synony-
mous term, if any such can be found ; or in the direct way already alluded
to : " White is a name connoting the attribute whiteness." Let us see,
however, whether the analysis of the meaning of the name, that is, the
"breaking down of that meaning into several parts, admits of being carried
farther. Without at present deciding this question as to the word white,
it is obvious that in the case of rational some further explanation may be
given of its meaning than is contained in the proposition, " Rational is that
which possesses the attribute of reason ;" since the attribute I'eason itself
admits of being defined. And here we must turn our attention to the def-
initions of attributes, or rather of the names of attributes, that is, of ab-
stract names.
In regard to such names of attributes as are connotative, and express
attributes of those attributes, there is no difficulty : like other connotative
names, they are defined by declaring their connotation. Thus the word
foult may be defined, "a quality productive of evil or inconvenience."
Sometimes, again, the attribute to be defined is not one attribute, but a
union of several : we have only, therefore, to put together the names of all
the attributes taken separately, and we obtain the definition of the name
which belongs to them all taken together; a definition which will corre-
spond exactly to that of the corresponding concrete name. For, as we de-
fine a concrete name by enumerating the attributes which it connotes, and
as the attributes connoted by a concrete name form the entire signification
of the corresponding abstract name, the same enumeration will serve for
the definition of both. Thus, if the definition of a human being be this,
" a being, corporeal, animated, rational, shaped so and so," the definition of
humanity will be corporeity and animal life, combined with rationality,
and with such and such a shape.
When, on the other hand, the abstract name does not express a compli-
DEFINITION. 107
«ation of attributes, but a single attribute, we must remember that every
attribute is grounded on some fact or phenomenon, from which, and which
alone, it derives its meaning. To that fact or phenomenon, called in a for-
mer chapter the foundation of the attribute, we must, therefore, have re-
course for its definition. Now, the foundation of the attribute may be
:a phenomenon of any degree of complexity, consisting of many different
parts, either co-existent or in succession. To obtain a definition of the attri-
bute, we must analyze the phenomenon into these parts. Eloquence, for
■example, is the name of one attribute only ; but this attribute is grounded
■on extei-nal effects of a compUcated nature, flowing from acts of the person
to whom we ascribe the attribute ; and by resolving this phenomenon of
causation into its two parts, the cause and the effect, we obtain a definition
•of eloquence, viz. the power of influencing the feelings by speech or writing.
A name, therefore, whether concrete or abstract, admits of definition,
provided we are able to analyze, that is, to distinguish into parts, the attri-
bute or set of attributes which constitute the meaning both of the concrete
name and of the corresponding abstract: if a set of attributes, by enumer-
ating them ; if a single attribute, by dissecting the fact or phenomenon
(whether of perception or o'f internal consciousness) which is the foundation
■of the attribute. But, further, even when the fact is one of our simple
feelings or states of consciousness, and therefore unsusceptible of analy-
sis, the names both of the object and of the attribute still iidmit of defini-
tion ; or rather, would do so if all our simple feelings had names. "White-
ness may be defined, the property or power of exciting the sensation of
white. A white object may be defined, an object which excites the sensation
of white. The only names which are unsusceptible of definition, because
their meaning is unsusceptible of analysis, are the names of the simple feel-
ings themselves. These are in the same condition as proper names. They
are not indeed, like proper names, unmeaning ; for the words sensation
of white signify, that the sensation which I so denominate resembles other
sensations which I remember to have had before, and to have called by that
name. But as we have no words by which to recall those former sensations,
except the very word which we seek to define, or some other which, being
exactly synonymous with it, requires definition as much, words can not un-
fold the signification of this class of names ; and we are obliged to make a
direct appeal to the personal experience of the individual whom we address.
§ 3. Having stated what seems to be the true idea of a Definition, I pro-
ceed to examine some opinions of philosophers, and some popular concep-
tions on the subject, which conflict more or less with that idea.
The only adequate definition of a name is, as already remarked, one which
■declares the facts, and the whole of the facts, which the name involves in
its signification. But with most persons the object of a definition does not
embrace so much ; they look for nothing more, in a definition, than a guide
to the correct use of the term — a protection against applying it in a man-
ner inconsistent with custom and convention. Any thing, therefore, is to
thera a sufficient definition of a term, which will serve as a correct index
to what the term cfonotes; though not embracing the whole, and some-
times, perhaps, not even any part, of what it connotes. This gives rise to
two sorts of imperfect, or unscientific definition ; Essential but incomplete
Definitions, and Accidental Definitions, or Descriptions. In the former, a
■connotative name is defined by a part only of its connotation ; in the latter,
Jby something which forms no part of the connotation at all.
108 NAMES AND PEOPOSITIONS.
An example of the first kind of imperfect definitions is the following!
Man is a rational animal. It is impossible to consider this as a complete-
definition of the word Man, since (as before remarked) if we adhered to it
we should be obliged to call the Houyhnhnms men ; but as there happen t*
be no Houyhnhnms, this imperfect definition is sufficient to mark out and
distinguish from all other things, the objects at present denoted by "man;"
all the beings actually known to exist, of whom the name is predicable^
Though the word is defined by some only among the attributes which it
connotes, not by all, it happens that all known objects which possess the
enumerated attributes, possess also those which are omitted : so that the
field of predication which the word covers, and the employment of it which,
is conformable to usage, are as well indicated by the inadequate definitioa
as by an adequate one. Such definitions, however, are always liable to be
overthrown by the discovery of "new objects in nature.
Definitions of this kind are what logicians have had in view, when they
laid down the rule, that the definition of a species should be per genus et
differentiam. Differentia being seldom taken to mean the whole of the
peculiarities constitutive of the species, but some one of those peculiarities
only, a complete definition would be per genus et differentias, rather than
differentiam. It would include, with the name of the superior genus, not
merely some attribute which distinguishes the species intended to be de-
fined from all other species of the same genus, but all the attributes im-
plied in the name of the specieSj which the name of the superior genus
has not already implied. The assertion, however, that a definition must
of necessity consist of a genus and differentiae, is not tenable. It was early
remarked by logicians, that the summum genus in any classification, hav-
ing no genus superior to itself, could not be defined in this manner. Yet
we have seen that all names, except those of our elementary feelings, are
susceptible of definition in the strictest sense ; by setting forth in words
the constituent parts of the fact or phenomenon, of which the connotation
of every word is ultimately composed.
§ 4. Although the first kind of imperfect definition (which defines a con-
notative term by a part only of what it connotes, but a part sufficient to
mark out correctly the boundaries of its denotation), has been considered
by the ancients, and by logicians in general, as a complete definition ; it has
always been deemed necessary that the attributes employed should really
form part of the connotation ; for the rule was that the definition must be
drawn from the essence of the class ; and this would not have been the case
if it had been in any degree made up of attributes not connoted by the
name. The second kind of imperfect definition, therefore, in which the
name of a class is defined by any of its accidents — that is, by attributes
which are not included in its connotation — has been rejected from the rank
of genuine Definition by all logicians, and has been termed Description.
This kind of imperfect definition, however, takes its rise from the samS'
cause as the other, namely, the willingness to accept as a definition any thing
which, whether it expounds the meaning of the name or not, enables us tc
discriminate the things denoted by the name from all other things, and con-
sequently to employ the term in predication without deviating from estab-
lished usage. This purpose is duly answered by stating any (no matter
what) of the attributes which are common to the whole of the class, and
peculiar to it; or any combination of attributes which happens to be pe-
culiar to it, though separately each of those attributes may be common to
DEFINITION. 109
it with some other thingig. It is only necessary that the definition (or de-
«cviption) thus formed, should.be convertible with the name which it pro-
fesses to define ; that is, should be exactly co-extensive with it, being pred-
icable of every thing of which it is predicable, and of nothing of which it
is not predicable; though the attributes specified may have no connection
with tliose which mankind had in view when they formed or recognized the
■class, and gave it a name. The following are cori-ect definitions of Man,
according to this test : Man is a mammiferous animal, having (by nature)
two hands (for the human species answers to this description, and no other
animal does) : Man is an animal who cooks liis food : Man is a featherless
biped.
What would otherwise be a mere description, may be raised to the rank
of a real definition by the peculiar purpose which the speaker or writer
has in view. As was seen in the preceding chapter, it may, for the ends
of a particular art or science, or for the more convenient statement of an
author's particular doctrines, be advisable to give to some general name,
without altering its denotation, a special connotation, different from its or-
dinary one. When this is done, a definition of the name by means of the
attributes which make up the special connotation, though in general a mere
accidental definition or description, becomes on the particular occasion and
for the particular purpose a complete and genuine definition. This actual-
ly occurs with respect to one of the preceding examples, " Man is a mam-
miferous animal having two hands," which is the scientific definition of
man, considered as one of the species in Cuvier's distribution of the animal
kingdom.
In cases of this sort, though the definition is still a declaration of the
meaning which in the particular instance the name is appointed to convey,
it can not be said that to state the meaning of the word is the purpose of
the definition. The purpose is not to expound a name, but a classification.
The special meaning which Cuvier assigned to the word Man (quite foreign
to its ordinary meaning, though involving no change in the denotation of
the word), was incidental to a plan of arranging animals into classes on a
certain principle, that is, according to a certain set of distinctions. And
since the definition of Man according to the ordinary connotation of the
word, though it would have answered every other purpose of a definition,
would not have pointed out the place which the species ought to occupy
in that particular classification ; he gave the word a special connotation,
that he might be able to define it by the kind of attributes on which, for
reasons of scientific convenience, he had resolved to found his division of
animated nature.
Scientific definitions, whether they are definitions of scientific terms, or
of common terms used in a scientific sense, are almost always of the kind
last spoken of: their main purpose is to serve as the landmarks of scien-
tific classification. And since the classifications in any science are con-
tinually modified as scientific knowledge advances, the definitions in the
sciences are also constantly vai"ying. A striking instance is afforded by
the words Acid and Alkali, especially the former. As experimental dis-
covery advanced, the substances classed with acids have been constantly
multiplying, and by a natural consequence the attributes connoted by the
word have receded and become fewer. At first it connoted the attributes,
of combining with an alkali to form a neutral substance (called a salt) ;
being compounded of a base and oxygen ; causticity to the taste and touch ;
fluidity, etc. The true analysis of muriatic acid, into chlorine and hydro-
110 NAMES AND PROPOSITIONS.
gen, caused the second property, composition from a base and oxygen, to
be excluded from the connotation. The same discovery fixed the attention
of chemists upon hydrogen as an important element in acids ; and mora
recent discoveries having led to the recognition of its presence in sulphuric,
nitric, and many other acids, where its existence was not previously sus-
pected, there is now a tendency to include the presence of this element in
the connotation of the word. But carbonic acid, silica, sulphurous acid,
have no hydrogen in their composition ; that property can not, therefore,
be connoted by the term, unless those substances are no longer to be con-
sidered acids. Causticity and fluidity have long since been excluded from,
the characteristics of the class, by the inclusion of silica and many other
substances in it ; and the formation of neutral bodies by combination with
alkalis, together with such electro-chemical peculiarities as this is supposed
to imply, are now the only differentiae which form the fixed connotation of
the word Acid, as a term of chemical science.
What is true of the definition of any term of science, is of course true of
the definition of a science itself; and accordingly (as observed in the In-
troductdry Chapter of this work), the definition of a science must neces-
sarily be progressive and provisional. Any extension of knowledge or al-
teration in the current opinions respecting the subject-matter, may lead to
a change more or less extensive in the particulars included in the science ;
and its composition being thus altered, it may easily happen that a different
set of characteristics will be found better adapted as differentiae for defin-
ing its name.
In the same manner in which a special or technical definition has for its
object to expound the artificial classification out of which it grows; the
Aristotelian logicians seem to have imagined that it was also the business
of ordinary definition to expound the ordinary, and what they deemed the
natural, classification of things, namely, the division of them into Kinds;
and to show the place which each Kind occupies, as superior, collateral, or
subordinate, among other Kinds. This notion would account for the rule
that all definition must necessarily be per genus et differentiam, and would
also explain why a single differentia was deemed sufficient. But to ex-
pound, or express in words, a distinction of Kind, has already been shown
to be an impossibility : the very meaning of a Kind is, that the properties
which distinguish it do not grow out of one another, and can not therefore
be set forth in words, even by implication, otherwise than by enumerating
them all : and all are not known, nor are ever likely to be so. It is idle,
therefore, to look to this as one of the purposes of a definition : while, if it
be only required that the definition of a Kind should indicate what kinds
include it or are included by it, any definitions which expound the connota-
tion of the names will do this : for the name of each class must necessarily
connote enough of its properties to fix the boundaries of the class. If the
definition, therefore, be a full statement of the connotation, it is all that a
definition can be required to be.*
* Professor Bain, in his Logic, takes a peculiar view of Definition. He holds (i., 71) with
the present work, that "the definition in its full import, is the sum of all the properties con-
noted by the name ; it exhausts the meaning of a word." But he regards the meaning of ft
general name as including, not indeed all the common properties of the class named, but all
of them that are ultimate properties, not resolvable into one another. " The enumeration of
the attributes of oxygen, of gold, of man, should be an enumeration of the final (so far as can
be made out), the underivable, powers or functions of each," and nothing less than this is a
complete Definition (i., 75). An independent property, not derivable from other properties,
even if previously unknown, yet as soon as discovered becomes, according to him, part of tha
DEFINITION. Ill
§ S. Of the two incomplete and popular modes of definition, and in wliat
they differ from the complete or philosophical mode, enough has now been
said. We shall next examine an ancient doctrine, once generally prevalent
and still by no means exploded, which I regard as the source of a great part
of the obscurity hanging over some of the most important processes of the
understanding in the pursuit of truth. According to this, the definitions
of which we have now treated are only one of two sorts into which defini-
tions may be divided, viz., definitions of names, and definitions of things.
The former are intended to explain the meaning of a term ; the latter, the
nature of a thing ; the last being incomparably the most important.
This opinion was held by the ancient philosophers, and by their follow-
ers, with the exception of the Nominalists; but as the spirit of modern
metaphysics, until a recent period, has been on the whole a Nominalist
spirit, the notion of definitions of things has been to a certain extent in
abeyance, still continuing, however, to breed confusion in logic, by its con-
sequences indeed rather than by itself. Yet the doctrine in its own proper
form now and then breaks out, and has appeared (among other places)
where it was scarcely to be expected, in a justly admired word, Archbishop
Whately's Logic* In a review of that work published by me in the West-
meaning of the term, and should be included in the definition. "When we are told that dia-
mond, which we know to be a transparent, glittering, hard, and high-priced substance, is com-
posed of carbon, and is combustible, we must put these additional properties on the same level
as the rest ; to us they are henceforth connoted by the name " (i., 73). Consequently the
propositions that diamond is composed of carbon, and that it is combustible, are regarded by
Mr. Bain as merely verbal propositions. He carries this doctrine so far as to say that unless
mortality can be shown to be a consequence of the ultimate laws of animal organization, moi'-
tality is connoted by man, and " Man is Mortal " is a merely verbal proposition. And one of
the peculiarities (I think a disadvantageous peculiarity) of his able and valuable treatise, is
the large number of propositions requiring proof, and learned by experience, which, in con-
formity with this doctrine, he considers as not real, but verbal, propositions.
The objection I have to this language is that it confounds, or at least confuses, a much
more important distinction than that which it draws. The only reason for dividing Proposi-
tions into real and verbal, is in order to discriminate propositions which convey information
about facts, from those which do not. A proposition which affirms that an object has a given
attribute, while designating the object by a name which already signifies the attribute, adds
no information to that which was already possessed by all who understood the name. But
when this is said, it is implied that, by the signification of a name, is meant the signification
attached to it in the common usage of life. I can not think we ought to say that the meaning
of a word includes matters of fact which are unknown to every person who uses the word un-
less he has learned them by special study of a particular department of Nature ; or that because
a few persons are aware of these matters of fact, the affirmation of them is a proposition con-
veying no information. I hold that (special scientific connotation apart) a name means, or
connotes, only the properties which it is a mark of in the general mind ; and that in the case
of any additional properties, however uniformly found to accompany tliese, it remains possible
that a thing which did not possess the properties might still be thought entitled to the name.
Buminant, according to Mr. Bain's use of language, connotes cloven-hoofed, since the two
properties are always found together, and no connection has ever been discovered between
them: but ruminant does not mean cloven-hoofed; and were an animal to be discovered
which chews the cud, but has its feet undivided, I venture to say that it would still be called
ruminant.
* In the fuller discussion which Archbishop Whately has given to this subject in his later
editions, he almost ceases to regard the definitions of names and those of things as, in any im-
portant sense, distinct. He seems (9th ed., p. 145) to limit the notion of a Eeal Definition to
one which "explains anything more of the nature of the thing than is implied in the name;"
(including under the word " implied," not only what the name connotes, but every thing which
can be deduced by reasoning from the attributes connoted). Even this, as he adds, is usually
called not a Definition, but a Description ; and (as it seems to me) rightly so called. A De-
scription, I conceive, can only be ranked among Definitions, when taken (as in the case of the
zoological definition of man) to fulfill the true office of a Definition, by declaring the connota-
tion given to a word in some special use, as a term of science or art : which special conno-
112 NAMES AND PROPOSITIONS.
minster Review for January, 1828, and containing some opinions which I
no longer entertain, I find the following observations on the question now
before us ; observations with which my present view of that question is
still sufficiently in accordance.
" The distinction between nominal and real definitions, between defini-
tions of words and what are called definitions of things, though conforma-
ble to the ideas of most of the Aristotelian logicians, can not, as it appears
to us, be maintained. We apprehend that no definition is ever intended to
' explain and unfold the nature of a thing.' It is some confirmation of our
opinion, that none of those writers who have thought that there were dejBni-
tions of things, have ever succeeded in discovering any criterion by which
the definition of a thing can be distinguished from any other proposition
relating to the thing. The definition, they say, unfolds the nature of the
thing: but no definition can unfold its whole nature; and every proposi-
tion in which any quality whatever is predicated of the thing, unfolds some
part of its nature. The true state of the case we take to be this. All
definitions are of names, and of names only ; but, in some definitions, it is
clearly apparent, that nothing is intended except to explain the meaning of
the word ; while in others, besides explaining the meaning of the word, it
is intended to be implied that there exists a thing, cori-esponding to the
word. Whether this be or be not implied in any given case, can not be
collected from the mere form of the expression. 'A centaur is an animal
with the upper parts of a man and the lower parts of a horse,' and 'A tri-
angle is a rectilineal figure with three sides,' are, in form, expressions pre-
cisely similar; although in the former it is not implied that any thing, con-
formable to the term, really exists, while in the latter it is ; as may be seen
by substituting in both definitions, the word means for is. In the first
expression, 'A centaur means an animal,' etc., the sense would remain un-
changed: in the second, 'A triangle means,' etc., the meaning would be al-
tered, since it would be obviously impossible to deduce any of the truths
of geometry from a proposition expressive only of the manner in which we
intend to employ a particular sign.
"There are, therefore, expressions, commonly passing for definitions,
which include in themselves more than the mere explanation of the meaning
of a term. But it is not correct to call an expression of this sort a peculiar
kind of definition. Its difference from the other kind consists in this, that
it is not a definition, but a definition and something more. The definition
above given of a triangle, obviously comprises not one, but two proposi-
tions, perfectly distinguishable. The one is, ' There may exist a figure,
bounded by three straight lines ;' the other, ' And this figure may be termed
a triangle.' The former of these propositions is not a definition at all : the
tation of course would not be expressed by the proper definition of the word in its ordinary
employment.
Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately, understands by a
Eeal Definition one which contains less than the Nominal Definition, provided only that what
it contains is sufiicient for distinction. "By real definition I mean such an explanation of
the word, be it the whole of the meaning or only part, as will be sufficient to separate the
things contained under that word from all others. Thus the following, I believe, is a complete
definition of an elephant : An animal which naturally drinks by drawing the water into its
nose, and then spurting it into its mouth." — Formal Logic, p. 36. Mr. De Morgan's gen-
eral proposition and his example are at variance ; for the peculiar mode of drinking of the
elephant certainly forms no part of the meaning of the word elephant. It could not be said,
because a person happened to be ignorant of this property, that he did not know what an
elephant means.
DEFINITION. 113
latter is a mere nominal definition, or explanation of the use and applica-
tion of a term. The first is susceptible of truth or falsehood, and may
therefore be made the foundation of a train of reasoning. The latter can
neither be true nor false ; the only character it is susceptible of is that of
conformity or disconformity to the ordinary usage of language."
There is a real distinction, then, between definitions of names, and what
are erroneously called definitions of things ; but it is, that the latter, along
with the meaning of a name, covertly asserts a matter of fact. This covert
assertion is not a definition, but a postulate. The definition is a mere iden-
tical proposition, which gives information only about the use of language,
and from which no conclusions affecting matters of fact can possibly be
drawn. The accompanying postulate, on the other hand, affirms a fact,
which may lead to consequences of every degree of importance. It affirms
the actual or possible existence of Things possessing the combination of
attributes set forth in the definition ; and this, if true, may be foundation
sufficient on which to build a whole fabric of scientific truth.
We have already made, and shall often have to repeat, the remark, that
the philosophers who overthrew Realism by no means got rid of the con-
sequences of Realism, but retained long afterward, in their own philosophy,
numerous propositions which could only have a rational meaning as part
of a Realistic system. It had been handed down from Aristotle, and prob-
ably from earlier times, as an obvious truth, that the science of Geometry
is deduced from definitions. This, so long as a definition was considered
to be a proposition " unfolding the nature of the thing," did well enough.
But Hobbes followed, and rejected utterly the notion that a definition de-
clares the nature of the thing, or does any thing but state the meaning of
a name ; yet he continued to affirm as broadly as any of his predecessors,
that the apx^i, pi'incipia, or original premises of mathematics, and even of
all science, are definitions ; producing the singular paradox, that systems
of scientific truth, nay, all truths whatever at which we arrive by reasoning,
a>-e deduced from the arbitrary conventions of mankind concerning the sig-
nification of words.
To save the credit of the doctrine that definitions are the premises of
scientific knowledge, the proviso is sometimes added, that they are so only
under a certain condition, namely, that they be framed conformably to the
phenomena of nature ; that is, that they ascribe such meanings to terms as
shall suit objects actually existing. But this is only an instance of the at-
tempt so often made, to escape from the necessity of abandoning old lan-
guage after the ideas which it expresses have been exchanged for contrary
ones. From the meaning of a name (we are told) it is possible to infer
physical facts, provided the name has corresponding to it an existing thing.
But if this proviso be necessary, from which of the two is the inference
really drawn ? From the existence of a thing having the properties, or
from the existence of a name meaning them ?
Take, for instance, any of the definitions laid down as premises in Euclid s
Elements ; the definition, let us say, of a circle. This, being analyzed, con-
sists of two propositions ; the one an assumption with respect to a matter
of fact, the other a genuine definition. " A figure may exist, having all the
points in the line which bounds it equally distant from a single point with-
in it :" " Any figure possessing this property is called a circle." Let us
look at one of the demonstrations which are said to depend on this defini-
tion, and observe to which of the two propositions contained in it the deni-
onstration reallv anneals. " About the centre A, describe the circle BCD.
114 NAMES AND PROPOSITIONS.
Here is an assumption that a figure, such as the definition expresses, map.
be described ; which is no other than the postulate, or covert assumption,
involved in the so-called definition. But whether that figure be called a.
circle or not is quite immaterial. The purpose would be as well answered,
in all respects except brevity, were we to say, " Through the point B, draw
a line returning into itself, of which every point shall be at an equal dis-
tance from the point A." By this the definition of a circle would be got
rid of, and rendered needless ; but not' the postulate implied in it ; without
that the demonstration could not stand. The circle being now described,
let us proceed to the consequence. " Since B C D is a circle, the radius
B A is equal to the radius C A." B A is equal to C A, not because B C I>
is a circle, but because B C D is a figure with the radii equal. Our war-
rant for assuming that such a figure about the centre A, with the radius^
B A, may be made to exist, is the postulate. Whether the admissibility
of these postulates rests on intuition, or on proof, may be a matter of dis-
pute ; but in either case they are the premises on which the theorems de-
pend ; and while these are retained it would make no difference in the cer-
tainty of geometrical truths, though every definition in Euclid, and every
technical term therein defined, were laid aside.
It is, perhaps, superfluous to dwell at so much length on what is so near-
ly self-evident ; but when a distinction, obvious as it may appear, has been
confounded, and by powerful intellects, it is better to say too much than
too little for the purpose of rendering such mistakes impossible in future.
I will, therefore detain the reader while I point out one of the absurd con-
sequences flowing from the supposition that definitions, as such, are the
premises in any of our reasonings, except such as relate to words only. If
this supposition were true, we might argue correctly from true premises,
and arrive at a false conclusion. We should only have to assume as a
premise the definition of a nonentity ; or rather of a name which has nO'
entity corresponding to it. Let this, for instance, be our definition :
A dragon is a serpent breathing flame.
This proposition, considered only as a definition, is indisputably correct.
A dragon is a serpent breathing flame : the word means that. The tacit
assumption, indeed (if there were any such understood assertion), of the ex-
istence of an object with properties corresponding to the definition, would,,
in the present instance, be false. Out of this definition we may carve the
premises of the following syllogism :
A dragon is a thing which breathes flame :
A dragon is a serpent :
From which the conclusion is.
Therefore some serpent or serpents breathe flame :
an unexceptionable syllogism in the first mode of the third figure, in which
both premises are true and yet the conclusion false ; which every logician
knows to be an absurdity. The conclusion being false and the syllogism
correct, the premises can not be true. But the premises, considered as
parts of a definition, are true. Therefore, the premises considered as parts
of a definition can not be the real ones. The real premises must be—
A dragon is a really existing thing which breathes flame :
A dragon is a really existing serpent :
which implied premises being false, the falsity of the conclusion presents
no absurdity.
If we would determine what conclusion follows from the same ostensible
premises when the tacit assumption of real existence is left out, let us, ac-
DEFINITION. 115
cording to the recommendation in a previous page, substitute means for is.
"We then have —
Dragon is a word meaning a thing which breathes flame :
Dragon is a word meaning a serpent :
From which the conclusion is,
Some word or words which mean a serpent, also mean a thing which
breathes flame :
where the conclusion (as well as the premises) is true, and is the only kind
of conclusion which can ever follow from a definition, namely, a proposition
relating to the meaning of words.
There is still another shape into which we may transform this syllogism.
We may suppose the middle term to be the designation neither of a thing
nor of a name, but of an idea. We then have —
The idea of a dragon is an idea of a thing which breathes flame :
The idea of a dragon is an idea of a serpent :
Therefoi-e, there is an idea of a serpent, which is an idea of a
thing breathing flame.
Here the conclusion is true, and also the premises ; but the premises are
not definitions. They are propositions afiirming that an idea existing in
the mind, includes certain ideal elements. The truth of the conclusion fol-
lows from the existence of the psychological phenomenon called the idea of
a dragon ; and therefore still from the tacit assumption of a matter of fact.*
When, as in this last syllogism, the conclusion is a proposition respecting
an idea, the assumption on which it depends may be merely that of the ex-
istence of an idea. But when the conclusion is a proposition concerning a
Thing, the postulate involved in the definition which stands as the apparent
premise, is the existence of a thing conformable to the definition, and not
merely of an idea conformable to it. This assumption of real existence we
always convey the impression that we intend to make, when we profess to
define any name which is already known to be a name of really existing
objects. On this account it is, that the assumption was not necessarily
implied in the definition of a dragon, while there was no doubt of its be-
ing included in the definition of a circle.
• In the only attempt which, so far as I know, has been made to refute the preceding argu-
mentation, it is maintained that in the first foi-m of the syllogism,
A dragon is a thing which breathes flame,
A dragon is a serpent.
Therefore some serpent or serpents breathe flame,
"there is just as much truth in the conclusion as there is in the premises, or rather, no more
in the latter than in the former. If the general name serpent includes both real and imaginaiy
serpents, there is no falsity in the conclusion ; if not, there is falsity in the minor premise. "
Let us, then, tiy to set out the syllogism on the hypothesis that the name serpent includes
imaginaiy serpents. We shall find that it is now necessary to alter the predicates ; for it can
not be asserted that an imaginary creature breathes flame ; in predicating of it such a fact, we
assert by the most positive implication that it is real, and not imaginary. The conclusion must
run thus, "Some sei-pent or serpents either do or are imagined to breathe flame." And to
prove this conclusion by the instance of dragons, the premises must be, A dragon is imagined
as breathing flame. A dragon is a (real or imaginary) serpent : from which it undoubtedly
follows, that there are serpents which are imagined to breathe flame ; but the major premise
is not a definition, nor part of a definition ; which is all that I am concerned to prove.
Let us now examine the other assertion — that if the word serpent stands for none but real
serpents, the minor premise (a dragon is a serpent) is false. This is exactly what I have my-
self said of the premise, considered as a statement of fact : but it is not false as part of the
definition of a dragon ; and since the premises, or one of them, must be false (the conclusion
being so), the real premise can not be the definition, which is true, but the statement of fact,
which is false.
116 NAMES AND PKOPOSITIONS.
§ 6. One of the circumstances which have contvibuted to keep up the
notion, that demonstrative truths follow from definitions rather than from
the postulates implied in those definitions, is, that the postulates, even in
those sciences which are considered to surpass all others in demonstrative
certainty, are not always exactly true. It is not true that a circle exists, or
can be described, which has all its radii exactly equal. Such accuracy ia
ideal only; it is not found in nature, still less can it be reajized by art.
People had a difiiculty, therefore, in conceiving that the most certain of all
conclusions could rest on premises which, instead of being certainly true,
are certainly not true to the full extent asserted. This apparent paradox
will be examined when we come to ti'eat of Demonstration ; where we shall
be able to show that as much of the postulate is true, as is required to sup-
port as much as is true of the conclusion. Philosophers, however, to whom
this view had not occurred, or whom it did not satisfy, have thought it in-
dispensable that there should be found in definitions something more cer-
tain, or at least more accurately true, than the implied postulate of the real
existence of a corresponding object. And this something they flattered
themselves they had found, when they laid it down that a definition is a
statement and analysis not of the mere meaning of a word, nor yet of the
nature of a thing, but of an idea. Thus, the proposition, "A circle is a
plane figure bounded by a line all the points of which are at an equal dis-
tance from a given point within it,'' was considered by them, not as an as-
sertion that any real circle has that property (which would not be exactly
true), but that we conceive a circle as having it; that our abstract idea of
a circle is an idea of a figure with its radii exactly equal.
Conformably to this it is said, that the subject-matter of mathematics,
and of every other demonstrative science, is not things as they really exist,
but abstractions of the mind. A geometrical line is a line without breadth ;
but no such line exists in nature; it is a notion merely suggested to the
mind by its experience of nature. The definition (it is said) is a definition
of this mental line, not of any actual line : and it is only of the mental line,
not of any line existing in nature, that the theorems of geometry are ac-
curately true.
Allowing this doctrine respecting the nature of demonstrative truth to
be correct (which, in a subsequent place, I shall endeavor to prove that it
is not) ; even on that supposition, the conclusions which seem to follow
from a definition, do not follow from the definition as such, but from an
implied postulate. Even if it be true that there is no object in nature an-
swering to the definition of a line, and that the geometrical properties of
lines are not true of any lines in nature, but only of the idea of a line ; the
definition, at all events, postulates the real existence of such an idea : it as-
sumes that the mind can frame, or rather has framed, the notion of length
without breadth, and without any other sensible property whatever. To
me, indeed, it appears that the mind can not form any such notion ; it can
not conceive length without breadth ; it can only, in contemplating objects,
attend to their length, exclusively of their other sensible qualities, and so
determine what properties may be predicated of them in virtue of their
length alone. If this be true, the postulate involved in the geometrical
definition of a line, is the real existence, not of length without breadth, but
merely of length, that is, of long objects. This is quite enough to support
all the truths of geometry, since every property of a geometrical line is
really a property of all physical objects in so far as possessing length. But
even what I hold to be the false doctrine on the subject, leaves the conclu-
DEFINITION. Ill
sion that our reasonings are grounded on the matters of fact postulated in
definitions, and not on the definitions themselves, entirely unaffected ; and
accordingly this conclusion is one which I have in common with Dr. Whe-
well, in his Philosophy of the Inductive Sciences: though, on the nature
of demonstrative truth. Dr. Whe well's opinions are greatly at variance with
mine. And here, as in many other instances, I gladly acknowledge that his
writings ai'e eminently serviceable in clearing from confusion the initial
steps in the analysis of the mental processes, even where his views respect-
ing the ultimate analysis are such as (though with unfeigned respect) I can
not but regard as fundamentally erroneous.
§ T. Although, according to the opinion here presented. Definitions are
properly of names only, and not of things, it does not follow from this that
definitions are arbitrary. How to define a name, may not only be an in-
quiry of considerable difficulty and intricacy, but may involve considera-
tions going deep into the nature of the things which are denoted by the
name. Such, for instance, are the inquiries which form the subjects of the
most important of Plato's Dia,logues; as, "What is rhetoric?" the topic o'f
the Gorgias, or, "What is justice?" that of the Republic. Such, also, is
the question scornfully asked by Pilate, " What is truth ?" and the funda^
mental question with speculative moralists in all ages, " What is virtue ?"
It would be a mistake to represent these difficult and noble inquiries as
having nothing in view beyond ascertaining the conventional meaning of
a name. They are inquiries not so much to determine what is, as what
should be, the meaning of a name ; which, like other practical questions of
terminology, requires for its solution that we should enter, and sometimes
enter very deeply, into the properties not merely of names but of the
things named.
Although the meaning of every concrete general name resides in the at-
tributes which it connotes, the objects were named before the attributes ;
as appears from the fact that in all languages, abstract names are mostly
compounds or other derivatives of the concrete names which correspond to
them. Connotative names, therefore, were, after proper names, the first
which were used : and in the simpler cases, no doubt, a distinct connotation
was present to the minds of those who first used the name, and was dis-
tinctly intended by them to be conveyed by it. The first person who used
the word white, as applied to snow or to any other object, knew, no doubt,
very well what quality he intended to predicate, and had a perfectly dis-
tinct conception in his mind of the attribute signified by the name.
But where the resemblances and differences on which our classifications
are founded are not of this palpable and easily determinable kind ; especial-
ly where they consist not in any one quality but in a number of qualities,
the effects of which, being blended together, are not very easily discrimi-
nated, and referred each to its true source ; it often happens that names
are applied to namable objects, with no distinct connotation present to the
minds of those who apply them. They are only influenced by a general
resemblance between the new object and all or some of the old familiar
objects which they have been accustomed to call by that name. This, as
we have seen, is the law which even the mind of the philosopher must fol-
low, in giving names to the simple elementary feelings of our nature : but,
where the things to ba named are complex wholes, a philosopher is not
content with noticing a general resemblance; he examines what the resem-
blance consists in : and he only gives the same name to things which re-
118 NAMES AND PROPOSITIONS.
semble one another in the same definite particulars. The philosopher,
therefore, habitually employs his general names with a definite connota-
tion. But language was not made, and can only in some small degree be
mended, by philosophers. In the minds of the real arbiters of language,
general names, especially where the classes they denote can not be brought
before the tribunal of the outward senses to be identified and discriminated,
connote little more than a vague gross resemblance to the things which
they were earliest, or have been most, accustomed to call by those names.
When, for instance, ordinary persons predicate the words just or unjust
of any action, noble or mean of any sentiment, expression, or demeanor,
statesman or cliarlatan of any personage figuring in politics, do they mean
to affirm of those various subjects any determinate attributes, of whatever
kind ? No : they merely recognize, as they think, some likeness, more or
less vague and loose, between these and some other things which they
have been accustomed to denominate or to hear denominated by those ap-
pellations.
_ Language, as Sir James Mackintosh used to say of governments, "is not
made, but grows." A name is not imposed at once and by previous pur-
pose upon a class of objects, but is first applied to one thing, and then ex-
tended by a series of transitions to another and another. By this process
(as has been remarked by several writers, and illustrated with great force
and clearness by Dngald Stewart in his Philosophical Essays) a name not
unfrequently passes by successive links of resemblance from one object to
another, until it becomes applied to things having nothing in common with
the first things to which the name was given ; which, however, do not, for
that reason, drop the name; so that it at last denotes a confused huddle of
objects, having nothing whatever in common ; and connotes nothing, not
even a vague and general resemblance. When a name has fallen into this
state, in which by predicating it of any object we assert literally nothing
about the object, it has become unfit for the purposes either of thought or
of the communication of thought; and dan only be made sei-viceable by
stripping it of some part of its multifarious denotation, and confining it to
objects possessed of some attributes in common, which it may be made to
connote. Such are the inconveniences of a language which " is not made,
but grows." Like the governments which are in a similar case, it may be
compared to a road which is not made but has made itself : it requires con-
tinual mending in order to be passable.
From this it is already evident, why the question respecting the defini-
tion of an abstract name is often one of so much difficulty. The question,
What is justice? is, in other words, What is the attribute which mankind
mean to predicate when they call an action just? To which the first an-
swer is, that having come to no precise agreement on the point, they do
not mean to predicate distinctly any attribute at all. Nevertheless, all be-
lieve that there is some common attribute belonging to all the actions which
they are in the habit of calling just. The question, then must be, whether
there is any such common attribute ? and, in the first place, whether man-
kind agree sufficiently with one another as to the particular actions which
they do or do not call just, to render the inquiry, what quality those ac-
tions have-in common, a possible one : if so, whether the actions really have
any quality in common ; and if they have, what it is. Of these three, the
first alone is an inquiry into usage and convention ; the other two are inqui-
ries into matters of fact. And if the second question (whether the actions
form a class at all) has been answered negatively, there remains a fourth,
DEFINITION. 119
•often more arduous than all the rest, namely, how best to form a class arti-
:ficially, which the name may denote.
And here it is fitting to remark, that the study of the spontaneous growth
of languages is of the utmost importance to those who would logically re-
model them. The classifications rudely made by established language, when
retouched, as they almost all require to be, by the hands of the logician,
are often themselves excellently suited to his purposes. As compared with
the classifications of a philosopher, they are like the customary law of a
country, which has grown up as it were spontaneously, compared with laws
methodized and digested into a code : the former are a far less perfect in-
strument than the latter; but being the result of a long, though unscien-
tific, course of experience, they contain a mass of materials which may be
made very usefully available in the formation of the systematic body of
written law. In like manner, the established grouping of objects under a
■common name, even when founded only on a gross and general resemblance,
is evidence, in the first place, that the resemblance is obvious, and therefore
•considerable; and, in the next place, that it is a resemblance, which has
struck great numbers of persons during a series of years and ages. Even
when a name, by successive extensions, has come to be applied to things
among which there does not exist this gross resemblance common to them
all, still at every step in its progress we shall find such a resemblance. And
these transitions of the meaning of words are often an index to real con-
nections between the things denoted by them, which might otherwise escape
the notice of thinkers ; of those at least who, from using a different lan-
guage, or from any difference in their habitual associations, have fixed their
attention in preference on some other aspect of the things. The history of
philosophy abounds in examples of such oversights, committed for want of
perceiving the hidden link that connected together the seemingly disparate
meanings of some ambiguous word.*
Whenever the inquiry into the definition of the name of any real object
-consists of any thing else than a mere comparison of authorities, we tacit-
ly assume that a meaning must be found for the name, compatible with its
continuing to denote, if possible all, but at any rate the greater or the more
important part, of the things of which it is commonly predicated. The in-
quiry, therefore, into the definition, is an inquiry into the resemblances and
-differences among those things : whether there be any resemblance running
through them all ; if not, through what portion of them such a general re-
semblance can be traced : and finally, what are the common attributes, the
possession of which gives to them all, or to that portion of them, the char-
acter of resemblance which has led to their being classed together. When
these common attributes have been ascertained and specified, the name
which belongs in common to the resembling objects acquires a distinct in-
* "Pew people" (I hare said in another place) "have reflected how great a knowledge
of Things is required to enable a man to aifirm that any given argument turns wholly upon
words. There is, perhaps, not one of the leading terms of philosophy which is not used in
almost innumerable shades of meaning, to express ideas more or less widely different from
one another. Between two of these ideas a sagacious and penetrating mind will discern, as
it were intuitively, an unobvious link of connection, upon which, though perhaps unable to
give a logical account of it, he will found a perfectly valid argument, which his critic, not
having so keen an insight into the Things, will mistake for a fallacy turning on the double
meaning of a term. And the greater the genius of him who thus safely leaps over the chasm,
the greater will probably be the crowing and vainglory of the mere logician, who, hobbling
■after him, evinces his own superior wisdom by pausing on its brink, and giving up as desper-
ate his proper business of bridging it over."
120 NAMES AND PROPOSITIONS.
stead of a vague connotation ; and by possessing this distinct connotation,
becomes susceptible of definition.
In giving a distinct connotation to the general name, the philosopher will
endeavor to fix upon such attributes as, while they are common to all the
things usually denoted by the name, are also of greatest importance in them-
selves ; either directly, or from the number, the conspicuousness, or the in-
teresting character, of the consequences to which they lead. He will select,
as far as possible, such differentiae as lead to the greatest number of inter-
esting propria. For these, rather than the more obscure and recondite
quaUties on which they often depend, give that general character and as-
pect to a set of objects, which determine the groups into which they natu-
rally fall. But to penetrate to the more hidden agreement on which these
obvious and superficial agreements depend, is often one of the most diffi-
cult of scientific problems. As it is among the most difllicult, so it seldom
fails to be among the most important. And since upon the result of this
inquiry respecting the causes of the properties of a class of things, there in-
cidentally depends the question what shall be the meaning of a woi-d ; some
of the most profound and most valuable investigations which philosophy
presents to us, have been introduced by, and have offered themselves under
the guise of, inquiries into the definition of a name.
BOOK II.
OF REASONING.
^ &iiop,ff^Ev<^v h nvToiv Xsyoi^iv vSr,, Sti riviov, Kai ttoti, rat wuie yivirai wag mWoyuTuoc
v<,Tepov St XiKTBOv TTEpt a,ro5i.?£a.f nporipov ydp nepi ,Tv\\o^iO^Lov \eKTkov,v wipi dnJsd-
*"?? ' ^"' ';'' "aOoXovjuMoy uyai tov avWoyiG^ov. H p^v ydp d7r65«?.c, miKKoyiauoc nc 6
itvXKoytanos Si ov^ag,airoSults.—ABiST:.,Analyt. Prior., \A.,ca.f.^. i r :. <.
CHAPTER I.
OF DTFEEENCE, OK REASONING, IN GENERAL.
§1. In the preceding Book, we have been occupied not with the nature
of Proof, but with the nature of Assertion : the import conveyed by a Prop-
osition, whether that Proposition be true or false ; not the means by which
to discriminate true from false Propositions. The proper subject, however,
of Logic is Proof. Before we could understand what Proof is, it was nec-
essary to understand what that is to which proof is applicable ; what that
is which can be a subject of belief or disbelief, of affirmation or denial ;
what, in short, the different kinds of Propositions assert.
_ This preliminary inquiry we have prosecuted to a definite result. Asser-
tion, in the first place, relates either to the meaning of words, or to some
property of the things which words signify. Assertions respecting the
meaning of words, among which definitions are the most important, hold a
place, and an indispensable one, in philosophy ; but as the meaning of words
is essentially arbitrai-y, this class of assertions are not susceptible of truth
or falsity, nor therefore of proof or disproof. Assertions respecting Things,
or what may be called Real Propositions, in contradistinction to verbal
ones, are of various sorts. We have analyzed the import of each sort, and
have ascertained the nature of the things they relate to, and the nature of
what they severally assert respecting those things. We found that what-
ever be the form of the proposition, and whatever its nominal subject or
predicate^ the real subject of every proposition is some one or more facts
or phenomena of consciousness, or some one or more of the hidden causes
or powers to which we ascribe those facts ; and that what is predicated or
asserted, either in the affirmative or negative, of those phenomena or those
powers, is always either Existence, Order in Place, Order in Time, Causa-
tion, or Resemblance. This, then, is the theory of the Import of Proposi-
tions, reduced to its ultimate elements : but there is another and a less ab-
struse expression for it, which, though stopping short in an earlier stage of
the analysis, is sufficiently scientific for many of the purposes for which
such a geu.eral expression is required. This expression recognizes the com-
monly received distinction between Subject and Attribute, and gives the
following as the analysis of the meaning of propositions: — Every Proposi-
122 KEASONING.
tion asserts, that some given subject does or does not possess some attri-
bute; or that some attribute is or is not (either in all or in some portioiii
of the subjects in which it is met with) conjoined with some other attri-
bute.
We shall now for the present take our leave of this portion of our in-
quiry, and proceed to the peculiar problem of the Science of Logic, name-
ly, how the assertions, of which we have analyzed the import, are proved
or disproved ; such of them, at least, as, not being amenable to direct con-
sciousness or intuition, are appropriate subjects of proof.
We say of a fact or statement, that it is proved, when we believe its truth
by reason of some other fact or statement from which it is said to follow.
Most of the propositions, whether affirmative or negative, universal, partic-
ular, or singular, which we believe, are not believed on their own evidence,
but on the ground of something previously assented to, from which they
are said to be inferred. To infer a proposition from a previous proposi-
tion or propositions ; to give credence to it, or claim credence for it, as a
conclusion from something else ; is to reason, in the most extensive sense-
of the terra. There is a narrower sense, in which the name reasoning is-
confined to the form of inference which is termed ratiocination, and of
which the syllogism is the general type. The reasons for not conforming
to this restricted use of the term were stated in an earlier stage of our in-
quiry, and additional motives will be suggested by the considerations on.
which we are now about to enter.
§ 2. In proceeding to take into consideration the cases in which infer-
ences can legitimately be drawn, we shall first mention some cases in which
the inference is apparent, not real ; and which require notice chiefly that
they may not be confounded with cases of inference properly so called.
This occurs when the proposition ostensibly inferred from another, appears^
on analysis to be merely a repetition of the same, or part of the same, as-
sertion, which was contained in the first. All the cases mentioned in books-
of Logic as examples of equipollency or equivalence of propositions, are
of this nature. Thus, if we were to argue, No man is incapable of reason,,
for every man is rational ; or. All men are mortal, for no man is exempt
from death ; it would be plain that we were not proving the proposition,,
but only appealing to another mode of wording it, which may or may not
be more readily comprehensible by the hearer, or better adapted to suggest
the real proof, but which contains in itself no shadow of proof.
Another case is where, from a universal proposition, we affect to infer
another which differs from it only in being particular : as All A is B, there-
fore Some A is B : No A is B, therefore Some A is not B. This, too, is not
to conclude one proposition from another, but to repeat a second time some-
thing which had been asserted at first; with the difference, that we do not
here repeat the whole of the previous assertion, but only an indefinite part
of it.
A third case is where, the antecedent having affirmed a predicate of a.
given subject, the consequent affirms of the same subject something already
connoted by the former predicate : as, Socrates is a man, therefore Socrates
is a living creature ; where all that is connoted by living creature was af-
firmed of Socrates when he was asserted to be a man. If the propositions
are negative, we must invert their order, thus : Socrates is not a living crea-
ture, therefore he is not a man ; for if we deny the less, the greater, whick
includes it, is already denied by implication. These, therefore, are not reat-
INFERENCE IN GENERAL. 123
ly cases of inference ; and yet the trivial examples by which, in manuals of
Logic, the rules of the syllogism are illustrated, are often of this ill-chosen
kind ; formal demonstrations ol conclusions to which whoever understands
the terms used in the statement of the data, has already, and consciously,
assented.*
The most complex case of this sort of apparent inference is what is called
the Conversion of propositions; which consists in turning the predicate
into a subject, and the subject into a predicate, and framing out of the same
terms thus reversed, another proposition, which must be true if the former
is true. Thus, from the particular affirmative proposition. Some A is B,
we may infer that Some B is A. From the universal negative, No A is B,
we may conclude that No B is A. From the universal affirmative proposi-
tion, All A is B, it can not be inferred that all B is A ; though all water is
liquid, it is not implied that all liquid is water ; but it is implied that some
liquid is so ; and hence the proposition, All A is B, is legitimately convert-
ible into Some B is A. This process, which converts a universal propo-
sition into a particular, is termed conversion p&r accidens. From the prop-
osition, Some A is not B, we can not even infer that some B is not A;
though some men are not Englishmen, it does not follow that some English-
men are not men. The only mode usually recognized of converting a par-
ticular negative proposition, is in the form. Some A is not B, therefore
something which is not B is A ; and this is termed conversion by contra-
position. In this case, however, the predicate and subject ai-e not merely
reversed, but one of them is changed. Instead of [A] and [B], the terms
of the new proposition are [a thing which is not B], and [A]. The origi-
nal proposition. Some A is not B, is first' changed into a proposition equi-
pollent with it, Some A is " a thing which is not B ;" and the proposition,
being now no longer a particular negative, but a particular affirmative, ad-
mits of conversion in the first mode, or as it is called, simple conversion.!
In all these cases there is not really any inference; there is in the con--
clusion no new truth, nothing but what was already asserted in the prem-
ises, and obvious to whoever apprehends them. The fact asserted in the
conclusion is either the very same fact, or part of the fact, asserted in the
original proposition. This follows from our previous analysis of the Im-
port of Propositions. When we say, for example, that some lawful sov-
ereigns are tyrants, what is the meaning of the assertion ? That the attri-
butes connoted by the term " lawful sovereign," and the attributes connoted
by the term " tyrant," sometimes co-exist in the same individual. Now this
is also precisely what we mean, when we say that some tyrants are lawful
sovereigns ; which, therefore, is not a second proposition inferred from the
first, any more than the English translation of Euclid's Elements is a col-
lection of theorems different from and consequences of, those contained in
the Greek original. Again, if we assert that no great general is a rash
man, we mean that the attributes connoted by " great general," and those
connoted by " rash," never co-exist in the same subject ; which is also the
exact meaning which would be expressed by saying, that no rash man is a
* The different cases of EqaipoUency, or "Equivalent Propositional Forms," are set forth
with some fuUness in Professor Bain's Logic. One of the commonest of these changes of
expression, that from affirming a proposition to denying its negative, or mce versa^ Mr. Bam
designates, very happily, by the name Obversion. ...>■„
t As Sir William Hamilton has pointed out, "Some A is not B may also be converted in
the following form : " No B is some A." Some men are not negroes ; therefore. No negroes
are some men (e. g., Europeans).
124 REASONING.
great general. When we say that all quadrtipeds are warm-blooded, we
assert, not only that the attributes connoted by " quadruped " and those
connoted by " warm-blooded " sometimes co-exist, but that the former nev-
er exist without the latter: now the proposition. Some warm-blooded crea-
tures are quadrupeds, expresses the first half of this meaning, dropping the
latter half; and therefore has been already affirmed in the antecedent prop-
osition. All quadrupeds are warm-blooded. But that all warni-blooded
creatures are quadrupeds, or, in other words, that the attributes connoted
by "warm-blooded" never exist without those connoted by "quadruped,"
has not been asserted, and can not be inferred. In order to re-assert, in an
inverted form, the whole of what was affirmed in the proposition. All quad-
rupeds are warm-blooded, we must convert it by contraposition, thus, Noth-
ing which is not warm-blooded is a quadruped. This proposition, and the
one from which it is derived, are exactly equivalent, and either of them may
be substituted for the other ; for, to say that when the attributes of a quad-
ruped are present, those of a warm-blooded creature are present, is to say
that when the latter are absent the former are absent.
In a manual for young students, it would be proper to dwell at greater
length on the conversion and equipollency of propositions. For though
that can not be called reasoning or inference which is a mere re-assertion in
different words of what had been asserted before, there is no more impor-
tant intellectual habit, nor any the cultivation of which falls more strictly
within the province of the art of logic, than that of discerning rapidly and
surely the identity of an assertion when disguised under diversity of lan-
guage. That important chapter in logical treatises which relates to the Op-
position of Propositions, and the excellent technical language which logic
provides for distinguishing the different kinds or modes of opposition, are
of use chiefly for this purpose. Such considerations as these, that contrary
propositions may both be false, but can not both be true ; that subcontrary
propositions may both be true, but can not both be false ; that of two con-
tradictory propositions one must be true and the other false ; that of two
subalternate propositions the truth of the universal proves the truth of the
particular, and the falsity of the particular proves the falsity of the univer-
sal, but not vich versa;* are apt to appear, at first sight, very technical and
mysterious, but when explained, seem almost too obvious to require so form-
al a statement, since the same amount of explanation which is necessary
to make the principles intelligible, would enable the truths which they con-
vey to be apprehended in any particular case which can occur. In this
respect, however, these axioms of logic are on a level with those of mathe-
matics. That things which are equal to the same thing are equal to one
another, is as obvious in any particular case as it is in the general state-
ment : and if no such general maxim had ever been laid down, the demon-
strations in Euclid would never have halted for any difficulty in stepping
across the gap which this axiom at present serves to bridge over. Yet no
*No AisB}'=°""'^™=-
AH A is B ) , A- ^ ■
Some A is not b| contradictories.
Some A is b} ''''° contradictories.
Some i 1 1} -^ fome 1 1^ L b} -P-'^'^ -''^•»--'-
INFERENCE IN GENERAL. 126
one has ever censured writers on geometry, for placing a list of these ele-
mentary generalizations at the head of their treatises, as a first exercise to
the learner of the faculty which will be required in him at every step, that
of apprehending a general truth. And the student of logic, in the discus-
sion even of such truths as we have cited above, acquires habits of cir-
cumspect interpretation of words, and of exactly measuring the length and
breadth of his assertions, which are among the most indispensable condi-
tions of any considerable mental attainment, and which it is one of the
primary objects of logical discipline to cultivate.
§ 3. Having noticed, in order to exclude from the province of Reasoning
or inference properly so called, the cases in which the progression from one
truth to another is only apparent, the logical consequent being a mere rep-
etition of the logical antecedent ; we now pass to those which are cases of
inference in the proper acceptation of the term, those in which we set out
from known truths, to arrive at others really distinct from them.
Reasoning, in the extended sense in which I use the term, and in which
it is synonymous with Inference, is popularly said to be of two kinds : rea-
soning from particulars to generals, and reasoning from generals to partic-
ulars ; the former being called Induction, the latter Ratiocination or Syllo-
gism. It will presently be shown that there is a third species of i-easoning,
which falls under neither of these descriptions, and which, nevertheless, is
not only valid, but is the foundation of both the others.
It is necessary to observe, that the expressions, reasoning from particu-
lars to generals, and reasoning from generals to particulars, are recom-
mended by brevity rather than by precision, and do not adequately mark,
without the aid of a commentary, the distinction between Induction (in the
sense now adverted to) and Ratiocination. The meaning intended by these
expressions is, that Induction is inferring a proposition from propositions
less general than itself, and Ratiocination is inferring a proposition from
propositions equally or more general. When, from the observation of a
number of individual instances, we ascend to a general proposition, or when,
by combining a number of general propositions, we conclude from them
another proposition still more general, the process, which is substantially
the same in both instances, is called Induction. When from a general prop-
osition, not alone (for from a single proposition nothing can be concluded
which is not involved in the terms), but by combining it with other propo-
sitions, we infer a proposition of the same degree of generality with itself,
or a less general proposition, or a proposition merely individual, the process
is Ratiocination. When, in short, the conclusion is more general than the
largest of the premises, the argument is commonly called Induction ; when
less general, or equally general, it is Ratiocination.
As all experience begins with individual cases, and proceeds from them
to generals, it might seem most conformable to the natural order of thought
that Induction should be treated of before we touch upon Ratiocination.
It will, however, be advantageous, in a science which aims at tracing our
acquired knowledge to its sources,.that the inquirer should commence with
the latter rather than with the earlier stages of the process of constructing
our knowledge ; and should trace derivative truths backward to the truths
from which they are deduced, and on which they depend for their evidence,
before attempting to point out the original spring from which both ulti-
mately take their rise. The advantages of this order of proceeding in the
present instance will manifest themselves as we advance, in a manner su-
perseding the necessity of any further justification or explanation.
126 REASONING.
Of Induction, therefore, we shall say no more at present, than that it at
least is, without doubt, a process of real inference. The conclusion in an
induction embraces more than is contained in the premises. The principle
or law collected from particular instances, the general proposition in which
we embody the result of our experience, covers a much larger extent of
ground than the individual experiments which form its basis. A principle
ascertained by experience, is more than a mere summing up of what has
been specifically observed in the individual cases which have been exam-
ined ; it is a generalization grounded on those cases, and expressive of our
belief, that what we there found true is true in an indefinite number of
cases which we have not examined, and are never likely to examine. The
nature and grounds of this inference, and the conditions necessary to make
it legitimate, will be the subject of discussion in the Third Book : but that
such inference really takes place is not susceptible of question. In every
induction we proceed from truths which we knew, to truths which we did
not know ; from facts certified by observation, to facts which we have not
observed, and even to facts not capable of being now observed ; future
facts, for example ; but which we do not hesitate to believe on the sole evi-
dence of the induction itself.
Induction, then, is a real process of Reasoning or Inference. Whether,
and in what sense, as much can be said of the Syllogism, remains to be de-
termined by the examination into which we are about to enter.
CHAPTER II.
OF EATIOCINATIOlf, OE SYLLOGISM.
§ 1. The analysis of the Syllogism has been so accurately and fully per-
formed in the common manuals of Logic, that in the present work, which
is not designed as a manual, it is sufficient to recapitulate, memorice cmisd,
the leading results of that analysis, as a foundation for the remarks to be
afterward made on the functions of the Syllogism, and the place which it
holds in science.
To a legitimate syllogism it is essential that there should be three, and
no more than three, propositions, namely, the conclusion, or proposition to
be proved, and two other propositions which together prove it, and which
are called the premises. It is essential that there should be three, and no
more than three, terms, namely, the subject and predicate of the conclu-
sion, and another called the middle term, which must be found in both
premises, since it is by means of it that the other two terms are to be con-
nected together. The predicate of the conclusion is called the major term
of the syllogism; the subject of the conclusion is called the minor term.
As there can be but tbyee terms, the major and minor ternis juasLeachJie
'found in one, and only one^ of the premises, together with the middleieaa.
which is in therajjoiii. The premise which contains the middle term and
the major 'term is called the major premise; that which contains the mid-
dle term and the minor term is called the minor premise.
Syllogisms are divided by some logicians into three figures, by others
into four, according to the position of the middle terra, which may either
be the subject in both premises, the predicate in both, or the subjectia
one and the predicate in the other. The most common case is that in which.
RATIOCINATION, OE SYLLOGISM.
127
the middle term is the subject of the major premise and the predicate of
the minor. This is reckoned as the first figure. When the middle term is
the predicate in both premises, the syllogism belongs to the second figure ;
when it is the subject in both, to the third. In the fourth figure the mid-
dle term is the subject of the minor premise and the predicate of the major.
Those writers who reckon no more than three figures, include this case in
the first.
Each figure is divided into moods, according to what are called the quan
tity and quality of the propositions, that is, according as they are universal
■or particular, affirmative or negative. The following are examples of all
the legitimate moods, that is, all those in which the conclusion correctly
follows from the premises. A is the minor term, C the major, B the mid-
dle term.
FIRST FIGURE.
All B is C
All A is B
therefore
All A is C
Ifo C is B
All A is B
therefore
No A is C
No B is 0
All A is B
the'^efore
No A is C
All B is C
Some A is B
therefore
Some A is C
SECOND FIGTHIB.
All C is B No C is B
No A is B Some A is B
therefore therefore
No A is C Some A is not C
No B is C
Some A is B
therefore
Some A is not C
All C is B
Some A is not B
therefore
Some A is not C
All B is C No B is C
All B is A All B is A
therefore therefore
Some A is C Some A is not C
THIRD FIGURE.
Some B is C All B is C
All B is A
therefore
Some A is C
Some B is A
therefore
Some A is C
Some B is not C No B is C
All B is A Some B is A
therefore therefore
Some A is not C Some A is notC
FOURTH FIGURE.
All C is B All C is B Some C is B No C is B No C is B
All B is A No B is A All B is A All B is A Some B is A
therefore therefore therefore therefore therefore
Some A is C Some A is not C Some A is C Some A is not C Some A is not C
In these exemplars, or blank forms for making syllogisms, no place is
assigned to singular propositions ; not, of course, because such proposi-
tions are not used in ratiocination, but because, their predicate being af-
firmed or denied of the whole of the subject, they are i-anked, for the pur-
poses of the syllogism, with universal propositions. Thus, these two syllo-
gisms—
All men are mortal. All men are mortal,
All kings are men, Socrates is a man,
therefore therefore
All kings are mortal, Socrates is mortal,
are arguments precisely similar, and are both ranked in the first mood of
the first figure.*
* Professor Bain denies the claim of Singular Propositions to be classed, for the purposes
of ratiocination, with Universal ; though they come within the designation which he himself
proposes as an equivalent for Universal, that of Total. He would even, to use his own ex-
pression, banish them entirely from the syllogism. He takes as an example,
Socrates is wise,
Socrates is poor, therefore
Some poor men are wise,
or more properly (as he observes) "one poor man is wise." "Now, if wise, poor, and a
man, are attributes belonging to the meaning of the word Socrates, there is then no march of
128 EEASONING.
The reasons why syllogisms in any of the above forms are legitimate,
that is, why, if the premises are true, the conclusion must inevitably be so,
and why this is not the case in any other possible mood (that is, in any
other combination of universal and particular, affirmative and negative
propositions), any person taking interest in these inquiries may be pre-
sumed to have either learned from the common-school books of the syllo-
gistic logic, or to be capable of discovering for himself. The reader may,
however, be referred, for every needful explanation, to Archbishop Whate-
ly's Elements of Logic, where he will find stated with philosophical pre-
cision, and explained with remarkable perspicuity, the whole of the com-
mon doctrine of the syllogism.
All valid ratiocination ; all reasoning by which, from general propositions
reasoning at all. We have given in Socrates, inter alia, the facts wise, poor, and a man, and
we merely repeat the concurrence which is selected from the whole aggregate of properties
making up the whole, Socrates. The case is one under the head ' Greater and Less Connota-
tion ' in Equivalent Prepositional Forms, or Immediate Inference.
" But the example in this form does not do justice to the syllogism of singulars. We must
suppose both propositions to be real, the predicates being in no way involved in the subject.
Thus
Socrates was the master of Plato,
Socrates fought at Delium,
The master of Plato fought at Delium.
" It may fairly be doubted whether the transitions, in this instance, are any thing more
than equivalent forms. For the proposition ' Socrates was the master of Plato and fought at
Delium,' compounded out of the two premises, is obviously nothing more than a grammatical
abbreviation. No one can say that there is here any change of meaning, or any thing beyond
a verbal modification of the original form. The next step is, ' The master of Plato fought at
Delium,' which is the previous statement cut down by the omission of Socrates. It contents
itself with reproducing a part of the meaning, or saying less than had been previously said.
The full equivalent of the affirmation is, ' The master of Plato fought at Delium, and the
master of Plato was Socrates :' the new form omits the last piece of information, and gives
only the first. Now, we never consider that we have made a real inference, a step in advance,
when we repeat less than we are entitled to say, or drop from a complex statement some por-
tion not desired at the moment. Such an operation keeps strictly within the domain of equiv-
alence, or Immediate Inference. In no way, therefore, can a syllogism with two singular
premises be viewed as a genuine syllogistic or deductive inference." (^Logic, i., 159.) '
The first argument, as will have been seen, rests upon the supposition that the name Soc-
rates has a meaning ; that man, wise, and poor, are parts of this meaning ; and that by predi-
cating them of Socrates we convey no information ; a view of the signification of names
which, for reasons already given,* I can not admit, and which, as applied to the class of names
which Socrates belongs to, is at war with Mr. Bain's own definition of a Proper Name (i., 148),
"a single meaningless mark or designation appropriated to the thing." Such names, Mr.
Bain proceeded to say, do not necessarily indicate even human beings : much less then does
the name Socrates include the meaning of wise or poor. Otherwise it would follow that if
Socrates had grown rich, or had lost his mental faculties by illness, he would no longer have
been called Socrates.
The second part of Mr. Bain's argument, in which he contends that even when the premises
convey real information, the conclusion is merely the premises with a part left out, is applica-
ble, if at all, as much to universal propositions as to singular. In every syllogism the con-
clusion contains less than is asserted in the two premises taken together. Suppose the syllo-
gism to be
All bees are intelligent.
All bees are insects, therefore
Some insects are intelligent :
one might use the same liberty taken by Mr. Bain, of joining together the two premises as if
they were one — "All bees are insects and intelligent" — and might say that in omitting the
middle term bees we make no real inference, but merely reproduce part of what had been pre-
viously said. Mr. Bain's is really an objection to the syllogism itself, or at all events to the
third figure : it has no special applicability to singular propositions.
* Note to § 4 of the chapter on Definition, supra, pp. 110, 111.
KATIOCINATION, OR SYLLOGISM. 129
previously admitted, other propositions equally or less general are inferred ;
may be exhibited in some of the above forms. The whole of Euclid, for
example, might be thrown without diiEculty into a series of syllogisms,
regular in mood and figure.
Though a syllogism framed according to any of these formulae is a valid
argument, all correct ratiocination admits of being stated in syllogisms of
the first figure alone. The rules for throwing an argument in any of the
other figures into the first figure, are called rules for the reduction of syl-
logisms. It is done by the conversion of one or other, or both, of the prem-
ises. Thus an argument in the first mood of the second figure, as —
No C is B
All A is B
therefore
No A is C,
may be reduced as follows. The proposition. No C is B, being a universal
negative, admits of simple conversion, and may be changed into No B is
C, which, as we showed, is the very same assertion in other words — the
same fact differently expressed. This transformation having been effected,
the argument assumes the following form :
No B is C
All A is B
therefore
No A is C,
which is a good syllogism in the second mood of the first figure. Again,
an argument in the first mood of the third figure must resemble the fol-
lowing :
All B is C
All B is A
therefore
Some A is C,
where the minor premise. All B is A, conformably to what was laid down
in the last chapter respecting universal affirmatives, does not admit of sim-
ple conversion, but may be converted per accidens, thus. Some A is B ;
which, though it does not express the whole of what is asserted in the
proposition All B is A, expresses, as was formerly shown, part of it, and
must therefore be true if the whole is true. We have, then, as the re-
sult of the reduction, the following syllogism in the third mood of the first
figure :
All B is C
Some A is B,
from which it obviously follows, that
Some A is C.
In the same manner, or in a manner on which after these examples it is
not necessary to enlarge, every mood of the second, third, and fourth fig-
ures may be reduced to some one of the four moods of the first. In other
words, every conclusion which can be proved in any of the last three fig-
ures, may be proved in the first figure from the same premises, with a
slight alteration in the mere manner of expressing them. Every valid ra-
tiocination, therefore, may be stated in the first figure, that is, in one of the
following forms :
9
130 EEASONIKG.
Every B is C No B is C
AHA ). R AHA ). xj
SomeAr^^' Some A ^^ ^'
therefore therefore
AHA [. p No A is )p
Some A P^ ^- Some A is not j ^*
Or, if more significant symbols are preferred :
To prove an affirmative, the argument must admit of being stated in this
form:
All animals are mortal ;
All men )
Some men V are animals ;
Socrates )
therefore
All men \
Some men V are mortal.
Socrates )
To prove a negative, the argument must be capable of being expressed
in this form :
No one who is capable of self-control is necessarily vicious ;
All negroes )
Some negroes [• are capable of self-control ;
Mr. A's negro )
therefore
No negroes are )
Some negroes are not I necessarily vicious.
Mr. A's negro is not )
Though all ratiocination admits of being thrown into one or the other of
these forms, and sometimes gains considerably by the transformation, both
in clearness and in the obviousness of its consequence ; there are, no doubt,
cases ia which the argument falls more naturally into one of the other three
figures, and in which its conclusiveness is more apparent at the first glance
in those figures, than when reduced to the first. Thus, if the proposition
were that pagans may be virtuous, and the evidence to prove it were the
example of Aristides ; a syllogism in the third figure,
Aristides was virtuous,
Aristides was a pagan,
therefore
Some pagan was virtuous,
would be a more natural mode of stating the argument, and would carry
conviction more instantly home, than the same ratiocination strained into
the first figure, thus —
Aristides was virtuous,
Some pagan was Aristides,
therefore
Some pagan was virtuous.
A German philosopher, Lambert, whose JVeues Organon (published in
the year 1764) contains among other things one of the most elaborate and
complete expositions which had ever been made of the syllogistic doctrine,
has expressly examined what sort of arguments fall most naturally and suit-
ably into each of the four figures ; and his investigation is characterized by
RATIOCINATION, OR SYLLOGISM. 131
■great ingenuity and clearness of thought.* The argument, however, is one
and the same, in whichever figure it is expressed ; since, as we have already
seen, the premises of a syllogism in the second, third, or fourth figure, and
those of the syllogism in the first figure to which it may be reduced, are
the same premises in every thing except language, or, at least, as much of
them as conti-ibutes to the proof of the conclusion is the same. We are
therefore at liberty, in conformity with the general opinion of logicians, to
consider the two elementary forms of the first figure as the universal types
of all correct ratiocination ; the one, when the conclusion to be proved is
affirmative, the other, when it is negative ; even though certain arguments
may have a tendency to clothe themselves in the forms of the second, third,
and fourth figures ; which, however, can not possibly happen with the only
■class of arguments which are of firsWate scientific importance, those in
which the conclusion is a universal aflSrmative, such conclusions being sus-
■ceptible of proof in the first figure alone.f
• His conclusions are, "The first figure is suited to the discovery or proof of the properties
of a thing ; the second to the discovery or proof of the distinctions between things ; the third
to the discoveiy or proof of instances and exceptions ; the fourth to the discovery, or exclu-
sion, of the different species of a genus." The reference of syllogisms in the last three figures
to the dictum de omni et nulla is, in Lamhert's opinion, strained and unnatnral : to each of
the three belongs, according to him, a separate axiom, co-ordinate and of equal authority with
that dictum, and to which he gives the names of dictum de diversn for the second figure,
■dictum de exemplo for the third, and dictum de reciproco for the fourth. See part i., or Dia-
imologie, chap, iv., § 229 et seqq. Mr. Bailey {Theory of Reasoning, 2d ed., pp. 70-74)
takes a similar view of the subject.
t Since this chapter was written, two treatises have appeared (or rather a treatise and a
fragment of a treatise), which aim at a further improvement in the theory of the forms of
ratiocination : Mr. De Morgan's " Formal Logic ; or, the Calculus of Inference, Necessary
and Probable;" and the "New Analytic of Logical Forms," attached as an Appendix to Sir
"William Hamilton's Discussions on Philosophy, and at greater length, to his posthumous Lec-
tures on Logic.
In Mr. De Morgan's volume — abounding, in its more popular parts, with valuable observa-
tions felicitously expressed — the principal feature of originality is an attempt to bring within
strict technical rules the cases in which a conclusion can be drawn from premises of a form
usually classed as particular. Mr. De Morgan observes, veiy justly, that from the premises
most is are Cs, most Bs are As, it may be concluded with certainty that some As are Cs,
since two portions of the class B, each of them comprising more than half, must necessarily
in part consist of the same individuals. Following out this line of thought, it is equally evi-
dent that if we knew exactly what proportion the " most " in each of the premises bear to the
«ntire class B, we could increase in a corresponding degree the definiteness of the conclusion.
Thus if 60 per cent, of B are included in C, and 70 per cent, in A, 30 per cent, at least must
be common to both ; in other words, the number of As which are Cs, and of Cs which are
As, must be at least equal to 30 per cent, of the class B. Proceeding on this conception of
"numerically definite propositions," and extending it to such forms as these: — "45 Xs (or
more) are each of them one of 70 Ys," or "45 Xs (or more) are no one of them to be found
among 70 Ys," and examining what inferences admit of being drawn from the various coin-
binations which may be made of premises of this description, Mr. De Morgan establishes uni-
versal formulae for such inferences ; creating for that purpose not only a new technical lan-
guage, but a formidable array of symbols analogous to those of algebra.
Since it is undeniable that inferences, in the cases examined by Mr. De Morgan, can legiti-
mately be drawn, and that the ordinary theory takes no account of them, I will not say that
it was not worth while to show in detaU how these also could be reduced to formulae as rigor-
ous as those of Aristotle. What Mr. De Morgan has done was worth doing once (perhaps
more than once, as a school exercise) ; but I question if its results are worth studying and
mastering for any practical purpose. The practical use of technical forms of reasoning is to
bar out f^acies : but the fallacies which require to be guarded against in ratiocination properly
so called, arise from the incautious use of the common forms of language ; and the logician
must track the fallacy into that territory, instead of waiting for it on a territory of his own.
While he remains among propositions which have acquired the numerical precision of the
Calculus of Probabilities, the enemy is left in possession of the only ground on which he can
be formidable. And since the propositions (short of universal) on which a thinker has to de-
132 REASONING.
§ 2. On examining, then, these two general formulae, we find that in
both of them, one premise, the major, is a universal proposition; and ac-
pend, either for purposes of speculation or of practice, do not, except in a few peculiar cases,
admit of any numerical precision ; common reasoning can not be translated into Mr. De
Morgan's forms, which therefore can not serve any purpose as a test of it.
Sir William Hamilton's theory of the " quantification of the predicate " may be described as
follows :
"Logically" d quote his words) "we ought to take into account the quantity, always un-
derstood in thought, but usually, for manifest reasons, elided in its expression, not only of the
subject, but also of the predicate of a judgment. " All A is B, is equivalent to all A is some
B. No A is B, to No A is any B. Some A is B, is tantamount to some A is some B.
Some A is not B, to Some A is not any B. As in these forms of assertion the predicate is
exactly co-extensive with the subject, they all admit of simple conversion ; and by this we
obtain two additional forms — Some B is all A, and No B is some A. We may also make
the assertion All A is all B, which will be true if the classes A and B are exactly co-extensive.
The last three forms, though conveying real assertions, have no place in the ordinary classifi-
cation of Propositions. All propositions, then, being supposed to be translated into this lan-
guage, and written each in that one of the preceding forms which answers to its signification,
there emerges a new set of syllogistic rules, materially different from the common ones. A
general view of the points of difference may be given in the words of Sir W. Hamilton {Dis-
cussions, 2d ed., p. 651) :
"The revocation of the two terms of a Proposition to their true relation ; a proposition be-
ing always an equation of its subject and its predicate.
"The consequent reduction of the Conversion of Propositions from three species to one — ^
that of Simple Conversion.
" The reduction of all the General Laws of Categorical Syllogisms to a single Canon.
" The evolution fiom that one canon of all the Species and varieties of Syllogisms.
"The abrogation of all the Special Laws of Syllogism.
" A demonstration of the exclusive possibility of Three Syllogistic Figures ; and (on new
gi-ounds) the scientific and final abolition of the Fourth.
"A manifestation that Figure is an unessential variation in syllogistic form ; and the con-
sequent absurdity of Reducing the syllogisms of the other figures to the first.
"An enouncement of one Organic Principle for each Figure.
"A determination of the true number of the Legitimate Moods ; with
" Their amplification in number (thirty-six) ;
"Their numerical equality under all the figures ; and
"Their relative equivalence, or virtual identity, throughout every schematic difference.
"That, in the second and third figures, the extremes holding both the same relation to the'
middle term, there is not, as in the first, an opposition and subordination between a term ma-
jor and a term minor, mutually containing and contained, in the counter wholes of Extension
and Comprehension.
"Consequently, in the second and third figures, there is no determinate major and minor
premises, and there are two indifferent conclusions : whereas in the first the premises are de-
terminate, and there is a single proximate conclusion. "
■This doctrine, like that of Mr. De Morgan previously noticed, is a real addition to the syl-
logistic theory ; and has moreover this advantage over Mr. De Morgan's "numerically definite
Syllogism," that the forms it supplies are really available as a test of the correctness of ratioc-
ination ; since propositions in the common form may always have their predicates quantified,
and so be made amenable to Sir W. Hamilton's rules. Considered, however, as a contribution
to the Science of Logic, that is, to the analysis of the mental processes concerned in reasoning,
the new doctrine appears to me, I confess, not merely superfluous, but erroneous ; since the
form in which it clothes propositions does not, like the ordinary foi-m, express what is in the
mind of the speaker when he enunciates the proposition. I can not think Sir William Ham-
ilton right in maintaining that the quantity of the predicate is " always understood in thought."
It is implied, but is not present to the mind of the person who asserts the proposition. The
quantification of the predicate, instead of being a means of bringing out more cleariy the mean-
ing of the proposition, actually leads the mind out of the proposition, into another order of
ideas. For when we say, All men are mortal, we simply mean to affirm the attribute mor-
tality of all men ; without thinking at all of the class mortal in the concrete, or troubling our-
selves about whether it contains any other beings or not. It is only for some artificial pur-
pose that we ever look at the proposition in the aspect in which the predicate also is thought
of as a class-name, either including the subject only, or the subject and something more. (See
above, p. 77, 78.)
For a fuller discussion of this subject, see the twenty-second chapter of a work already re-
ferred to, "An Examination of Sir William Hamilton's Philosophy."
RATIOCINATION, OR SYLLOGISM. 133
cording as this is affirmative or negative, the conclusion is so too. All
ratiocination, therefore, starts from a general proposition, principle, or as-
sumption : a proposition in which a predicate is affirmed or denied of an
entire class ; that is, in which some attribute, or the negation of some
attribute, is asserted of an indefinite number of objects distinguished
by a common characteristic, and designated, in consequence, by a common
name.
The other premise is always affirmative, and asserts that something (which
may be either an individual, a class, or part of a class) belongs to, or is in-
cluded in, the class respecting which something was affirmed or denied in
the major premise. It follows that the attribute affirmed or denied of the
entire class may (if that affirmation or denial was correct) be affirmed or
deniedof the object or objects alleged to be included in the class : and this
is precisely the assertion made in the conclusion.
Whether or not the foregoing is an adequate account of the constituent
parts of the syllogism, will be presently considered ; but as far as it goes it
is a true account. It has accordingly been generalized, and erected into a
logical maxim, on which all ratiocination is said to be founded, insomuch
that to reason, and to apply the maxim, are supposed to be one and the
same thing. The maxim is. That whatever can be affirmed (or denied) of
a class, may be affirmed (or denied) of every thing included in the class.
This axiom, supposed to be the basis of the syllogistic theory, is termed by
logicians the dictum de omni et nulla.
This maxim, however, when considered as a principle of reasoning, ap-
pears suited to a system of metaphysics once indeed generally received, but
which for the last two centuries has been considered as finally abandoned,
though there have not been wanting in our own day attempts at its revival.
So long as what are termed Universals were regarded as a peculiar kind of
substances, having an objective existence distinct from the individual ob-
jects classed under them, the dictum de om,ni conveyed an important mean-
ing ; because it expressed the intercommunity of nature, which it was nec-
essary on that theory that we should suppose to exist between those gen-
eral substances and the particular substances which were subordinated to
them. That every thing predicable of the universal was predicable of the
various individuals contained under it, was then no identical proposition,
but a statement of what was conceived as a fundamental law of the uni-
verse. The assertion that the entire nature and properties of the substan-
tia secunda formed part of the nature and properties of each of the indi-
vidual substances called by the same name ; that the properties of Man, for
example, were properties of all men ; was a proposition of real significance
when man did not m,ean all men, but something inherent in men, and vast-
ly superior to them in dignity. Now, however, when it is known that a
olass, a universal, a genus or species, is not an entity per se, but neither
more nor less than the individual substances themselves which are placed
in the class, and that there is nothing real in the matter except those objects,
a common name given to them, and common attributes indicated by the
name ; what, I should be glad to know, do w^e learn by being told, that
whatever can be affirmed of a class, may be affirmed of every object con-
tained in the class? The class is nothing but the objects contained in it:
and the dictum de omni merely amounts to the identical proposition, that
whatever is true of certain objects, is true of each of those objects. If all
ratiocination were no more than the application of this maxim to particular
cases, the syllogism would indeed be, what it has so often been declared to
134 KEASONING.
be, solemn trifling. The dictum de omni is on a par with another truth,
•which in its time was also reckoned of great importance, "'Whatever is,
is." To give any real meaning to the dictum de omni, we must consider
it not as an axiom, but as a definition ; we must look upon it as intended
to explain, in a circuitous and paraphrastic manner, the meaning of the
■word class.
An error which seemed finally refuted and dislodged from thought, often,
needs only put on a new suit of phrases, to be welcomed back to its old
quarters, and allowed to repose unquestioned for another cycle of ages.
Modern philosophers have not been sparing in their contempt for the scho-
lastic dogma that genera and species are a peculiar kind of substances, which
general substances being the only permanent things, while the individual
substances comprehended under them are in a perpetual flux, knowledge,,
■which necessarily imports stability, can only have relation to those general
substances or universals, and not to the facts or particulars included un-
der them. Yet, though nominally rejected, this very doctrine, whether dis-
guised under the Abstract Ideas of Locke (whose speculations, however, it
has less vitiated than those of perhaps any other writer who has been in-
fected with it), under the ultra-nominalism of Hobbes and Condillac,or the
ontology of the later German schools, has never ceased to poison philosophy.
Once accustomed to consider scientific investigation as essentially consist-
ing in the study of universals, men did not drop this habit of thought when
they ceased to regard universals as possessing an independent existence:
and even those who went the length of considering them as mere names,
could not free themselves from the notion that the investigation of truth
consisted entirely or partly in some kind of conjuration or juggle with those
names. When a philosopher adopted fully the Nominalist view of the
signification of general language, retaining along with it the dictum de
omni as the foundation of all reasoning, two such premises fairly put to-
gether were likely, if he was a consistent thinker, to land him in rather
startling conclusions. Accordingly it has been seriously held, by writers
of deserved celebrity, that the process of arriving at new truths by reason-
ing consists in tlie mere substitution of one set of arbitrary signs for an-
other; a doctrine which they suppose to derive iri-esistible confirmation
from the example of algebra. If there were any process in sorcery or
necromancy more preternatural than this, I should be much surprised.
The culminating point of this philosophy is the noted aphorism of Condil-
lac, that a science is nothing, or scarcely any thing, but une langue Men
faite; in other words, that the one sufficient rule for discovering the nature
and properties of objects is to name them properly : as if the reverse were
not the truth, that it is impossible to name them properly except in propor-
tion as we are already acquainted with their nature and properties. Can
it be necessary to say, that none, not even the most trivial knowledge with
respect to Things, ever was or could be originally got at by any conceivable
manipulation of mere names, as such ; and that what can be learned from
names, is only what somebody who used the names knew before ? Philo-
sophical analysis confirms the indication of common sense, that the func-
tion of names is but that of enabling us to remember and to communicate
our thoughts. That they also strengthen, even to an incalculable extent,
the power of thought itself, is most true : but they do this by no intrinsic-
and peculiar virtue ; they do it by the power inherent in an artificial mem-
ory, an instrument of which few have adequately considered the immense
potency. As an artificial memory, language truly is, what it has so oftett
RATIOCINATION, OE SYLLOGISM. 136,
been called, an instrument of thought ; but it is one thing to be the instru-
ment, and another to be the exclusive subject upon which the instrument
is exercised. We think, indeed, to a considerable extent, by means of
names, but what we think of, are the things called by those names ; and
there can not be a greater error than to imagine that thought can be car-
ried on with nothing in our mind but names, or that we can make the
names think for us.
§ 3.^ Those who considered the dictum de omni as the foundation of the
syllogism, looked upon arguments in a manner corresponding to the erro-
neous view which Hobbes took of propositions. Because there are some
propositions which are merely verbal, Hobbes, in order apparently that his
definition might be rigorously universal, defined a proposition as if no
propositions declared any thing except the meaning of words. If Hobbes-
was right; if no further account than this could be given of the import of
propositions ; no theory could be given but the commonly received one,
of the combination of propositions in a syllogism. If the minor premise
asserted nothing more than that something belongs to a class, and if the
major premise asserted nothing of that class except that it is included in
another class, the conclusion would only be that what was included in the-
lower class is included in the higher, and the result, therefore, nothing ex-
cept that the classification is consistent with itself. But we have seen that,
it is no sufficient account of the meaning of a proposition, to say that it
refers something to, or excludes something from, a class. Every proposi-
tion which conveys real information asserts a matter of fact, dependent on.
the laws of nature, and not on classification. It asserts that a given object
does or does not possess a given attribute ; or it asserts that two attri-
butes, or sets of attributes, do or do not (constantly or occasionally) co-ex-
ist. Since such is the purport of all propositions which convey any real
knowledge, and since ratiocination is a mode of acquiring real knowledge,
any theory of ratiocination which does not recognize this import of propo-
sitions, can not, we may be sure, be the true one.
Applying this view of propositions to the two premises of a syllogism,.
we obtain the following results. The major premise, which, as already
remarked, is always universal, asserts, that all things which have a certain
attribute (or attributes) have or have not along with it, a certain other at-
tribute (or attributes). The minor premise asserts that the thing or set
of things which are the subject of that premise, have the first-mentioned
attribute ; and the conclusion is, that they have (or that they have not), the
second. Thus in our former example.
All men are mortal,
Socrates is a man,
therefore
Socrates is mortal,
the subject and predicate of the major premise are connotative terms, de-
noting objects and connoting attributes. The assertion in the major prem-
ise is, that along with one of the two sets of attributes, we always find
the other : that the attributes connoted by " man " never exist unless con-
joined with the attribute called mortality. The assertion in the minor prem-
ise is that the individual named Socrates possesses the former attributes;
and it is concluded that he possesses also the attribute mortality. Or, if
both the premises are general propositions, as
136 REASONING.
All men are mortal,
All kings are men,
therefore
All kings are mortal,
the minor premise asserts that the attributes denoted by kingship only
€xist in conjunction with those signified by the word man. The major
asserts as before, that the last-mentioned attributes are never found without
the attribute of mortality. The conclusion is, that wherever the attributes
of kingship are found, that of mortality is found also.
If the major premise were negative, as. No men are omnipotent, it would
assert, not that the attributes connoted by " man " never exist without, but
that they never exist with, those connoted by " omnipotent :" from which,
together with the minor premise, it is concluded, that the same incompati-
bility exists between the attribute omnipotence and those constituting a
king. In a similar manner we might analyze any other example of the
syllogism.
If we generalize this process, and look out for the principle or law in-
volved in every such inference, and presupposed in every syllogism, the
propositions of which are any thing more than merely verbal; we find, not
the unmeaning dictum de omni et nulla, but a fundamental principle, or
rather two principles, strikingly resembling the axioms of mathematics.
The first, which is the principle of afiirmative syllogisms, is, that things
which co-exist with the same thing, co-exist with one another: or (still move
precisely) a thing which co-exists with another thing, which other co-exists
with a third thing, also co-exists with that third thing. The second is the
principle of negative syllogisms, and is to this effect : that a thing which
co-exists with another thing, with which other a third thing does not co-ex-
ist, is not co-existent with that third thing. These axioms manifestly relate
to facts, and not to conventions ; and one or other of them is the ground of
the legitimacy of every argument in which facts and not conventions are
the matter treated of.*
* Mr. Herbert Spencer (Principles of Psychology, pp. 125-7), though his theoiy of the syl-
logism coincides with all that is essential of mine, thinks it a logical fallacy to present the two
axioms in the text, as the regulating principles of syllogism. He charges me with falling
into the error pointed out by Archbishop Whately and myself, of confounding exact lilceness
with literal identity ; and maintains, that we ought not to say that Socrates possesses the
same attributes which are connoted by the word Man, but only that he possesses attributes
exactly like them : according to which phraseology, Socrates, and the attribute moitality,
are not two things co-existing with the same thing, as the axiom asserts, but two things co-
•existing with two different things.
The question between Mr. Spencer and me is merely one of language ; for neither of us (if
I understand Mr. Spencer's opinions rightly) believes an attribute to be a real thing, possessed
of objective existence ; we believe it to be a particular mode of naming our sensations, or our
expectations of sensation, when looked at in tlieir relation to an external object which excites
them. The question raised by Mr. Spencer does not, therefore, concern the properties of any
really existing thing, but the comparative' appropriateness, for philosophical pui-poses, of two
different modes of nsing a name. Considered in this point of view, the phraseology I have
employed, which is that commonly used by philosophers, seems to me to be the best. Mr.
Spencer is of opinion that because Socrates and Alcibiades are not the same man, the attri-
bute which constitutes them men should not be called the same attribute ; that because the
humanity of one man and that of another express themselves to our senses not by the same
individual sensations but by sensations exactly alike, humanity ought to be regarded as a dif-
ferent attribute in every different man. But on this showing, the humanity even of any one
man should be considered as different attributes now and half an hour hence ; for the sensa-
tions by which it will then manifest itself to my organs will not be a continuation of my pres-
ent sensations, but a repetition of them ; fresh sensations, not identical with, but only exactly
RATIOCINATION, OR SYLLOGISM. 137
§ 4. It remains to translate this exposition of tlie syllogism from the
one into the other of the two languages in which we formerly remai'ked*
that all propositions, and of course therefore all combinations of proposi-
tions, might be expressed. We observed that a proposition might be con-
sidered in two different lights ; as a portion of our knowledge of nature,
or as a memorandum for our guidance. Under the former, or speculative
aspect, an affirmative general proposition is an assertion of a speculative
truth, viz., that whatever has a certain attribute has a certain other attribute.
Under the other aspect, it is to be regarded not as a part of our knowledge,,
but as an aid for our practical exigencies, by enabling us, when we see or
learn that an object possesses one of the two attributes, to infer that it pos-
sesses the other ; thus employing the first attribute as a mark or evidence
of the second. Thus regarded, every syllogism comes within the following
general formula :
Attribute A is a mark of attribute B,
The given object has the mark A,
therefore
The given object has the attribute B.
Referred to this type, the arguments which we have lately cited as
specimens of the syllogism, will express themselves in the following
manner :
The attributes of man are a mark of the attribute mortality,
Socrates has the attributes of man,
therefore
Socrates has the attribute mortality.
like the present. If every general conception, instead of being "the One in the Many,'' were
considered to be as many different conceptions as there are things to which it is applicable,
there would be no snch thing as general language. A name would have no general meaning
if man connoted one thing when predicated of John, and another, though closely resembling,
thing when predicated of William. Accordingly a recent pamphlet asserts the impossibility
of general knowledge on this precise ground.
The meaning of any general name, is some outward or inward phenomenon, consisting, in
the last resort, of feelings ; and these feelings, if their continuity is for an instant broken, are
no longer the same feelings, in the sense of individual identity. What, then, is the common
something which gives a meaning to the general name ? Mr. Spencer can only say, it is the
similarity of the feelings ; and I rejoin, the attribute is precisely that similarity. The namea
of attributes are in their ultimate analysis names for the resemblances of our sensations (or-
other feelings). Every general name, whether abstract or concrete, denotes or connotes one
or more of those resemblances. It will not, probably, be denied, that if a hundred sensations
are undistinguishably alike, their resemblance ought to be spoken of as one resemblance, and
not a hundred resemblances which merely resemble one another. The things compared are
many, bat the something common to all of them must be conceived as one, just as the name
is conceived as one, though corresponding to numerically different sensations of sound each
time it is pronounced. The general term man does not connote the sensations derived once
from one man, which, once gone, can no more occur again than the same flash of light-
ning. It connotes the general type of the sensations derived always from all men, and the
power (always thought of as one) of producing sensations of that type. And the axiom
might be thus worded : Two types of sensation each of which co-exists with a third type,
co-exist with another ; or Two powers each of which co-exists with a third power co-exist
with one another.
Mr. Spencer has misunderstood me in another particular. He supposes that the co-exist-
ence spoken of in the axiom, of two things with the same third thing, means simultaneousness
in time. The co-existence meant is that of being jointly attributes of the same subject. The
attribute of being bom without teeth, and the attribute of having thirty-two teeth in mature
age, are in this sense co-existent, both being attributes of man, though ex vi termini never of
the same man at the same time.
• Supra, p. 93.
138 KEASONING.
And again,
The attributes of man are a mark of the attribute mortality,
The attributes of a king are a mark of the attributes of man,
therefore
The attributes of a king are a mark of the attribute mortality.
And, lastly,
The attributes of man are a mark of the absence of the attribute
omnipotence.
The attributes of a king are a mark of the attributes of man,
therefore
The attributes of a king are a mark of the absence of the attribute
signified by the word omnipotent
(or, are evidence of the absence of that attribute).
To correspond with this alteration in the form of the syllogisms, the ax-
ioms on which the syllogistic process is founded must undergo a corre-
sponding transformation. In this altered phraseology, both those axioms
may be brought under one general expression ; namely, that whatever has
any mark, has that which it is a mark of. Or, when the minor premise as
well as the major is universal, we may state it thus : Whatever is a mark
-of any mark, is a mark of that which this last is a mark of. To trace the
identity of these axioms with those previously laid down, may be left to the
intelligent reader. We shall find, as we proceed, the great convenience of
the phraseology into which we have last thrown them, and which is better
«,dapted than any I am acquainted with, to express with precision and force
what is aimed at, and actually accomplished, in every case of the ascertain-
ment of a truth by ratiocination.*
* Professor Bain {Logic, i., 157) considers the axiom (or rather axioms) here proposed as
a substitute for the dictum de omni, to possess certain advantages, but to be " unworkable as
a. basis of the syllogism. The fatal defect consists in this, that it is ill-adapted to bring out
the difference between total and partial coincidence of terms, the observation of which is the
■essential precaution in syllogizing correctly. If all the terms were co-extensive, the axiom
would flow on admirably ; A carries B, all B and none but B ; B carries C in Ihe same man-
ner ; at once A carries C, without limitation or resei-ve. But in point of fact, we know that
while A canies B, other things carry B also ; whence a process of limitation is required, in
transferring A to C through B. A (in common with other things) canies B ; B (in common
-\vith other things) carries C ; whence A (in common with other things) can-ies C. The ax-
iom provides no means of making this limitation ; if we were to follow A literally, we should
be led to suppose A and C co-extensive : for such is the only obvious meaning of ' the attri-
bute A coincides with the attribute C. '"
It is certainly possible that a careless learner here and there may suppose that if A carries
B, it follows that B canies A. But if any one is so incautious as to commit this mistake, the
very earliest lesson in the logic of inference, the Conversion of propositions, will con-ect it.
The first of the two forms in which I have stated the axiom, is in some degree open to Mr.
Bain's criticism : when B is said to co-exist with A (it must be by a lapsus calami that Mr.
Bain uses the wojd coincide), it is possible, in the absence of warning, to suppose the meaning
to be that the two things are only found together. But this misintei'pretation is excluded by
the other, or practical, form of the maxim ; Nota notes est nota rei ipsius. No one would be
in any danger of infening that because a is a mark of 6, b can never exist without a ; .'hat
because being in a confirmed consumption is a mark of being about to die, no one dies w'jo is
not in a consumption ; that because being coal is a mark of having come out of the earth,
nothing can come out of the earth except coal. Ordinary knowledge of English seems a
sufficient protection against these mistakes, since in speaking of a mark of any thing we are
never understood as implying reciprocity.
A more fundamental objection is stated by Mr. Bain in a subsequent passage (p. 168).
"The axiom does not accommodate itself to the type of Deductive Reasoning as contrasted
with Induction — the application of a general principle to a special case. Any thing that fails
to make prominent this circumstance is not adapted as a foundation for the syllogism." But
FUNCTIONS AND VALUE OF THE SYLLOGISM. 13»
CHAPTER III.
OF THE FUNCTIONS AND LOGICAL VALUE OF THE SYLLOGISM.
§ 1. We have shown what is the real nature of the truths with which
the Syllogism is conversant, in contradistinction to the more superficial
manner in which their import is conceived in the common theory; and
what are the fundamental axioms on which its probative force or conclu-
siveness depends. We have now to inquire, whether the syllogistic proc-
«ss, that of reasoning from generals to particulars, is, or is not, a process
of inference ; a progress from the known to the unknown : a means of com-
ing to a knowledge of something which we did not know before.
Logicians have been remarkably unanimous in their mode of answering
this question. It is universally allowed that a syllogism is vicious if there]
be any thing more in the conclusion than was assumed in the premises. I
But this is, in fact, to say, that nothing ever was, or can be, proved by syl-
logism, which was not known, or assumed to be known, before. Is ratioci-
nation, then, not a process of inference ? And is the syllogism, to which
the word reasoning has so often been represented to be exclusively appro-
priate, not really entitled to be called reasoning at all ? This seems an in-
evitable consequence of the doctrine, admitted by all writers on the sub-
ject, that a syllogism can prove no more than is involved in the premises.
Yet the acknowledgment so explicitly made, has not pi-evented one set of
writers from continuing to represent the syllogism as the correct analysis
of what the mind actually perforins in discovering and proving the lai'ger
half of the truths, whether of science or of daily life, which we believe ;
while those who have avoided this inconsistency, and followed out the gen-
eral theorem respecting the logical value of the syllogism to its legitimate
corollary, have been led to impute wselessness and frivolity to the syllogis-
tic theory itself, on the ground of the petitio principii which they allege
to be inherent in every syllogism. As I believe both these opinions to be
fundamentally erroneous, I must request the attention of the reader to cer-
tain considerations, without which any just appreciation of the true char-
acter of the syllogism, and the functions it performs in philosophy, appears
to me impossible ; but which seem to have been either overlooked, or in-
sufficiently adverted to, both by the defenders of the syllogistic theory and
by its assailants.
§ 2. It must be granted that in every syllogism, considered as an
though it may be proper to limit the term Deduction to the application of a general principle
to a special case, it has never been held that Ratiocination or Syllogism is subject to the same
limitation ; and the adoption of it would exclude a great amount of valid and conclusive syl-
logistic reasoning. Moreover, if the dictum de omni makes prominent the fact of the applica-
tion of a general principle to a particular case, the axiom I propose makes prominent the
condition which alone makes that application a real inference.
I conclude, therefore, that both forms have their value, and their place in Logic. The
dictum de omni should be retained as the fundamental axiom of the logic of mere consistency,
often called Formal Logic ; nor have I ever quaiTeled with the use of it in that character,
nor proposed to banish it from treatises on Formal Logic. But the other is the proper axiom
for the logic of the pursuit of truth by way of Deduction ; and the recognition of it can alone
show how it is possible that deductive reasoning can be a road to truth.
140 EEASOOTNG.
argument to prove the conclusion, there is a petitio principii. When
we say,
All men are mortal,
Socrates is a man,
therefore
Socrates is mortal ;
it is unanswerably urged by the adversaries of the syllogistic theory, that
the pi-oposition, Socrates is mortal, is presupposed in the moi-e general as-
sumption. All men are mortal : that we can not be assured of the moitali-
Sty of all men, unless we are already certain of the mortality of every indi-
vidual man : that if it be still doubtful whether Socrates, or any other in-
dividual we choose to name, be mortal or not, the same degree of uncer-
tainty must hang over the assertion. All men are mortal: that the general/
principle, instead of being given as evidence of the particular case, can not
itself be taken for true without exception, until every shadow of doubt
which could afEect any case comprised with it, is dispelled by evidence
aliundd; and then what remains for the syllogism to prove? That, in
short, no re'asoning from generals to particulars can, as such, prove any
thing : since from a general principle we can not infer any particulars, but
those which the principle itself assumes as known.
This doctrine appears to me irrefi-agable ; and if logicians, though una-
ble to dispute it, have usually exhibited a strong disposition to explain it
away, this was not because they could discover any flaw in the argument
itself, but because the contrary opinion seemed to rest on arguments equal-
ly indisputable. In the syllogism last referred to, for example, or in any of
those which we previously constructed, is it not evident that the conclu-
sion may, to the person to whom the syllogism is presented, be actually
and hona fide, a new truth? Is it not matter of daily experience that
truths previously unthought of, facts which have not been, and can not be,,
directly observed, are arrived at by way of general reasoning? We be-
lieve that the Duke of Wellington is mortal. We do not know this by di-
rect observation, so long as he is not yet dead. If we were asked how,
this being the case, we know the duke to be mortal, we should probably
answer. Because all men are so. Hei-e, therefore, we arrive at the knowl-
edge of a truth not (as yet) susceptible of observation, by a reasoning'
which admits of being exhibited in the following syllogism :
All men are mortal.
The Duke of Wellington is a man,
therefore
The Duke of Wellington is mortal.
And since a large portion of our knowledge is thus acquired, logicians
have persisted in representing the syllogism as a process of inference or
proof ; though none of them has cleared up the difficulty which arises from
the inconsistency between that assertion, and the principle, that if there be
any thing in the conclusion which was not already asserted in the premi-
ses, the argument is vicious. For it is impossible to attach any serious-
scientific value to such a mei'e salvo, as the distinction drawn between be-
ing involved hy implication in the premises, and being directly asserted in
them. When Archbishop Whately says* that the object of reasoning is
" merely to expand and unfold the assertions wrapped up, as it were, and ,,
* Logic, p. 239 C9th ed.).
FUNCTIONS AND VALUE OF THE SYLLOGISM. 141
implied in those with which we set out, and to bring a person to perceive
-and acknowledge the full force of that which he has admitted," he does
not, I think, meet the real difficulty requiring to be explained, namely, how
it happens that a science, like geometry, can be all " wrapped up " in a
few definitions and axioms. Nor does this defense of the syllogism differ
much from what its assailants urge against it as an accusation, when they
■charge it with being of no use except to those who seek to press the con-
sequences of an admission into which a person has been entrapped without
having considered and understood its full force. When you admitted the
major premise, you asserted the conclusion; but, says Archbishop Whate-
ly, you asserted it ' by implication merely : this, however, can here only
mean that you asserted it unconsciously ; that you did not know you were
asserting it ; but, if so, the difficulty revives in this shape — Ought you not
to have known? Were you warranted in asserting the general proposi-
tion without having satisfied yourself of the truth of every thing which it
fairly includes? And if not, is not the syllogistic sxX, prima facie what its
assailants affirm it to be, a contrivance for catching you in a trap, and hold-
ing you fast in it ?*
§ 3. From this difficulty there appears to be but one issue. The propo-
sition that the Duke of Wellington is mortal, is evidently an inference ; it
is got at as a conclusion from something else; but do we, in reality, con- 1;
elude it from the proposition. All men are mortal? I answer, no. i
The error committed is, I conceive, that of overlooking the distinction be-
tween two parts of the process of philosophizing, the inferring part, and the
registering part ; and ascribing to the latter the functions of the former.
The mistake is that of referring a person to his own notes for the origin of
his knowledge. If a person is asked a question, and is at the moment una-
ble to answer it, he may refresh his memory by turning to a memorandum
which he carries about with him. But if he were asked, how the fact came
to his knowledge, he would scarcely answer, bec^se' it was set down in his
note-book : unless the book was written, like, the Koran, with a quill from
the wing of the angel Gabriel. '"^
Assuming that the proposition, The^jDuke of Wdllington^, mortal, is
immediately an inference from the pi'ogjMitiijirs'^iS.raen are,ir5rtal ; whence
do we derive our knowledge of,, tfcjvgeneral truth .' "tSi course from ob-
servation. Now, all which pair /.an observe are individual cases. From
these all general truths mapt be/drawn,and into these they may be again
resolved; for a generafeiMsitb i& "SS* ^° aggregate of particular truths; a
comprehensive expr^ioiT, i«^;which an indefinite number of individual
facts are affirmeel,; or *denie(j 'at once. But a general proposition is not
merely a compendiou^formlfor recording and preserving in the memory a ,
number of particnlarlijicts. all of which have been observed. Generaliza- j
* It is hardly necessary to say, that I am not contending for any such absurdity as that we
actually "ought to have known" and considered the case of eveiy individual man, past, pres-
ent, and future, before affirming that all men are mortal : although this interpretation has been,
strangely enough, put upon the preceding observations. There is no difference between me
and Archbishop Whately, or any other defender of the syllogism, on the practical part of the
matter ; I am only pointing out an inconsistency in the logical theory of it, as conceived by
almost all writers. I do not say that a person who affirmed, before the Duke of Wellington
was bom, that all men are mortal, knew that the Duke of Wellington was mortal ; but I do
say that he asserted it ; and I ask for an explanation of the apparent logical fallacy, of ad-
ducing in proof of the Duke of Wellington's mortality, a general statement which presupposes
it) Finding no sufficient resolution of this difficulty in any of the writers on Logic, I have
attempted to supply
142 REASONING.
I tion is not a process of mere naming, it is also a process of inference.
From instances which we have observed, we feel warranted in concluding,
that what we found true in those instances, holds in all similar ones, past,
present, and future, however numerous they may be. We then, by that
valuable contrivance of language which enables us to speak of many as if
I they were one, record all that we have observed, together with all that we
'; infer from our observations, ia one concise expression; and have thus only
'one proposition, instead of an endless number, to remember or to commu-
nicate. The results of many observations and inferences, and instructions
for making innumerable inferences in unforeseen cases, are compressed
into one short sentence.
When, therefore, we conclude from the death of John and Thomas, and
every other person we ever heard of in whose case the experiment had
been fairly tried, that the Duke of Wellington is mortal like the rest; we
may, indeed, pass through the generalization. All men are mortal, as an in-
termediate stage; but it is not in the latter half of the process, the de-
scent from all men to the Duke of Wellington, that the inference resides.
The inference is finished when we have asserted that all men are mortal.
What remains to be performed afterward is merely deciphering our own
notes.
Archbishop Whately has contended that syllogizing, or reasoning from
generals to particulars, is not, agreeably to the vulgar idea, a peculiar mode
of reasoning, but the philosophical analysis of the mode in which all men
reason, and must do so if they reason at all. With the deference due to so
high an authority, I can not help thinking that the vulgar notion is, in this
case, the more correct. If, from our experience of John, Thomas, etc., who
once were living, but are now dead, we are entitled to conclude that all hu-
man beings are mortal, we might surely without any logical inconsequence
have concluded at once from those instances, that the Duke of Wellington
is mortal. The nVnH^ '^^ John, Thomas, and others is, after all, tlie
whole evidence wjrfH^^H^the mortality of the Duke of Wellington. Not
one iota is adcreiJ^to the"S|^f by interpolating a general proposition.
Since J;he individiS||||,Bfe^ 18^1^*?^® evidence we can possess, evidence
"^rlTljh no logical form^nf^^wn^^^exhoose to throw it can make greater
than it is ; and since tha^eviJlMiceemvfcyier sufficient in itself, or, if insuf-
ficient for the one purpose, e^ltoi blBHH^ent for the other ;T am una-
ble to see why we should be foi'W^He^^^^j^the shortest cut from these
sufiicient premises to the conclu8iOT,^BW!ii^Baked to travel the "high
priori road," by the arbitrary fiat of ^RjiSj^'-Jh^ot perceive why it
should be impossible to journey from (^SH^Hn^nother unless we
"march up a hill, and then march down a^H^p#t may be the safest
road, and there may be a resting-place at tht\ t(^of the hill, affording a
commanding view of the surrounding country]; but for the mere purpose
of arriving at our journey's end, our taking that road is perfectly optional ;
it is * question of time, trouble, and danger. \
Not only may we reason from particulars toiparticulars without passing
through generals, but we perpetually do so re /son. All our earliest infer-
ences are of this nature. From the first dawi of intelligence we draw in-
ferences, but years elapse before we learn ijie use of general language.
The child, who, having burned his fingers, avoids to thrust them again into
the fire, has reasoned or inferred, though he has never thought of the gen-
eral maxim. Fire burns. He knows from memory that he has been burn-
ed, and on this evidence believes, when he sees a candle, that if he puts his
FUNCTIONS AND VALUE OF THE SYLLOGISM. 143
finger into the flame of it, he will be burned again. He believes this in ev-
ery case which happens to arise ; but without looking, in each instance, be-
yond the present case. He is not generalizing; he is inferring a partic-
ular from particulars. In the same way, also, brutes reason. There is
no ground for attributing to any of the lower animals the use of signs, of
such a nature as to render general propositions possible. But those ani-
mals profit by experience, and avoid what they have found to cause them
pain, in the same manner, though not always with the same skill, as a
human creature. Not only the burned child, but the burned dog, dreads
the fire.
I believe that, in point of fact, when drawing inferences from our per-
sonal experience, and not from maxims handed down to us by books or
tradition, we much oftener conclude from particulars to particulars directly,
than through the intermediate agency of any general proposition. We are
constantly reasoning from ourselves to other people, or from one person to
another, without giving ourselves the trouble to erect our observations into
general maxims of human or external nature. When we conclude that some
person will, on some given occasion, feel or act so and so, we sometimes-
judge from an enlarged consideration of the manner in which human beings
in general, or persons of some particular character, are accustomed to feel
and act ; but much oftener from merely recollecting the feelings and con-
duct of the same person in some previous instance, or from considering
how we should feel or act ourselves. It is not only the village matron,
who, when called to a consultation upon the case of a neighbor's child, pro-
nounces on the evil and its remedy simply on the recollection and authority
of what she accounts the similar case of her Lucy. We all, where we have
no definite maxims to steer by, guide ourselves in the same way : and if we
have an extensive experience, and retain its impressions strongly, we may
acquire in this manner a very considerable power of accurate judgment,
which we may be utterly incapable of justifying or of communicating to
others. Among the higher order of practical intellects there have been
many of whom it was remarked how admirably they suited their means to
their ends, without being able to give any sufficient reasons for what they
did ; and applied, or seemed to apply, recondite principles which they were
wholly unable to state. This is a natural consequence of having a mind
stored with appropriate particulars, and having been long accustomed to
reason at once from these to fresh particulars, without practicing the habit
of stating to one's self or to others the corresponding general propositions.
An old warrior, on a rapid glance at the outlines of the ground, is able at
once to give the necessary orders for a skillful arrangement of his troops ;
though if he has received little theoretical instruction, and has seldom been
called upon to answer to other people for his conduct, he may never have
had in his mind a single general theorem respecting the relation between
ground and array. But his experience of encampments, in circumstances
more or less similar, has left a number of vivid, unexpressed, ungeneralized
analogies in his mind, the most appropriate of which, instantly suggesting
itself, determines him to a judicious arrangement.
The skill of an uneducated person in the use of weapons, or of tools, is
ofa precisely similar nature. The savage who executes unerringly the ex-
act throw which brings down his game, or his enemy, in the manner most
suited to his purpose, under the operation of all the conditions necessarily
involved, the weight and form of the weapon, the direction and distance of
the object, the action of the wind, etc., owes this power to a long series of
144 REASONING.
previous experiments, the results of which he certainly never framed into
any verbal theorems or rules. The same thing may generally be said of
any other extraordinary manual dexterity. Not long ago a Scotch manu-
facturer procured from England, at a high rate of wages, a working dyer,
famous for producing very fine colors, with the view of teaching to his
other workmen the same skiU. The workman came ; but his mode of pro-
portioning the ingredients, in which lay the secret of the effects he pro-
duced, was by taking them up in handfuls, while the common method was
to weigh them. The manufacturer sought to make him turn his handling
system into an equivalent weighing system, that the general principle of
his peculiar mode of proceeding might be ascertained. This, however, the
man found himself quite unable to do, and therefore could impart his skill
to nobody. He had, from the individual cases of his own experience, es-
tablished a connection in his mind between fine effects of color, and tactual
perceptions in handling his dyeing materials; and from these perceptions
he could, in any particular case, infer the means to be employed, and the
effects which would be produced, but could not put othei-s in possession of
the grounds on which he proceeded, from having never generalized them
in his own mind, or expressed them in language.
Almost every one knows Lord Mansfield's advice to a man of practical
good sense, who, being appointed governor of a colony, had to preside in
its courts of justice, without previous judicial practice or legal education.
The advice was to give his decision boldly, for it would probably be right ;
but never to venture on assigning reasons, for they would almost infallibly
be wrong. In cases like this, which are of no uncommon occurrence, it
would be absurd to suppose that the bad reason was the source of the
good decision. Lord Mansfield knew that if any reason were assigned it
would be necessarily an afterthought, the judge being in fact guided by
impressions from past experience, without the circuitous process of fram-
ing general principles from them, and that if he attempted to frame any
such he would assuredly fail. Lord Mansfield, however, would not have
doubted that a man of equal experience who had also a mind stored with
general propositions derived by legitimate induction. from that experience,
would have been greatly preferable as a judge, to one, however sagacious,
who could not be trusted with the explanation and justification of his own
judgments. The cases of men of talent performing wonderful things they
know not how, are examples of the rudest and most spontaneous form of
the operations of superior minds. It is a defect in them, and often a
source of errors, not to have generalized as they went on ; but general-
ization, though a help, the most important indeed of all helps, is not an
essential.
Even the scientifically instructed, who possess, in the form of general
propositions, a systematic record of the results of the experience of man-
kind, need not always revert to those general propositions in order to ap-
ply that experience to a new case. It is justly remarked by Dugald Stew-
art, that though the reasonings in mathematics depend entirely on the
axioms, it is by no means necessary to our seeing the conclusiveness of
the proof, that the axioms should be expressly adverted to. "When it is
inferred that AB is equal to CD because each of them is equal to EF, the
most uncultivated understanding, as soon as the propositions were under-
stood, would assent to the inference, without having ever heard of the gen-
eral truth that " things which are equal to the same thing are equal to one
another." This remark of Stewart, consistently followed out, goes to the
FUNCTIONS AND VALUE OF THE SYLLOGISM. 145
root, as I conceive, of the philosophy of ratiocination ; and it is to be re-
gretted that he himself stopped short at a much more limited application
of it. He saw that the general propositions on which a reasoning is said
to depend, may, in certain cases, be altogether omitted, without impairing
its probative force. But he imagined this to be a peculiarity belonging
to axioms; and argued from it, that axioms are not the foundations or first
principles of geometry, from which all the other truths of the science are
eynthetically deduced (as the laws of motion and of the composition of
forces in dynamics, the equal mobility of fluids in hydrostatics, the laws of
reflection and r'efraction in optics, are the first principles of those sciences) ;
but are merely necessary assumptions, self-evident indeed, and the denial
of which would annihilate all demonstration, but from which, as premises,
nothing can be demonstrated. In the present, as in many other instances,
this thoughtful and elegant writer has perceived an important truth, but
only by halves. Finding, in the case of geometrical axioms, that general
names have not any talismanic virtue for conjuring new truths out of the
well where they lie hid, and not seeing that this is equally true in every
other case of generalization, he contended that axioms are in their nature
barren of consequences, and that the really fruitful truths, the real first
principles of geometry, are the definitions ; that the definition, for exam-
ple, of the circle is to the properties of the circle, what the laws of equi-
librium and of the pressure of the atmosphere are to the rise of the mer-
cury in the Torricellian tube. Yet all that he had asserted respecting the
function to which the axioms are confined in the demonstrations of geome-
try, holds equally true of the definitions. Every demonsti-ation in Euclid
might be crrried on without them. This is apparent from the ordinary
process of proving a proposition of geometry by means of a diagram.
What assumption, in fact, do we set out from, to demonstrate by a dia-
gram any of the properties of the circle? Not that in all circles the i-adii
are equal, but only that they are so in the circle ABC. As our warrant
for assuming this, we appeal, it is true, to the definition of a circle in gen-
eral; but it is only necessary that the assumption be granted in the case of
the particular circle supposed. From this, which is not a general but a sin-
gular proposition, combined with other propositions of a similar kind, some
of which when generalized are called definitions, and other axioms, we
prove that a certain conclusion is true, not of all circles, but of the partic-
ular circle ABC ; or at least would be so, if the facts precisely accorded
with our assumptions. The enunciation, as it is called, that is, the gener-
al theorem which stands at the head of the demonstration, is not the propo-
sition actually demonstrated. One instance only is demonstrated : but the
process by which this is done, is a process which, when we consider its
nature, we perceive might be exactly copied in an indefinite number of oth-
er instances ; in every instance which conforms to certain conditions. The
contrivance of general language furnishing us with terms which connote
these conditions, we are able to assert this indefinite multitude of truths
in a single expression, and this expression is the general theorem. _ By
dropping the use of diagrams, and substituting, in the demonstrations,
general phrases for the letters of the alphapet, we might prove the general
theorem directly, that is, we might demonstrate all the cases at once ; and
to do this we must, of course, employ as our premises, the axioms and
definitions in their general form. But this only means, that if we can
prove an individual conclusion by assuming an individual fact, then in
■whatever case we are warranted in making an exactly similar assumption,
10
146 REASONING.
we may draw an exactly similar conclusion. The definition is a sort of
notice to ourselves and others, what assumptions we think ourselves en-
titled to make. And so in all cases, the general propositions, whether
called definitions, axioms, or laws of nature, which we lay down at the
beginning of our reasonings, are merely abridged statements, in a kind of
short-hand, of the particular facts, which, as occasion arises, we either
think we may proceed on as proved, or intend to assume. In any one
demonstration it is etiough if we assume for a particular case suitably se-
lected, what by the statement of the definition or principle we announce
that we intend to assume in all cases which may arise. The definition of
the circle, therefore, is to one of Euclid's demonstrations, exactly what, ac-
cording to Stewart, the axioms are ; that is, the demonstration does not
depend on it, but yet if we deny it the demonstration fails. The proof
does not rest on the general assumption, but on a similar assumption con-
fined to the particular case : that case, however, being chosen as a speci-
men or paradigm of the whole class of cases included in the theorem, there
can be no ground for making the assumption in that case which does not.
exist in every other ; and to deny the assumption as a general truth, is to
deny the right of making it in the particular instance.
There are, undoubtedly, the most ample reasons for stating both the
i principles and the theorems in their general form, and these will be ex-
i plained presently, so far as explanation is requisite. But, that unpracticed
' learners, even in making use of one theorem to demonstrate another, rea-
son rather from particular to particular than from the general proposition,
is manifest from the difficulty they find in applying a theorem to a case in
which the configuration of the diagram is extremely unlike that of the dia-
gram by which the original theorem was demonstrated. A dilficulty
which, except in cases of unusual mental power, long practice can alone re-
move, and removes chiefly by rendering us familiar with all the configura-
tions consistent with the general conditions of the theorem.
§ 4. From the considerations now adduced, the following conclusions
seem to be established. All inference is from particulars to particulars;
General propositions are merely registers of such inferences already made,,
and short formulse for making more: The major premise of a syllogism,
consequently, is a formula of this description : and the conclusion is not an
inference drawn from the formula, but an inference drawn according to
the formula : the real logical antecedent, or premise, being the particular
facts from which the general proposition was collected by induction.
Those facts, and the individual instances which supplied them, may have
been forgotten : but a record remains, not indeed descriptive of the facts
themselves, but showing how those cases may be distinguished, respecting
which, the facts, when known, were considered to warrant a given infer-
ence. According to the indications of this record we draw our conclusion :
which is, to all intents and purposes, a conclusion from the forgotten facts.
For this it is essential that we should read the record correctly: and the
rules of the syllogism are a set of precautions to insure our doing so.
This view of the functions of the syllogism is confirmed by the consid-
eration of precisely those cases which might be expected to be least favor-
able to it, namely, those in which ratiocination is independent of any pre-
vious induction. We have already observed that the syllogism, in the or-
dinary course of our reasoning, is only the latter half of the process of
traveling from premises to a conclusion. There are, however, some pecul-
FUNCTIONS AND VALUE OF THE SYLLOGISM. 147
iar cases in which it is the whole process. Particulars alone are capable
?<»f being subjected to observation; and all knowledge which is derived
from observation, begins, therefore, of necessity, in particulars ; but our
knowledge may, in cases of certain descriptions, be conceived as coming to
us from other sources than observation. It may present itself as coming
f i-om testimony, which, on the occasion and for the purpose in hand, is ac-
cepted as of an authoritative character : and the information thus commu-
nicated, may be conceived to comprise not only particular facts but general
propositions, as when a scientific doctrine is accepted without examination
on the authority of writers, or a theological doctrine on that of Scripture.
Or the generalization may not be, in the ordinary sense, an assertion at all,
but a command ; a law, not in the philosophical, but in the moral and po-
litical sense of the term : an expression of the desire of a superior, that we,
or any number of other persons, shall conform our conduct to certain gen-
eral instructions. So far as this asserts a fact, namely, a volition of the
legislator, that fact is an individual -fact, and the proposition, therefore, is
not a general proposition. But the description therein contained of the
conduct which it is the will of the legislator that his subjects should ob-
serve, is general. The proposition asserts, not that all men are any thing,
but that all men shall do something.
In both these cases the generalities are the original data, and the partic-
ulars are elicited from them by a process which correctly resolves itself
into a series of syllogisms. The real nature, however, of the supposed de-
ductive process, is evident enough. The only point to be determined is,
whether the authority which declared the general proposition, intended to
include this case in it; and whether the legislator intended his command
to apply to the present case among others, or not. This is ascertained by
examining whether the case possesses the marks by which, as those author-
ities have signified, the cases which they meant to certify or to influence
may be known. The object of the inquiry is to make out the witness's or
the legislator's intention, through the indication given by their words.
This is a question, as the Germans express it, of hermeneutics. The opera-
tion is not a process of inference, but a process of interpretation.
In this last phrase we have obtained an expression which appears to me
to characterize, more aptly than any other, the functions of the syllogism
in all cases. When the premises are given by authority, the function of
Reasoning is to ascertain the testimony of a witness, or the will of a
legislator, by interpreting the signs in which the one has intimated his as-
sertion and the other his command. In like manner, when the premises
are derived from observation, the function of Reasoning is to ascertain
what we (or our predecessors) formei'ly thought might be inferred from
the observed facts, and to do this by interpreting a memorandum of ours,
or of theirs. The memorandum reminds us, that from evidence, more or
less carefully weighed, it formerly appeared that a certain attribute might
be inferred wherever we perceive a certain mark. The proposition. All
men are mortal (for instance) shows that we have had experience fiom
which we thought it followed that the attributes connoted by the term man,
are a mark of mortality. But when we conclude that the Duke of Wel-
lington is mortal, we do not infer this from the memorandum, but from
the former experience. All that we infer from the memorandum is our
own previous belief, (or that of those who transmitted to us the proposi-
tion)^^ concerning the inferences which that former experience would war-
rant. ;
148 REASONING.
This view of the nature of the syllogism renders consistent and intel-
ligible what otherwise remains obscure and confused in the theory of
Archbishop Whately and other enlightened defenders of the syllogistic
doctrine, respecting the limits to which its functions are confined. They
, affirm in as explicit terms as can be used, that the sole office of general
' reasoning is to prevent inconsistency in our opinions ; to prevent us from
. assenting to any thing, the truth of which would contradict something to
which we had previously on good grounds given our assent. And they
tell us, that the sole ground which a syllogism affords for assenting to the
i conclusion, is that the supposition of its being false, combined with the
I supposition that the premises are true, would lead to a contradiction in
i terms. Now this would be but a lame account of the real grounds which
we have for believing the facts which we learn from reasoning, in contra-
i, distinction to observation. The true reason why we believe that the Duke
. of Wellington will die, is that his fathers, and our fathers, and all other
persons who were contemporary with them, have died. Those facts are the
real premises of the reasoning. But we are not led to infer the conclusion
from those premises, by the necessity of avoiding any verbal inconsistency.
There is no contradiction in supposing that all those persons have died,
, and that the Duke of "Wellington may, notwithstanding, live forever. But
; there would be a contradiction if we first, on the ground of those same
premises, made a general assertion including and covering the case of the
i Duke of Wellington, and then refused to stand to it in the individual case..
There is an inconsistency to be avoided between the memorandum we
I make of the inferences which may be justly drawn in future cases, and
the inferences we actually draw in those cases when they arise. With
ithis view we interpret our own formula, precisely as a judge interprets a
law : in order that we may avoid drawing any inferences not conformable
to our former intention, as a judge avoids giving any decision not conform-
able to the legislator's intention. The rules for this interpretation are the
rules of the syllogism : and its sole purpose is to maintain consistency be-
tween the conclusions we draw in every particular case, and the previous
general directions for drawing them; whether those general directions
were framed by ourselves as the result of induction, or were received
by us from an authority competent to give them.
§ 5. In the above observations it has, I think, been shown, that, though
there is always a process of reasoning or inference where a syllogism is
used, the syllogism is not a correct analysis of that process of reasoning or
^ inference ; which is, on the contrary (when not a mere inference from tes-
timony), an inference from particulars to particulars ; authorized by a pre-
vious inference from particulars to generals, and substantially the same with
it ; of the nature, therefore, of Induction. But while these conclusions ap-
pear to me undeniable, I must yet enter a protest, as strong as that of Arch-
r bishop Whately himself, against the doctrine that the syllogistic art is use-
i less for the purposes of reasoning. The reasoning lies in the act of gener-
j alization, not in interpreting the record of that act ; but the syllogistic form
; is an indispensable collateral security for the correctness of the generaliza-
tion itself.
It has already been seen, that if we have a collection of particulars suffi-
\ cient for grounding an induction, we need not frame a general proposition ;
we may reason at once from those particulars to other particulars. But it
: is to be remarked withal, that whenever, from a set of particular cases, we
can legitimately draw any inference, we may legitimately make our infer-
FUNCTIONS AND VALUE OF THE SYLLOGISM. 149
ence a general one. If, from observation and experiment, we can conclude
to one new case, so may we to an indefinite number. If that which has
held true in our past experience will therefore hold in time to come, it will
hold not merely in some individual case, but in all cases of some given
description. Every induction, therefore, which suffices to prove one fact,
proves an indefinite multitude of facts : the experience which justifies a sin-
gle prediction must be such as will suifice to bear out a general theorem.
This theorem it is extremely important to ascertain and declare, in its
broadest form of generality ; and thus to place before our minds, in its full
extent, the whole of what our evidence must prove if it proves any thing.
This throwing of the whole body of possible inferences from a given set
of particulars, into one general expression, operates as a security for their
being just inferences, in more ways than one. First, the general principle
presents a larger object to the imagination than any of the singular prop-
ositions which it contains. A process of thought which leads to a com-
prehensive generality, is felt as of greater importance than one which ter-
minates in an insulated fact; and the mind is, even unconsciously, led to
bestow greater attention upon the process, and to weigh more carefully
the sufficiency of the experience appealed to, for supporting the inference
grounded upon it. There is another, and a more important, advantage.
In reasoning from a course of individual observations to some new and un-
observed case, which we are but imperfectly acquainted with (or we should
not be inquiring into it), and in which, since we are inquiring into it, we
probably feel a peculiar interest ; there is very little to prevent us from
giving way to negligence, or to any bias which may affect our wishes or
our imagination, and, under that influence, accepting insufficient evidence
as sufficient. But if, instead of concluding straight to the particular case,
we place before ourselves an entire class of facts — the whole contents of a
general proposition, every tittle of which is legitimately inferable fi-om our
premises, if that one particular conclusion is so ; there is then a considera-
ble likelihood that if the premises are insufficient, and the general inference
therefore, groundless, it will comprise within it some fact or facts the re-
verse of which we already know to be true; and we shall thus discover
the error in our generalization by a reductio ad impossibile.
Thus if, during the reign of Marcus Aurelius, a subject of the Roman
empire, under the bias naturally given to the imagination and expectations
by the lives and characters of the Antonines, had been disposed to expect
that Commodus would be a just ruler; supposing him to stop there, he
might only have been undeceived by sad experience. But if he reflected
that this expectation could not be justifiable unless from the same evidence
he was >.' irranted in concluding some general proposition, as, for instance,
that all Uoman emperors are just. rulers; he would immediately have
thougbl^f Nero, Domitian, and other instances, which, showing the falsity
of the 'mineral conclusion, and therefore the insufficiency of the premises,
would li;.ve warned him that those premises could not prove in the insitance
of Commodus, what they were inadequate to prove in any collection of
cases in which his was included.
Tlie advantage, in judging whether any controverted inference is legiti-
mate, of referring to a parallel case, is universally acknowledged. But by
ascending to the general proposition, we bring under our view not one par-
allel case only, but all possible parallel cases at once ; all cases to which the
same set of evidentiary considerations are applicable.
WheHj'T.herefore, we argue from a number of known cases to another case
150 REASONING.
supposed to be analogous, it is always possible, and generally advantageous,
to divert our argument into the circuitous channel of an induction from
those known cases to a general proposition, and a subsequent application
of that general proposition to the unknown case. This second part of the
operation, which, as before observed, is essentially a process of interpreta-
tion, will be resolvable into a syllogism or a series of syllogisms, the majors
of which will be general propositions embracing whole classes of cases ;
every one of which propositions must be true in all its extent, if the argu-
ment is maintainable. If, therefore, any fact fairly coming within the
range of one of these general propositions, and consequently asserted by it,
is known or suspected to be othei" than the proposition asserts it to be, this
mode of stating the argument causes us to know or to suspect that the
original observations, which are the real grounds of our conclusion, are not
sufficient to support it. And in proportion to the greater chance of our
detecting the inconclusiveness of our evidence, will be the increased reli-
ance we are entitled to place in it if no such evidence of defect shall appear.
The value, therefore, of the syllogistic form, and of the rules for using it
correctly, does not consist in their being the form and the rules according
to which our reasonings are necessarily, or even usually, made ; but in their
furnishing us with a mode in which those reasonings may always be repre-
sented, and which is admirably calculated, if they are inconclusive, to bring
their inconclusiveness to light. An induction from particulars to generals,
followed by a syllogistic process from those generals to other particulars, is
a form in which we may always state our reasonings if we please. It is
not a form in which we must reason, but it is a form in which we may rea-
son, and into which it is indispensable to throw our reasoning, when thei*e
is any doubt of its validity : though when the case is familiar and little
complicated, and there is no suspicion of error, we may, and do, reason at
once from the known particular cases to unknown ones.*
These are the uses of syllogism, as a mode of verifying any given argu-
ment. Its ulterior uses, as respects the general course of our intellectual
operations, hardly require illustration, being in fact the acknowledged uses
of general language. They amount substantially to this, that the induc-
tions may be made once for all: a single careful interrogation of experi-
ence may suffice, and the result may be registered in the form of a general
proposition, which is committed to memory or to writing, and from which
afterward we have only to syllogize. The particulars of our experiments
may then be dismissed from the memory, in which it would be impossible
to retain so great a multitude of details ; while the knowledge which those
details afEorded for future use, and which would otherwise be lost as soon
as the observations were forgotten, or as their record became too bulky for
reference, is retained in a commodious and immediately available shape by
means of general language.
Against this advantage is to be set the countervailing inconvenience, that
inferences originally made on insufficient evidence become consecrated, and,
as it were, hardened into general maxims ; and the mind cleaves to them
• The language of ratiocination would, I think, be brought into eloeer agreement with the
real nature of the process, if the general propositions employed in reasoning, instead of being
in the form All men are mortal, or Every man is mortal, were expressed in the form Any
man is mortal. This mode of expression, exhibiting as the type of all reasoning from expe-
rience " The men A, B, C, etc., are so and so, therefore any man is so and so," would much
better manifest the true idea — that inductive reasoning is always, at bottom, inference from
particulars to particulars, and that the whole function of general propositions in reasoning, is
to vouch for the legitimacy of such inferences.
FUNCTIONS AND VALUE OF THE SYLLOGISM. 151
-from habit, after it has outgrown any liability to be misled by similar falla/'
-cious appearances if they were now for the first time presented ; but hav-
ing forgotten the particulars, it does not think of revising its own formel
decision. An inevitable drawback, which, however considerable in itself,
forms evidently but a small set-off against the immense benefits of general
language.
The use of the syllogism is in truth no other than the use of general
propositions in reasoning. We can reason without them ; in simple and
, obvious cases we habitually do so; minds of great sagacity can do it in
,' cases not simple and obvious, provided their experience supplies them with
instances essentially similar to every combination of circumstances likely
to arise. But other minds, and the same minds where they have not the
same pre-eminent advantages of personal experience, are quite helpless
without the aid of general propositions, wherever the case presents the
-smallest complication ; and if we made no general proposiXions, few per-
sons would get much beyond those simple inferences which are drawn by
', the more intelligent of the brutes. Though not necessary to reasoning,
\ -general propositions are necessary to any considerable progress in reason-
\ ing. It is, therefore, natural and indispensable to separate the process of
investigation into two parts ; and obtain general formulae for determining
•what inferences may be drawn, before the occasion arises for drawing the
inferences. The work of drawing them is then that of applying the for-
mulae ; and the rules of syllogism are a system of securities for the correct-
-tiess of the application.
§ 6. To complete the series of considerations connected with the philo-
sophical character of the syllogism, it is requisite to consider, since the syl-
logism is not the universal type of the reasoning process, what is the real
type. This resolves itself into the question, what is the nature of the mi-
nor premise, and in what manner it contributes to establish the conclusion :
for as to the major, we now fully understand, that the place which it nom-
inally occupies in our reasonings, properly belongs to the individual facts
or observations of which it expresses the general result; the major itself
being no real part of the argument, but an intermediate halting-place for
the mind, interposed by an artifice of language between the real premises
and the conclusion, by way of a security, which it is in a most material de-
gree, for the correctness of the process. The minor, however, being an in-^
dispensable part of the syllogistic expression of an argument, without!
-doubt either is, or corresponds to, an equally indispensable part of the ar- j
-gument itself, and we have only to inquire what part.
It is perhaps worth while to notice here a speculation of a philosopher
to whom mental science is much indebted, but who, though a very pene-
trating, was a very hasty thinker, and whose want of due circumspection
rendered him fully as remarkable for what he did not see, as for what he
saw. I allude to Dr. Thomas Brown, whose theory of ratiocination is pe-
•culiar. He saw the petitio principii which is inherent in every syllogism,
if we consider the major to be itself the evidence by which the conclusion
is proved, instead of being, what in fact it is, an assertion of the existence
■ of evidence sufficient to prove any conclusion of a given description. See-
ing this, Dr. Brown not only failed to see the immense advantage, in point
of security for correctness, which is gained by interposing this step be-
tween the real evidence and the conclusion ; but he thought it incumbent
•on him to strike out the major altogether from the reasoning process, with-
152 REASONING. *■
out substituting any thing else, and maintained that our reasonings 'consist
only of the minor premise and the conclusion, Socrates is a man, therefore
Socrates is mortal : thus actually suppressing, as an unnecessary step in
the arwuraent, the appeal to former experience. The absurdity of this was
disguised from him by the opinion he adopted, that reasoning is merely an-
alyzing our own general notions, or abstract ideas ; and that the proposi-
tion, Socrates is mortal, is evolved from the proposition, Socrates is a man,
simply by recognizing the notion of mortality as akeady contained in the
notion we form of a man.
After the explanations so fully entered into on the subject of proposi-
tions, much further discussion can not be necessary to make the radical
error of this view of ratiocination apparent. If the word man connoted
mortality; if the meaning of "mortal" were involved in the meaning of
" man ;" we might, undoubtedly, evolve the conclusion from the minor
alone, because the minor would have already asserted it. But if, as is in
fact the case, the word man does not connote mortality, how does it appear
that in the mind of every person who admits Socrates to be a man, the
idea of man must include the idea of .mortality ? Dr. Brown could not
help seeing this difficulty, and in order to avoid.it, was led, contrary to his
intention, to re-establish, under another name, that step in the argument
which corresponds to the major, by affirming the necessity of previously
perceiving the relation between the idea of man and the idea of mortal. If
the reasoner has not previously perceived this relation, he will not, says Dr.
Brown, infer because Socrates is a man, that Socrates is mortal. But even
this admission, though amounting to a surrender of the doctrine that an
argument consists of the minor and the conclusion alone, will not save the
remainder of Dr. Brown's theory. The failure, of assent to the argument
does not take place merely because the reasoner, for want of due analysis,
does not perceive that his idea of man includes the idea of mortality; it
takes place, much more commonly, because in his mind that relation be-
tween the two ideas has never existed. And in truth it never does exist,
except as the result of experience. Consenting, for the sake of the argu-
ment, to discuss the question on a supposition of which we have recog-
nized the radical incorrectness, namely, that the meaning of a proposition
relates to the ideas of the things spoken of, and not to the things them-
selves ; I must yet observe, that the idea of man, as a universal idea, the
common property of all rational creatures, can not involve any thing but
what is strictly implied in the name. If any one includes in his own pri-
vate idea of man, as no doubt is always the case, some other attributes, such
for instance as mortality, he does so only as the consequence of experience,
after having satisfied himself that all men possess that attribute : so that
whatever the idea contains, in any person's mind, beyond what is included
in the conventional signification of the word, has been added to it as the
result of assent to a proposition ; while Dr. Brown's theory requires us to
suppose, on the contrary, that assent to the proposition is produced by
evolving, through an analytic process, this very element out of the idea.
This theory, therefoi-e, may be considered as sufficiently refuted ; and the
minor premise must be regarded as totally insufficient to prove the conclu-
sion, except with the assistance of the major, or of that which the major
rapi'esents, namely, the various singular propositions expressive of the se-
ries of observations, of which the generalization called the major premise is
the result.
In the argument, then, which proves that Socrates is mortal, one indis-
FUNCTIONS AND VALUE OF THE SYLLOGISM. I53
pensable part of the premises will be as follows : " My father, and my fa-
ther's father, A, B, C, and an indefinite number of other persons, were mor-
tal;" which is only an expression in different words of the observed fact
that they have died. This is the major premise divested of the petitio
principii, and cut down to as much as is really known by direct evidence.
In order to connect this proposition with the conclusion Socrates is mor-
tal, the additional link necessary is such a proposition as the following:
" Socrates resembles my father, and my father's father, and the other indi-
viduals specified." This proposition we assert when we say that Socrates
is a man. By saying so we likewise assert in what respect he resembles
them, namely, in the attributes connoted by the word man. And we con-
clude that he further resembles them in the attribute mortality.
§ 1. We have thus obtained what we were seeking, a universal type of
the reasoning process. We find it resolvable in all cases into the follow-
ing eleinents : Certain individuals have a given attribute ; an individual or
Individuals resemble the former in certain other attributes ; therefore they
resemble them also in the given attribute. This type of ratiocination does
not claim, like the syllogism, to be conclusive' from the mere form of the
expression ; nor can it possibly be so. That one proposition does or does
not assert the very fact which was already asserted in another, may appear
from the form of the expression, that is, from a comparison of the lan-
guage; but when the two propositions assert facts which are bona fide
different, whether the one fact proves the other or not can never appear
from the language, but must depend on other considei-ations. Whether,
from the attributes in which Socrates resembles those men who have here-
tofore died, it is allowable to infer that he resembles them also in being
mortal, is a question of Induction ; and is to be decided by the principles
or canons which we shall hereafter recognize as tests of the correct per-
formance of that great mental operation.
Meanwhile, however, it is certain, as before remarked, that if this infer-
ence can be drawn as' to Socrates, it can be drawn as to all others who re-
semble the observed individuals in the same attributes in which he resem-
bles them; that is (to express the thing concisely) of all mankind. If,
therefore, the argument be admissible in the case of Socrates, we are at lib-
erty, once for all, to treat the possession of the attributes of man as a mark,
or satisfactory evidence, of the attribute of mortality. This we do by lay-
ing down the universal proposition, All men are mortal, and interpreting
this, as occasion arises, in its application to Socrates and others. By this
means we establish a very convenient division of the entire logical opera-
tion into two steps ; first, that of ascertaining what attributes are marks
of mortality ; and, secondly, whether any given individuals possess those
marks. And it will generally be advisable, in our speculations on the rea-
soning process, to consider this double operation as in fact taking place,
and all reasoning as carried on in the form into which it must necessarily
be thrown to enable us to apply to it any test of its correct performance.
Although, therefore, all processes of thought in which the ultimate prem-
ises are particulars, whether we conclude from particulars to a general for-
nmla, or from particulai-s to other particulars according to that formula, are
equally Induction ; we shall yet, conformably to usage, consider the name
Induction as more peculiarly belonging to the process of establishing^ the
general proposition, and the remaining operation, which is substantially
that of interpreting the general proposition, we shall call by its usual name,
154 KEASONING.
Deduction. And we shall consider every process by which any thing i?
inferred respecting an unobserved case, as consisting of an Induction fol-
lowed by a Deduction ; because, although the process needs not necessarily
be carried on in this foi-m, it is always susceptible of the form, and must
be thrown into it when assurance of scientific accuracy is needed and de-
sired.
§ 8. The theory of the syllogism laid down in the preceding pages, has
obtained, among other important adhesions, three of peculiar value : tliose-
of Sir John Herschel,* Dr. Whewell,! and Mr. Bailey ;J Sir John Herschel
considering the doctrine, though not strictly " a discovery," having been
anticipated by Berkeley,§ to be " one of the greatest steps which have yet
been made in the philosophy of Logic." "When we consider" (to quote-
the further words of the same authority) " the inveteracy of the habits and.
prejudices which it has cast to the winds," there is no cause for misgiving
in the fact that other thinkers, no less entitled to consideration, have formed
a very different estimate of it. Their principal objection can not be bet-
ter or more succinctly stated than by borrowing a sentence from Archbish-
op Whately.|| "In every case where an inference is drawn from Induc-
tion (unless that name is to be given to a mere random guess without any
grounds at all) we must form a judgment that the instance or instances ad-
•duced are sufficient to authorize the conclusion ; that it is allowable to take
jthese instances as a sample warranting an inference respecting the whole
Iclass ;" and the expression of this judgment in words (it has been said by
jseveral of my critics) is the major premise.
I quite admit that the major is an affirmation of the sufficiency of the
evidence on which the conclusion rests. That it is so, is the very essence
of my own theory. And whoever admits that the major premise is only
this, adopts the theory in its essentials.
But I can not concede that this recognition of the sufficiency of the evi-
dence— that is, of the correctness of the induction — is a part of the induc-
tion itself ; unless we ought to say that it is a part of every thing we do,,
to satisfy ourselves that it has been done rightly. We conclude from
known instances to unknown by the impulse of the generalizing propensi-
ty; and (until after a considerable amount of practice and mental disci-
pline) the question of the sufficiency of the evidence is only raised by a re-
trospective act, turning back upon our own footsteps, and examining wheth-
er we were warranted in doing what we have provisionally done. To'
speak of this reflex operation as part of the original one, requiring to be
expressed in words in order that the verbal formula may correctly repre-
sent the psychological process, appears to me false psychology. 1^ We re-
view our syllogistic as well as our inductive processes, and recognize that-
* Review of Qiietelet on Probabilities, Essays, p. 367.
t Philosophy of Discovery, p. 289.
% Theory of Reasoning, chap, iv., to which I may refer for an able statement and enforce-
ment of the grounds of the doctrine.
§ On a recent careful reperusal of Berkeley's whole works, I have been unable to find this
doctrine in them. Sir John Herschel probably meant that it is implied in Berkeley's argu-
ment against abstract ideas. But I can not find that Berkeley saw the implication, or had:
ever asked himself what bearing his argument had on the theory of the syllogism. Still less
can I admit that the doctrine is (as has been aflirmed by one of my ablest and most candid;
f3ritics) " among the standing marks of what is called the empirical philosophy."
II Logic, book iv., chap, i., sect. 1.
f See the important chapter on Belief, in Professor Bain's great treatise, The Emotions ani-
the Will, pp. 581-4.
FUNCTIONS AND VALUE OF THE SYLLOGISM. 155
they have been correctly performed ; but logicians do not add a third
premise to the syllogism, to express this act of recognition. A careful
copyist verifies his transcript by collating it with the original ; and if no
error appears, he recognizes that the transcript has been correctly made.
But we do not call the examination of the copy a part of the act of copying.
The conclusion in an induction is inferred from the evidence itself, and
not from a recognition of the sufficiency of the evidence ; as I infer that
my friend is walking toward me because I see him, and not because I rec-
ognize that my eyes are open, and that eyesight is a means of knowledge.
In ail operations which require care, it is good to assure ourselves that
the process has been performed accurately ; but the testing of the proc-
ess is not the process itself; and, besides, may have been omitted alto-
gether, and yet the process be correct. It is precisely because that opera- j
tion is omitted in ordinary unscientific reasoning, that there is any thing '
gained in certainty by throwing reasoning into the syllogistic form. To
make sure, as far as possible, that it shall not be omitted, we make the test-
ing operation a part of the reasoning process itself. We insist that the
inference from particulars to particulars shall pass through a general propo-
sition. But this is a security for good reasoning, not a condition of all rea-
soning ; and in some cases not even a security. Our most familiar infer-
ences are all made before we learn the use of general propositions ; and a
person of untutored sagacity will skillfully apply his acquired experience
to adjacent cases, though he would bungle grievously in fixing the limits
of the appropriate general theorem. But though he may conclude rightly,
he never, properly speaking, knows whether he has done so or not ; he has
not tested his reasoning. Now, this is precisely what forms of reasoning
do for us. We do not need them to enable us to reason, but to enable us
to know whether we reason correctly.
In still further answer to the objection, it may be added that — even wh'e&
the test has been applied, and the sufficiency of the evidence recognized^
if it is sufficient to support the general proposition, it is sufficient also to\
support an inference from particulars to particulars without passing
through the general proposition. The inquirer who has logically satisfied
himself that the conditions of legitimate induction were realized in the
cases A, B, C, would be as much justified in concluding directly to the
Duke of Wellington as in concluding to all men. The general conclusion
is never legitimate, unless the particular one would be so too ; and in no
sense, intelligible to me, can the particular conclusion be said to be drawn
from the general one. Whenever there is ground for drawing any conclu-
sion at all from particular instances, there is ground for a general conclu-
sion ; but that this general conclusion should be actually drawn, howeverf
useful, can not be an indispensable condition of the validity of the inference
in the particular case. A man gives away sixpence by the same power byi
which he disposes of his whole fortune ; but it is not necessary to the le-
gality of the smaller act, that he should make a formal assertion of his rightj
to the greater one.
Some additional remarks, in reply to minor objections, are appended.*
* A writer in the "British Quarterly Review" (August, 1846), in a review of this treatise,
endeavors to show that there is no petitio principii in the syllogism, by denying that the
proposition. All men are mortal, asserts or assumes that Socrates is mortal. In support of
this denial, he argues that we may, and in fact do, admit the general proposition that all men
are moi-tal, without having particularly examined the case of Socrates, and even without
knowing whether the individual so named is a man or something else. But this of course
156 REASONING.
§ 9. The preceding considerations enable us to understand the true na-
ture of what is termed, by recent writers, Formal Logic, and the relation
was never denied. That we can and do draw conclusions concerning cases specifically un-
known to us, is the datum from which all who discuss this subject must set out. The ques-
tion is, in what terms the evidence, or ground, on which we draw these conclusions, may best
be designated — whether it is most correct to say, that the unknown case is proved by known
cases, or that it is proved by a general proposition including both sets of cases, the unknown
and the known ? I contend for the former mode of expression. I hold it an abuse of lan-
guage to say, that the proof that Socrates is mortal, is that all men are mortal. Turn it in
what way we will, this seems to me to be asserting that a thing is the J)roof of itself. Who-
ever pronounces the words, All men are mortal, has affirmed that Socrates is mortal, though
he may never have heard of Socrates ; for since Socrates, whether known to be so or not,
really is a man, he is included in the words, All men, and in every assertion of which they
are the subject. If the reviewer does not see that there is a difficulty here, I can only advise
him to reconsider the subject until he does : after which he will be a better judge of the suc-
cess or failure of an attempt to remove the difficulty. That he had reflected very little on the
point when he wrote his remarks, is shown by his oversight respecting the dictum de omni et
nulla. He acknowledges that this maxim as commonly expressed — "Whatever is true of a
class, is true of every thing included in the class," is a mere identical proposition, since the
class is nothing but the things included in it. But he thinks this defect would be cured by
wording the maxim thus— "Whatever is true of a class, is true of every thing which can be
shown to be a member of the class :" as if a thing could " be shown " to be a member of the
class without being one. If a class means the sum of all the things included in the class, the
things which can "be shown" to be included in it are part of the sum, and the dictum is at
much an identical proposition with respect to them as to the rest. One would almost imagine
that, in the reviewer's opinion, things are not members of a class until they are called up pub-
licly to take their place in it — that so long, in fact, as Socrates is not known to be a man, he
IS not a man, and any assertion which can be made concerning men does not at all regard
him, nor is affected as to its truth or falsity by any thing in which he is concerned.
The difference between the reviewer's theory and mine may be thus stated. Both admit
that when we say. All men are mortal, we make an assertion reaching beyond the sphere of
our knowledge of individual cases ; and that when a new individual, Socrates, is brought with-
in the field of our knowledge by means of the minor premise, we learn that we have already
made an assertion respecting Socrates without knowing it : our own general formula being, to
that extent, for the first time interpreted to us. But according to the reviewer's theory, the
smaller assertion is proved by the larger : vihile I contend, that both assertions are proved to-
gether, by the same evidence, namely, the grounds of experience on which the general asser-
tion was made, and by which it must be justified.
The reviewer says, that if the major premise included the conclusion, "we should be able
to affirm the conclusion without the intervention of the minor premise; but every one sees
that that is impossible." A similar argument is urged by Mr. De Morgan {Farmed Logic, p.
259): "The whole objection tacitly assumes the superfluity of the minor; that is, tacitly as-
sumes we know Socrates* to be a man as soon as we know' him to be Socrates." The objec-
tion would be well grounded if the assertion that the major premise includes the conclusion,
meant that it individually specifies all it includes. As, however, the only indication it gives is
a description by marks, we have still to compare any new individual with the marks ; and to
show that this comparison has been made, is the office of the minor. But since, by supposi-
tion, the new individual has the marks, whether we have ascertained him to have them or
not ; if we have affirmed the major premise, we have asserted him to be mortal. Now my
position is that this assertion can not be a necessary part of the argument. It can not be a
necessary condition of reasoning that we should begin by making an assertion, which is after-
ward to be employed in proving a part of itself. I can conceive only one way out of this dif-
ficulty, viz., that what really forms the proof is the other part of the assertion ; the portion of
it, the truth of which has been ascertained previously : and that the unproved part is bound
up in one formiihi with the proved part in mere anticipation, and as a memorandum of the
nature of the conclusions which we are prepared to prove.
With respect to the minor premise in its formal shape, the minor as it stands in the syllo-
gism, predicating of Socrates a definite class name, I readily admit that it is no more a neces-
sary part of reasoning than the major. When there is a major, doing its work by means of a
class name, minors are needed to interpret it : but reasoning can be carried on without either
the one or the other. They are not the conditions of reasoning, but a precaution against er-
roneous reasoning. The only minor premise necessary to reasoning in the example under
* Mr. De Morgan says "Plato," but to prevent confusion I have kept to my own exemphm.
FUNCTIONS AND VALUE OF THE SYLLOGISM. 15T
between it and Logic in the widest sense. Logic, as I conceive it, is the
entire theory of the ascertainment of reasoned or inferred truth. Formal
Logic, therefore, which Sir William Hamilton from his own point of view,
and Archbishop Whately from his, have represented as the whole of Logic
pi'operly so called, is really a very subordinate part of it, not being direct-
ly concerned with the process of Reasoning or Inference in the sense in
which that process is a part of the Investigation of Truth. What, then,
is Formal Logic ? The name seems to be properly applied to all that por-
tion of doctrine which relates to the equivalence of different modes of ex-
pression ; the rules for determining when assertions in a given form imply
or suppose the truth or falsity of other assertions. This includes the theo-
ry of the Import of Propositions, and of their Conversion, jEquipollence,
and Opposition ; of those falsely called Inductions (to be hereafter spoken
of)*, in which the apparent generalization is a mere abridged statement of
cases known individually ; and finally, of the syllogism : while the theory of
Naming, and of (what is inseparably connected with it) Definition, though
belonging still more to the other and larger kind of logic than to this, is a
necessary preliminary to this. The end aimed at-by Formal Logic, and\
attained by the observance of its precepts, is not truth, but consistency. |
It has been seen that this is the only direct purpose of the rules of the
syllogism ; the intention and effect of which is simply to keep our infer-
ences or conclusions in complete consistency with our general formulae or
directions for drawing them. The Logic of Consistency is a necessary
auxiliary to the logic of truth, not only because what is inconsistent with
itself or with other truths can not be true, but also because truth can only
be successfully pursued by drawing inferences from experience, which, if
warrantable at all, admit of being generalized, and, to test their warrant-
ableness, require to be exhibited in a generalized form ; after which the
correctness of their application to particular cases is a question which spe-
cially concerns the Logic of Consistency. This Logic, not requiring any
preliminary knowledge of the processes or conclusions of the various sci-
ences, may be studied with benefit in a much earlier stage of education
than the Logic of Truth : and the practice which has empirically obtained
of teaching it apart, through elementary treatises which do not attempt to
include any thing else, though the reasons assigned for the practice are in
general very far from philosophical, admits of philosophical justification.
consideration, is, Socrates is like A, B, C, and the other individuals who are known to have
died. And this is the only universal type of that step in the reasoning process which is rep-
resented by the minor. Experience, however, of the uncertainty of this loose mode of infer-
ence, teaches the expediency of determining beforehand what kind of likeness to the cases ob-
served, is necessary to bring an unobserved case within the same predicate ; and the answer
to this question is the major. The minor then identifies the precise kind of likeness possessed
by Socrates, as being the kind required by the formula. Thus the syllogistic major and the
syllogistic minor start into existence together, and are called forth by the same exigency.
When we conclude from personal experience without referring to any record — to any general
theorems, either written, or traditional, or mentally registered by ourselves as conclusions of
our own drawing — we do not use, in our thoughts, either a major or a minor, such as the syl-
logism puts into words. When, however, we revise this rough inference from particulars to
particulars, and substitute a careful one, the revision consists in selecting two syllogistic prem-
ises. But this neither alters nor adds to the evidence we had before ; it only puts us in a
better position for judging whether our inference from particulars to particulars is well
grounded.
* Infra, book iii., chap. ii.
158 EEASONING.
CHAPTER IV.
OF TEAmS OP REASONING, AND DEDUCTIVE SCIENCES.
§ 1. In our analysis of the syllogism, it appeared that the minor premise
always affirms a resemblance between a new case and some cases previous-
ly known ; while the major premise asserts something which, having been
found true of those known cases, we consider ourselves warranted in hold-
ing true of any other case resembling the former in certain given particu-
lars.
If all ratiocinations resembled, as to the minor premise, the examples
which were exclusively employed in the preceding chapter; if the resem-
blance, which that premise asserts, were obvious to the senses, as in the
proposition " Socrates is a man," or were at once ascertainable by direct
observation ; there would be no necessity for trains of reasoning, and De-
ductive or Ratiocinative Sciences would not exist. Trains of reasoning
exist only for the sake of extending an induction founded, as all inductions
must be, on observed cases, to other cases in which we not only can not di-
rectly observe the fact which is to be proved, but can not directly observe
even the mark which is to prove it.
§ 2. Suppose the syllogism to be, All cows ruminate, the animal which
is before me is a cow, therefore it ruminates. The minor, if true at all, is
obviously so: the only premise the establishment of which requires any
anterior process of inquiry, is the major ; and provided the induction of
which that premise is the expression was correctly performed, the conclu-
sion I'especting the animal now present will be instantly drawn ; because,
as soon as she is compared with the formula, she will be identified as being
included in it. But suppose the syllogism to be the following : All arsenic
is poisonous, the substance which is before me is arsenic, therefore it is poi-
sonous. The truth of the minor may not here be obvious at first sight;
it may not be intuitively evident, but may itself be known only by infer-
ence. It may be the conclusion of another argument, which, thrown into
the syllogistic form, would stand thus : Whatever when lighted produces
a dark spot on a piece of white porcelain held in the flame, which spot is
soluble in hypochloride of calcium, is arsenic ; the substance before me con-
forms to this condition ; therefore it is arsenic. To establish, therefore,
the ultimate conclusion. The substance before me is poisonous, requires a
process, which, in order to be syllogistically expressed, stands in need of
two syllogisms ; and we have a Train of Reasoning.
When, however, we thus add syllogism to syllogism, we are really add-
ing induction to induction. Two separate inductions must have taken
place to render this chain of inference possible ; inductions founded, prob-
ably, on different sets of individual instances, but which converge in their
results, so that the instance which is the subject of inquiry comes within
the range of them both. The record of these inductions is contained in
the majors of the two syllogisms. First, we, or others for us, have exam-
ined various objects which yielded under the given circumstances a dark
TRAINS OF REASONING. 159
«pot with the given property, and found that they possessed the properties
■connoted by the word arsenic ; they were metallic, volatile, their vapor had
« smell of garlic, and so forth. Next, we, or others for us, have examined
various specimens which possessed this metallic and volatile character,
whose vapor had this smell, etc., and have invariably found that they were
■poisonous. The first observation we judge that we may extend to all sub-
•stances whatever which yield that particular kind of dark spot ; the second,
to all metallic and volatile substances resembling those we examined ; and
•consequently, not to those only which are seen to be such, but to those
which are concluded to be such by the prior induction. The substance
tefore us is only seen to come within one of these inductions ; but by
means of this one, it is brought within the other. We are still, as before,
•concluding from particulars to particulars ; but we are now concluding
irom particulars observed, to other particulars which are not, as in the
simple case, seen to resemble them in material points, but inferred to do
«o, because resembling them in something else, which we have been led by
quite a different set of instances to consider as a mark of the former re-
semblance.
This first example of a train of reasoning is still extremely simple, the
series consisting of only two syllogisms. The following is somewhat more
■complicated : No government, which earnestly seeks the good of its sub-
jects, is likely to be overthrown ; some particular government earnestly seeks
the good of its subjects, therefore it is not likely to be overthrown. The ma-
jor premise in this argument we shall suppose not to be derived from con-
siderations a priorijhnt to-be a generalization from history, which, wheth-
■er correct or erroneous, must have been founded on observation of govern-
ments concerning whose desire of the good of their subjects there was no
doubt. It has been found, or thought to be found, that these were not
easily overthrown, and it has been deemed that those instances warranted
an extension of the same predicate to any and every government which
resembles them in the attribute of desiring earnestly the good of its sub-
jects. But does the government in question thus resemble them? This
may be debated pro and con by many arguments, and must, in any case, be
proved by another induction ; for we can not directly observe the senti-
ments and desires of the persons who carry on the government. To prove
the minor, therefore, we require an argument in this form : Every govern-
ment which acts in a certain manner, desires the good of its subjects; the
supposed government acts in that particular manner, therefore it desires
the good of its subjects. But is it true that the government acts in the
manner supposed ? This minor also may require proof ; still another in-
•duction, as thus : What is asserted by intelligent and disinterested witness-
■es, may be believed to be true ; that the government acts in this manner,
is asserted by such witnesses, therefore it may be believed to be true. The
argument hence consists of three steps. Having the evidence of our senses
that the case of the government under consideration resembles a number
of former cases^in the circumstance of having something asserted respect-
ing it by intelligent and disinterested witnesses, we infer, first, that, as in
those former instances, so in this instance, the assertion is true. Secondly,
what was asserted of the government being that it acts in a particular
■manner, and other governments or persons having been observed to act
in the same manner, the government in question is brought into known re-
semblance with those other governments or persons ; and since they were
Jsnown to desire the good of the people, it is thereupon, by a second indue-
160 REASONING.
tion, inferred that the particular government spoken of, desires the good of
the people. This brings that government into known resemblance with the
other, governments which were thought likely to escape revolutioUj and
thence, by a third induction, it is concluded that this particular govern-
ment is also likely to escape. Tliis is still reasoning from particulars to
particulars, but we now reason to the new instance irom three distinct sets
of former instances : to one only of those sets of instances do we directly
perceive the new one to be similar; but from that similarity we induc-
tively infer that it has the attribute by which it is assimilated to the next
Bet, and brought within the corresponding induction ; after which by a
repetition of the same operation we infer it to be similar to the third set,
and hence a third induction conducts us to the ultimate conclusion.
§ 3. Notwithstanding the superior complication of these examples, com-
pared with those by which in the preceding chapter we illustrated the
general theory of reasoning, every doctrine which we then laid down holds
equally true in these more intricate cases. The successive general proposi-
tions are not steps in the reasoning, are not intermediate links in the chain
of inference, between the particulars observed and those to which we ap-
ply the observation. If we had sufficiently capacious memories, and a suf-
ficient power of maintaining order among a huge mass of details, the rea-
soning could go on without any general propositions ; they are mere for-
mulae for inferring particulars from particulars. The principle of gener-
al reasoning is (as before explained), that if, from observation of certain
known particulars, what was seen to be true of them can be inferred to be
true of any others, it may be inferred of all others which are of a certain
description. And in order that we may never fail to draw this conclusion
in a new case when it can be drawn correctly, and may avoid drawing it
when it can not, we determine once for all what are the distinguishing marks
by which such cases may be recognized. The subsequent process is mere-
ly that of identifying an object, and ascertaining it to have those marks;
whether we identify it by the very marks themselves, or by others which
we have ascertained (through another and a similar process) to be marks
of those marks. The real inference is always from particulars to particu-
lars, from the observed instances to an unobserved one : but in drawing
this inference, we conform to a formula which we have adopted for our
guidance in such operations, and which is a record of the criteria by which
we thought we had ascertained that we might distinguish when the infer-
ence could, and when it could'not, be drawn. The real premises are the in-
dividual observations, even though they may have been forgotten, or, being
the observations of others and not of ourselves, may, to us, never have been
known : but we have before us proof that we or others once thought them
sufficient for an induction, and we have marks to show whether any new
case is one of those to which, if then known, the induction would have been
deemed to extend. These marks we either recognize at once, or by the
aid of other marks, which by another previous induction we collected to be
marks of the first. Even these marks of marks may only be recognized
through a third set of marks ; and we may have a train of reasoning, of
any length, to bring a new case within the scope of an induction ground-
ed on particulars its similarity to which is only ascertained in this indirect
manner.
Thus, in the preceding example, the ultimate inductive inference was,
that a certain government was not likely to be overthrown ; this inference
TRAINS OP REASONING. 161
was drawn according to a formula in which desire of the public good was
set down as a mark of not being likely to be overthrown ; a mark of this
mark yras, acting in a particular manner; and a mark of acting in that
manner was, being asserted to do so by intelligent and disinterested wit-
nesses : this mark, the government under discussion was recognized by the
senses as possessing. Hence that government fell within the last induc-
tion, and by it was brought within all the others. The perceived resem-
blance of the case to one set of observed particular cases, brought it into
known resemblance with another set, and that with a third.
In the more complex branches of knowledge, the deductions seldom con-
sist, as in the examples hitherto exhibited, of a single chain, a a mark of &,
J of c, e of d, therefore a a mark of d. They consist (to carry on the same
metaphor) of several chains united at the extremity, as thus : a a mark of
d,hoie,coif,def of n, therefore a S c a mark of n. Suppose, for exam-
ple, the following combination of circumstances: 1st, rays of light impin-
ging on a reflecting surface ; 2d, that surface parabolic ; 3d, those rays
parallel to each other and to the axis of the surface. It is to be proved
that the concourse of these three circumstances is a mark that the reflected
rays will pass through the focus of the parabolic surface. Now, each of
the three circumstances is singly a mark of something material to the case.
Kays of light impinging on a reflecting surface are a mark that those rays
will be reflected at an angle equal to the angle of incidence. The parabol-
ic form of the surface, is a mark that, from any point of it, a line drawn to
the focus and a line parallel to the axis will make equal angles with the
surface. And finally, the parallelism of the rays to the axis is a mai-k that
their angle of incidence coincides with one of these equal angles. The
three marks taken together are therefore a mark of all these three things
united. But the three united are evidently a mark that the angle of re-
flection must coincide with the other of the two equal angles, that formed
by a line drawn to the focus ; and this again, by the fundamental axiom
concerning straight lines, is a mark that the reflected rays pass through
the focus. Most chains of physical deduction are of this more complicated
type ; and even in mathematics such are abundant, as in all propositions
where the hypothesis includes numerous conditions: "If a, circle be taken,
and if within that circle a point be taken, not the centre, and if straight
lines be drawn from that point to the circumference, then," etc.
§ 4. The considerations now stated remove a serious difficulty from the
view we have taken of reasoning; which view might otherwise have
seemed not easily reconcilable with the fact that there are Deductive or
Ratiocinative Sciences. It might seem to follow, if all reasoning be induc-
tion, that the difficulties of philosophical investigation must lie in the in-
ductions exclusively, and that when these were easy, and susceptible of no
doubt or hesitation, there could be no science, or, at least, no difficulties in
science. The existence, for example, of an extensive Science of Mathemat-
ics, requiring the highest scientific genius in those who contributed to its
creation, and calling for a most continued and vigorous exertion- of intel-
lect in order to appropriate it when created, may seem hard to be accounted
for on the foregoing theory. But the considerations more recently adduced
remove the mystery, by showing, that even when the inductions themselves
are obvious, there may be much difficulty in finding whether the particular
case which is the subject of inquiry comes within them ; and ample room
for scientific ingenuity in so combining various inductions, as, by means of
11
162 KEASONING.
one within which the case evidently falls, to bring it within others in which
it can not be directly seen to be included.
When the more obvious of the inductions which can be made in any
science from direct observations, have been made, and general formulas
have been framed, determining the limits within which these inductions
are applicable ; as often as a new case can be at once seen to come within
one of the formulas, the induction is applied to the new case, and the busi-
ness is ended. But new cases are continually arising, which do not obvi-
ously come within any formula whereby the question we want solved in
respect of them could be answered. Let us take an instance from geome-
try : and as it is taken only for illustration, let the reader concede to us
for the present, what we shall endeavor to prove in the next chapter, that
the first principles of geometry are results of induction. Our example
shall be the fifth proposition of the first book of Euclid. The inquiry is,
Ai-e the angles at the base of an isosceles triangle equal or unequal? The
first thing to be considered is, what inductions we have, from which we can
infer equality or inequality. For inferring equality we have the following
formulae : Things which being applied to each other coincide, are equals.
Things which are equal to the same thing are equals. A whole and the
sum of its parts are equals. The sums of equal things are equals. . The
differences of equal things ai-e equals. There are no other original formu-
lae to prove equality. For inferring inequality we have the following: A
whole and its parts are unequals. The sums of equal things and unequal
things are unequals. The differences of equal things and unequal things
are unequals. In all, eight formulae. The angles at the base ot an isos-
celes triangle do not obviously come within any of these. The formulae
specify certain marks of equality and of inequality, but the angles can not
be perceived intuitively to have any of those marks. On examination it
appears that they have ; and we ultimately succeed in bringing them within
the formula, "The differences of equal things are equal." Whence comes
the difficulty of recognizing these angles as the differences of equal things ?
Because each of them is the difference not of one pair only, but of innu-
merable pairs of angles ; and out of these we had to imagine and select two,
which could either be intuitively perceived to be equals, or possessed some
of the marks of equality set down in the various formulae. By an exercise
of ingenuity, which, on the part of the first inveptor, deserves to be re-
garded as considerable, two pairs of angles were hit upon, which united
these requisites. First, it could be perceived intuitively that their differ-
ences were the angles at the base ; and, secondly, they possessed one of the
marks of equality, namely, coincidence when applied to one another. This
coincidence, however, was not perceived intui-
tively, but inferred, in conformity to another
formula.
For greater clearness, I subjoin an analysis
of the demonstration. Euclid, it will be re-
membered, demonstrates his fifth proposition
by means of the fourth. This it is not allow-
able for us to do, because we are undertaking
to trace deductive truths not to prior deduc-
tions, but to their original inductive founda-
^ tion. We must, therefore, use the premises of
the fourth proposition instead of its conclusion, and prove the fifth directly
from first pilnciples. To do so requires six formulas. (We must begin, as
TRAINS OF REASONING. 163
in Euclid, by prolonging the equal sides AB, AC, to equal distances, and
joining the extremities BE, DC.)
FiHST Formula. — T^e sums of equals are equal.
AD and AE are sums of equals by the supposition. Having that mark
of equality, they are concluded by this formula to be equal.
Second Formula. — Bqual straight lines or angles, being applied to one
another, coincide.
AC, AB, are within this formula by supposition ; AD, AE, have been
brought withm it by the preceding step. The angle at A considered as an
angle of the triangle ABE, and the same angle considered as an angle of
the triangle ACD, are of course within the formula. All these pairs, there-
fore, possess the property which, according to the second formula, is. a
mark that when applied to one another they will coincide. Conceive
them, then, applied to one another, by turning over the triangle ABE, and
laying it on the triangle ACD in such a manner that AB of the -one shall
lie upon AC of the other. Then, by the equality of the angles, AE will lie
on AD. But AB and AC, AE and AD are equals ; therefore they will co-
incide altogether, and of course at their extremities, D, E, and B, C.
Third Formula. — Straight lines, having their extremities coincident,
coincide.
BE and CD have been brought within this formula by the preceding in-
duction ; they will, therefore, coincide.
Fourth Formula. — Angles, having their sides coincident, coincide.
The third induction having shown that BE and CD coincide, and the
second that AB, AC, coincide, the angles ABE and ACD are thereby
brought within the fourth formula, and accordingly coincide.
• Fifth Formula. — Things which coincide are equal.
The angles ABE and ACD are brought within this formula by the in-
duction immediately preceding. This train of reasoning being also appli-
cable, mutatis mutandis, to the angles EBC, DCB, these also ai-e brought
within the fifth formula. And, finally.
Sixth Formula. — The differences of equals are equal.
The angle ABC being the difference of ABE, CBE, and the angle ACB
being the difference of ACD, DCB ; which have been proved to be equals ;
ABC and ACB are brought within the last formula by the whole of the
previous process.
The difficulty here encountered is chiefly that of figuring to ourselves
the two angles at the base of the triangle ABC as remainders made by cut-
ting one pair of angles out of another, while each pair shall be correspond-
ing angles of triangles which have two sides and the intervening angle
equal. It is by this happy contrivance that so many different inductions
are brought to bear upon the same particular case. And this not being
at all an obvious thought, it may be seen from an example so near the
threshold of mathematics, how much scope there may well be for scientific
dexterity in the higher branches of that and other sciences, in order so to
combine a few simple inductions, as to bring within each of them innumer-
able cases which are not obviously included in it ; and how long, and nu'
164 KEASONING.
merous, and complicated may be the processes necessary for bringing the
inductions together, even when each induction may itself be very easy and
simple. All the inductions involved in all geometry are comprised in those
simple ones, the formulae of which are the Axioms, and a few of the so-call-
ed Definitions. The remainder of the science is made up of the processes
employed for bringing unforeseen cases within these inductions; or (in syl-
logistic language) for proving the minors necessary to complete the syllo-
gisms ; the majors being the definitions and axioms. In those definitions
and axioms are laid down the whole of the marks, by an artful combina-
tion of which it has been found possible to discover and prove all that is
proved in geometry. The marks being so few, and the inductions which
furnish them being so obvious and familiar ; the connecting of several of
them together, which constitutes Deductions, or Trains of Reasoning,
forms the whole difficulty of the science, and, with a trifling exception, its
whole bulk ; and hence Geometry is a Deductive Science.
§ 5. It will be seen hereafter* that there are weighty scientific reasons
for giving to every science as much of the character of a Deductive Sci-
ence as possible ; for endeavoring to construct the science from the fewest
and the simplest possible inductions, and to make these, by any combina-
nations however complicated, suffice for proving even such truths, relating
to complex cases, as could be proved, if we chose, by inductions from spe-
cific experience. Every branch of natural philosophy was originally exper-
imental ; each generalization rested on a special induction, and was derived
from its own distinct set of observations and experiments. From being
sciences of pure experiment, as the phrase is, or, to speak more correctly,
sciences in which the reasonings mostly consist of no more than one step,
and are expressed by single syllogisms, all these sciences have become to
some extent, and some, of them in nearly the whole of their extent, sciences
of pure reasoning; whereby multitudes of truths, already known by induc-
tion from as many different sets of experiments, have come to be exhibited
as deductions or corollaries from inductive propositions of a simpler and
more universal character. Thus mechanics, hydrostatics, optics, acoustics,
thermology, have successively been rendered mathematical ; and astronomy
was brought by Newton within the laws of general mechanics. "Why it is
that the substitution of this circuitous mode of proceeding for a process
apparently much easier and more natural, is held, and justly, to be the
greatest triumph of the investigation of nature, we are not, in this stage
of our inquiry, prepared to examine. But it is necessary to remark, that
although, by this progressive transformation, all sciences tend to become
more and more Deductive, they are not, therefore, the less Inductive ; every
step in the Deduction is still an Induction. The opposition is not between
the terms Deductive and Inductive, but between Deductive and Experi-
mental. A science is experimental, in proportion as every new case, which
presents any peculiar features, stands in need of a new set of observations
and experiments — a fresh induction. It is deductive, in proportion as it
can draw conclusions, respecting cases of a new kind, by processes which
bring those cases under old inductions ; by ascertaining that cases which
can not be observed to have the requisite marks, have, however, marks of
those marks.
We can now, therefore, perceive what is the generic distinction between
* Infra, book iii., ch. It., § 3, and elsewhere.
TRAINS OF REASONING. 165
sciences which can be made Deductive, and those which must as yet re-
main Experimental. The difference consists in our having been able, or
not yet able, to discover marks of mai-ks. If by our various inductions we
have been able to proceed no further than to such propositions as these, a
a mark of b, or a and b marks of one another, c a mark of d, or c and d
marks of one another, without any thing to connect a ov b with c or d; we
have a science of detached and mutually independent generalizations, such
as these, that acids redden vegetable blues, and that alkalies color them
green ; from neither of which propositions could we, directly or indirectly,
infer the other : and a science, so far as it is composed of such proposi-
tions, is purely experimental. Chemistry, in the present state of our
knowledge, has not yet thrown off this character. There are other sci-
€nces, however, of which the propositions are of this kind : a a mark of b,
b a mark of c, o oi d,d of e, etc. In these sciences we can mount the lad-
der from a to e by a process of ratiocination; we can conclude that a is a
mark of e, and that every object which has the mark a has the property e,
although, perhaps, we never were able to observe a and e together, and al-
though even d, our only direct mark of e, may not be perceptible in those
objects, but only inferable. Or, varying the first metaphor, we may be
said to get from a to e underground : the marks b, c, d, which indicate the
route, must all be possessed somewhere by the objects concerning which
we are inquiring ; but they are below the surface : a is the only mark that
is visible, and by it we are able to trace in succession all the rest.
§ 6. We can now understand how an experimental may transform itself
into a deductive science by the mere progress of experiment. In an experi-
mental science, the inductions, as we have said, lie detached, as, a a mark of
i,c a mark oi d,e a mark of j'', and so on : now, a new set of instances, and
a consequent new induction, may at any time bridge over the interval be-
tween two of these unconnected arches ; b, for example, may be ascertained
to be a mark of c, which enables us thenceforth to prove deductively that
« is a mark of c. Or, as sometimes happens, some comprehensive induc-
tion may raise an arch high in the air, which bridges over hosts of them
at once ; b, d,f, and all the rest, turning out to be marks of some one thing,
or of things between which a connection has already been traced. As
when Newton discovered that the motions, whether regular or apparently
anomalous, of all the bodies of the solar system (each of which motions
had been inferred by a separate logical operation, from separate marks),
were all marks of moving round a common centre, with a centripetal force
varying directly as the mass, and inversely as the square of the distance
from that centre. This is the greatest example which has yet occurred of
the transformation, at one stroke, of a science which was still to a great de-
gree merely experimental, into a deductive science.
Transformations of the same nature, but on a smaller scale, continually
take place in the less advanced branches of physical knowledge, without
■enabling them to throw off the character of experimental sciences. Thus
with regard to the two unconnected propositions before cited, namely,
Acids redden vegetable blues. Alkalies make them green ; it is remarked by
Liebig, that all blue coloring matters which are reddened by acids (as well
as, reciprocally, all red coloring matters which are rendered blue by alka-
lies) contain nitrogen: and it "is quite possible that this circumstance may
one day furnish a bond of connection between the two propositions in
question, by showing that the antagonistic action of acids and alkalies in
166 REASONING.
producing or destroying the color blue, is the result of some one, more-
general, law. Although this connecting of detached generalizations is so
much gain, it tends but little to give a deductive character to any science
as a whole ; because the new courses of obsei'vation and expeiiraent, which
thus enable us to connect together a few general truths, usually make-
known to us a still greater number of unconnected new ones. Hence
chemistry, though similar extensions and simplifications of its generaliza-
tions are continually taking place, is still in the main an experimental sci-
ence; and is likely so to continue unless some comprehensive induction
should be hereafter arrived at, which, like Newton's, shall connect a vast
number of the smaller known inductions together, and change the whole
method of the science at once. Chemistry has already one great generali-
zation, which, though relating to one of the subordinate aspects of chemical
phenomena, possesses within its limited sphere this comprehensive charac-
ter; the principle of Dalton, called the atomic theory, or the doctrine of
chemical equivalents : which by enabling us to a certain extent to foresee
the proportions an which two substances will combine, before the experi-
ment has been tried, constitutes undoubtedly a source of new chemical
truths obtainable by deduction, as well as a connecting principle for all
truths of the same description previously obtained by experiment.
§ 7. The discoveries which change the method of a science from experi-
mental to deductive, mostly consist in establishing, either by deduction or
by direct experiment, that the varieties of a particular phenomenon uni-
formly accompany the varieties of some other phenomenon better known.
Thus the science of sound, which previously stood in the lowest rank of
merely experimental science, became deductive when it was proved by ex-
periment that every variety of sound was consequent on, and therefore a
mark of, a distinct and definable variety of oscillatory motion among the
particles of the transmitting medium. When this was ascertained, it fol-
lowed that every relation of succession or co-existence which obtained be-
tween phenomena of the more known class, obtained also between the
phenomena which correspond to them in the other class. Every sound,
being a mark of a particular oscillatory motion, became a mark of every
thing which, by the laws of dynamics, was known to be inferable fromi
that motion ; and every thing which by those same laws was a mark of any
oscillatory motion among the particles of an elastic medium, became a mark
of the corresponding sound. And thus many truths, not before suspected,
concerning sound, become deducible from the known laws of the propaga-
tion of motion through an elastic medium; while facts already empirically
known respecting sound, become an indication of corresponding properties
of vibrating bodies, previously undiscovered.
But the grand agent for transforming experimental into deductive sci-
ences, is the science of number. The properties of numbei-, alone among
all known phenomena, are, in the most rigorous sense, properties of all
things whatever. All things are not colored, or ponderable, or even ex-
tended ; but all things are numerable. And if we consider this science ia
its whole extent, from common arithmetic up to the calculus of variations,,
the truths already ascertained seem all but infinite, and admit of indefinite
extension. ,
These truths, though affirmable of all things whatever, of course apply
to them only in respect of their quantity. But if it comes to be discovered
that variations of quality in any class of phenomena, correspond regularly
TRAINS OF REASONING. 167
to variations of quantity either in those same or in some other phenomena ;
every formula of mathematics applicable to quantities which vary in that
particular manner, becomes a mark of a corresponding general truth re-
specting the variations in quality which accompany them: and the sci-
ence of quantity being (as far as any science can be) altogether deductive,
the theory of that particular kind of qualities becomes, to this extent, de-
ductive likewise.
The most striking instance in point which history affords (though not
an example of an experimental science rendered deductive, but of an un-
paralleled extension given to the deductive process in a science which was
deductive already), is the revolution in geometry which oi'iginated with
Descartes, and was completed by Clairaut. These great mathematicians
pointed out the importance of the fact, that to every variety of position in
points, direction in lines, oi- form in curves or surfaces (all of which are
Qualities), there corresponds a peculiar relation of quantity between either
two or three rectilineal co-ordinates; insomuch that if the law were known
according to which those co-ordinates vary relatively to one another, every
other geometrical property of the line or surface in question, whether re-
lating to quantity or quality, would be capable of being inferred. Hence
it followed that every geometrical question could be solved, if the corre-
sponding algebraical one could ; and geometry received an accession (act-
ual or potential) of new truths, corresponding to every property of num-
bers which the progress of the calculus had brought, or might in future
bring, to light. In the same general manner, mechanics, astronomy, and in
a less degree, every branch of natural philosophy commonly so called, have-
been made algebraical. The varieties of physical phenomena with whick
those sciences are conversant, have been found to answer to determinable-
varieties in the quantity of some circumstance or other ; or at least to va-
rieties of form or position, for which corresponding equations of quantity
had already been, or were susceptible of being, discovered by geometers.
In these various transformations, the propositions of the science of num-
ber do but fulfill the function proper to all propositions forming a train of
reasoning, viz., that of enabling us to arrive in an indirect method, by
marks of marks, at such of the properties of objects as we can not direct-
ly ascertain (or not so conveniently) by experiment. We travel from a.
given visible or tangible fact, through the truths of numbers, to the facts,
sought. The given fact is a mark that a certain relation subsists between
the quantities of some of the elements concerned ; while the fact sought
presupposes a certain relation between the quantities of some other ele-
ments : now, if these last quantities are dependent in some known manner
upon the former, or vic& versa, we can argue from the numerical relation
between the one set of quantities, to determine that which subsists be-
tween the other set ; the theorems of the calculus affording the intermedi-
ate links. And thus one of the two physical facts becomes a mark of the-
other, by being a mark of a mark of a mark of it.
168 REASONING.
CHAPTER V.
OF DEMONSTRATION, AND NBCESSAET TRUTHS.
§ 1. If, as laid down in the two preceding chapters, the foundation of
all sciences, even deductive or demonstrative sciences, is Induction ; if
every step in the ratiocinations even of geometry is an act of induction ;
and if a train of reasoning is but bringing many inductions to bear upon
the same subject of inquiry, and drawing a case within one induction by
means of another ; wherein lies the peculiar certainty always ascribed to
the sciences which are entirely, or almost entirely, deductive? Why are
they called the Exact Sciences ? Why are mathematical certainty, and the
evidence of demonstration, common phrases to express the very highest
degree of assurance attainable by reason ? Why are mathematics by al-
most all philosophers, and (by some) even those branches of natural phi-
losophy which, through the medium of mathematics, have been converted
into deductive sciences, considered to be independent of the evidence of
experience and observation, and characterized as systems of Necessary
Truth ?
The answer I conceive to be, that this character of necessity, ascribed to
the truths of mathematics, and (even with some reservations to be here-
after made) the peculiar certainty attributed to them, is an illusion ; in or-
der to sustain which, it is necessary to suppose that those truths relate to,
and express the properties of, purely imaginary objects. It is acknowl-
edged that the conclusions of geometry are deduced, partly at least, from
the so-called Definitions, and that those definitions are assumed to be cor-
rect representations, as far as they go, of the objects with which geometry
is conversant. Now we have pointed out that, from a definition as such,
no proposition, unless it be oiii concerning the meaning of a word, can ever
follow ; and that what apparently follows from a definition, follows in real-
ity from an implied assumption that there exists a real thing conformable
thereto. This assumption, in the case of the definitions of geometry, is not
strictly true : there exist no real things exactly conformable to the defini-
tions. There exist no points without magnitude ; no lines without breadth,
Tior perfectly straight; no circles with all their radii exactly equal, nor
squares with all their angles perfectly right. It will perhaps be said that
the assumption does not extend to the actual, but only to the possible, exist-
ence of such things. I answer that, according to any test we have of possi-
bility, they are not even possible. Their existence, so far as we can form
any judgment, would seem to be inconsistent with the physical constitu-
tion of our planet at least, if not of the universe. To get rid of this diffi-
culty, and at the same time to save the credit of the supposed system of
necessary truth, it is customary to say that the points, lines, circles, and
squares which are the subject of geometry, exist in our conceptions mere-
ly, and are part of our minds ; which minds, by working on their own ma-
terials, construct an a priori science, the evidence of_which is-p«rely men-
tal, and has nothing whatever to do with outward -experience. By how-
soever high authorities this doctrine may have been sanctioned, it appears
DEMONSTRATION, AND NECESSAUY TRUTHS. 169
to me psychologically incon-ect. The points, lines, circles, and squares
which any one has in his mind, are (I apprehend) simply copies of the
points, lines, circles, and squares which he has known in his experience.
Our idea of a point, I apprehend to be simply our idea of the minimum
visibile, the smallest portion of surface which we can see. A line, as de-
fined by geometers, is wholly inconceivable. We can reason about a line
as if it had no breadth ; because we have a power, which is the foundation
of all the control we can exercise over the operations of our minds ; the
power, when a perception is present to our senses, or a conception to our
intellects, of attenditig to a part only of that perception or conception, in-
stead of the whole. But we can not conceive' a, line without breadth ; we
can form no mental picture of such a line : all the lines which we have in
our minds are lines possessing breadth. If any one doubts this, we may
refer him to his own experience. I much question if any one who fancies
that he can conceive what is called a mathematical line, thinks so from the
evidence of his consciousness : I suspect it is rather because he supposes
that unless such a conception were possible, mathematics could not exist as
a science : a supposition which there will be no difficulty in showing to be
entirely groundless.
Since, then, neither in nature, nor in the human mind, do there exist any
objects exactly corresponding to the definitions of geometry, while yet that
science can not be supposed to be conversant about nonentities ; nothing
remains but to consider geometry as conversant with such lines, angles,
and figures, as really exist; and the definitions, as they are called, must be
regarded as some of our first and most obvious generalizations concerning
those naturar objects. The correctness of those generalizations, as gener-
alizations, is without a flaw : the equality of all the radii of a circle is true
of all circles, so far as it is true of any one : but it is not exactly true of
any circle; it is only nearly true; so nearly that no error of any impor-
tance in practice will be incurred by feigning it to be exactly true. When
we have occasion to extend these inductions, or their consequences, to cases
in which the error would be appreciable — to lines of pei-ceptible breadth
or thickness, parallels which deviate sensibly from equidistance, and the
like — we correct our conclusions, by combining with them a fresh set of
propositions relating to the aberration; just as we also take in proposi-
tions relating to the physical or chemical properties of the material, if those
properties happen to introduce any modification into the result; which
they easily may, even with respect to figure and magnitude, as in the case,,
for instance, of expansion by heat. So long, however, as there exists no
practical necessity for attending to any of the properties of the object ex-
cept its geometrical properties, or to any of the natural irregularities in
those, it is convenient to neglect the consideration of the other properties
and of the irregularities, and to reason as if these did not exist : according-
ly, we formally announce in the definitions, that we intend to proceed on
this plan. But it is an error to suppose, because we resolve to confine our
attention to a certain number of the properties of an object, that we there-
fore conceive, or have an idea of, the object, denuded of its other proper-
ties. We are thinking, all the time, of precisely such objects as we have
seen and touched, and with all the properties which naturally belong to-
them ; but, for scientific convenience, we feign them to be divested of all
properties, except those which are material to our purpose, and in regard
to which we design to consider them.
The peculiar accuracy, supposed to be characteristic of the first princi-
170 REASONING.
pies of geometry, thus appears to be fictitiojjs. The assertions on which
the reasonings of the science are founded, do not, any more than in other
sciences, exactly correspond with the fact ; but we suppose that they do
80, for the sake of tracing the consequences which follow from the suppo-
sition. The opinion of Dugald Stewart respecting the foundations of ge-
ometry, is, I conceive, substantially correct ; that it is built on hypotheses ;
that it owes to this alone the peculiar certainty supposed to distinguish it ;
und that in any science whatever, by reasoning from a set of hypotheses,
we may obtain a body of conclusions as certain as those of geometry, that
is, as strictly in accordance with the hypotheses, and as irresistibly compel-
ling assent, on condition that those hypotheses are true.*
When, therefore, it is affirmed that the conclusions of geometry are nec-
essary truths, the necessity consists in reality only in this, that they cor-
rectly follow frotn the suppositions from which they are deduced. Those
:suppositions are so far from being necessary, that they are not even true ;
they purposely depart, more or less widely,frora the truth. The only sense
in which necessity can be ascribed to tho conclusions of any scientific in-
vestigation, is that of legitimately following from some assumption, which,
by the conditions of the inquiry, is not to be questioned. In this relation,
-of course, the derivative truths of every deductive science must stand to
the inductions, or assumptions, on which the science is founded, and which,
■whether true or untrue, certain or doubtful in themselves, are always sup-
posed certain for the purposes of the particular science. And therefore
the conclusions of all deductive sciences were said by the ancients to be
necessary propositions. We have observed already that to be predicated
necessarily was characteristic of the predicable Proprium, and that a pro-
prium was any property of a thing which could be deduced from its es-
jsence, that is, from the pi'operties included in its definition.
§ 2. The important doctrine of Dugald Stewart, which I have endeav-
ored to enforce, has been contested by Dr. Whewell, both in the disserta-
tion appended to his excellent Mechanical Euclid, and in his elaborate
work on the Philosophy of the Inductive Sciences ; in which last he also
replies to an article in the Edinburgh Review (ascribed to a writer of
great scientific eminence), in which Stewart's opinion was defended against
bis former strictures. The supposed refutation of Stewart consists in
proving against him (as has also been done in this work) that the premises
■of geometry are not definitions, but assumptions of the real existence of
things corresponding to those definitions. This, however, is doing little for
Dr. Whewell's purpose ; for it is these very assumptions which are as-
serted to be hypotheses, and which he, if he denies that geometry is founded
* It is justly remarked by Professor Bain {Logic, ii., 134) that the word Hypothesis is here
used in a somewhat peculiar sense. An hypothesis, in science, usually means a supposition
not proved to be true, but surmised to be so, because if true it would account for certain
known facts ; and the final result of the speculation may be to prove its truth. The hypothe-
:ses spoken of in the text are of a different character ; they are known not to be literally true,
while as much of them as is true is not hypothetical, but certain. The two cases, however,
resemble in the circumstance that in both we reason, not from a truth, but from an assump-
tion, and the truth therefore of the conclusions is conditional, not categorical. This suffices
to justify, in point of logical propriety, Stewart's use of the term. It is of course needful to
bear in mind that the hypothetical element in the definitions of geometry is the assumption
that what is very nearly true is exactly so. This unreal exactitude might be called a fiction,
a,9 properly as an hypothesis ; but that appellation, still more than the other, would fail to
pouit out the close relation which exists between the fictitious point or line and the points
and lines of which we have experience.
DEMONSTRATION, AND NECESSAKY TRUTHS. Ill
on hypotheses, must show to be absolute truths. All he does, however, is
to observe, that they, at any rate, are not arbitrary hypotheses; that we
.should not be at liberty to substitute other hypotheses for them ; that not
■only " a definition, to be admissible, must necessarily refer to and agree
with some conception which we can distinctly frame in our thoughts," but
that the straight lines, for instance, which we define, must be " those by
which angles are contained, those by which triangles are bounded, those of
■which parallelism may be predicated, and the like."* And this is true ;
but this has never been contradicted. Those who say that the premises
•of geometry are hypotheses, are not bound to maintain them to be hypoth-
eses which have no relation whatever to fact. Since an hypothesis framed
for the purpose of scientific inquiry must relate to something which has
real existence (for there can be no science respecting nonentities), it fol-
lows that any hypothesis we make respecting an object, to facilitate our
fitudy of it, must not involve any thing which is distinctly false, and repug-
nant to its real nature : we must not ascribe to the thing any property
which it has not ; our liberty extends only to slightly exaggerating some
of those which it has (by assuming it to be completely what it really is
very nearly), and suppressing others, under the indispensable obligation of
restoring them whenever, and in as far as, their presence or absence would
make any material difference in the truth of our conclusions. Of this na-
ture, accordingly, are the first principles involved in the definitions of ge-
ometry. That the hypotheses should be of this particular character, is,
however, no further necessary, than inasmuch as no others could enable us
to deduce conclusions which, with due corrections, would be true of real
objects : and in fact, when our aim is only to illustrate truths, and not to
investigate them, we are not under any such restriction. We might sup-
pose an imaginary animal, and work out by deduction, from the known
laws of physiology, its natural history; or an imaginary commonwealth,
and from the elements composing it, might argue what would be its fate.
And the conclusions which we might thus draw from purely arbitrary hy-
potheses, might form a highly useful intellectual exercise : but as they could
only teach us what would be the properties of objects which do not really
exist, they would not constitute any addition to our knowledge of nature :
while, on the contrary, if the hypothesis merely divests a real object of
some portion of its properties, without clothing it in false ones, the conclu-
sions will always express, under known liability to correction, actual truth.
§ 3. But though Dr. Whewell has not shaken Stewart's doctrine as to
the hypothetical character of that portion of the first principles of geom-
etry which are involved in the so-called definitions, he has, I conceive, great-
ly the advantage of Stewart on another important point in the theory of
geometrical reasoning ; the necessity of admitting, among those first prin-
ciples, axioms as well as definitions. Some of the axioms of Euclid might,
no doubt, be exhibited in the form of definitions, or might be deduced, by
reasoning, from propositions similar to what are so called. Thus, if instead
of the axiom, Magnitudes which can be made to coincide are equal, we in-
troduce a definition, " Equal magnitudes are those which may be so ap-
plied to one another as to coincide ;" the three axioms which follow (Mag-
nitudes which are equal to the same are equal to one another — If equals
.are added to equals, the sums are equal — If equals are taken from equals,
* Mechanical Euclid, pp. 149 et seqq.
172 REASONING.
the remainders are equal), may be proved by an imaginary superposition,
resembling that by which the fourth proposition of the first book of Euclid
is demonstrated. But though these and several others may be struck out
of the list of first principles, because, though not requiring demonstration,
they are susceptible of it ; there will be found in the list of axioms two or
three fundamental truths, not capable of being demonstrated: among which
must be reckoned the proposition that two straight lines can not inclose a
space (or its equivalent. Straight lines which coincide in two points coin-
cide altogether), and some property of parallel lines, other than that which
constitutes their definition : one of the most suitable for the purpose being
that selected by Professor Playfair : " Two straight lines which intersect
each other can not both of them be parallel to a third straight line."*
The axioms, as well those which are indemonstrable as those which ad-
mit of being demonstrated, differ from that other class of fundamental
principles which are involved in the definitions, in this, that they are true
without any mixture of hypothesis. That things which are equal to the
same thing are equal to one another, is as true of the lines and figures in
nature, as it would be of the imaginary ones assumed in the definitions.
In this respect, however, mathematics are only on a par with most other
sciences. In almost all sciences there are some general propositions which
are exactly true, while the greater part are only more or less distant ap-
proximations to the truth. Thus in mechanics, the first law of motion (the
continuance of a movement once impressed, until stopped or slackened by
some resisting force) is true without qualification or error. The rotation
of the earth in twenty-four hours, of the same length as in our time, has
gone on since the first accurate observations, without the increase or dim-
inution of one second in all that period. These are inductions which
require no fiction to make them be received as accurately true : but along
with them there are others, as for instance the propositions respecting the
figure of the earth, which are but approximations to the truth ; and in or-
der to use them for the further advancement of our knowledge, we must
feign that they are exactly true, though they really want something of be-
ing so.
§ 4. It remains to inquire, what is the ground of our belief in axioms —
what is the evidence on which they rest ? I answer, they are experi-
mental truths; generalizations from observation. The proposition, Two
straight lines can not inclose a space — or, in other words, Two straight
lines which have once met, do not meet again, but continue to diverge —
is an induction from the evidence of our senses.
This opinion runs counter to a scientific prejudice of long standing and
great strength, and there is probably no proposition enunciated in this
work for which a more unfavorable reception is to be expected. It is,
however, no new opinion ; and even if it were so, would be entitled to be
judged, not by its novelty, but by the strength of the arguments by which
it can be supported. I consider it very fortunate that so eminent a cham-
* We might, it is true, insert this property into the definition of parallel lines, framing the
definition so as to require, both that when produced indefinitely they shall never meet, and
also that any straight line which intersects one of them shall, if prolonged, meet the other.
But by doing this we by no means get rid of the assumption ; we are still obliged to take for
granted the geometrical truth, that all straight lines in the same plane, which have the former
of these properties, have also the latter. For if it were possible that they should not, that is,
if any straight lines in the same plane, other than those which are parallel according to the
definition, had the property of never meeting although indefinitely produced, the demonstra-
tions of the subsequent portions of the theory of parallels could not be maintained.
DEMONSTEATION, AND NECESSAEY TEUTHS. 1V3
pion of the contrary opinion as Dr. Whewell lias found occasion for a most
elaborate treatment of the whole theory of axioms, in attempting to con-
struct the philosophy of the mathematical and physical sciences on the
basis of the doctrine against which I now contend. Whoever is anxious
that a discussion should go to the bottom of the subject, must rejoice to
«ee the opposite side of the question worthily represented. If what is
said by Dr. Whewell, in support of an opinion which he has made the
foundation of a systematic work, can be shown not to be conclusive, enough
will have been done, without going elsewhere in quest of stronger argu-
ments and a more powerful adversary.
It is not necessary to show that the truths which we call axioms are
originally suggested by observation, and that we should never have known
that two straight lines can not inclose a space if we had never seen a
straight line : thus much being admitted by Dr. Whewell, and by all, in
recent times, who have taken his view of the subject. But they contend,
that it is not experience which proves the axiom ; but that its truth is per-
ceived a priori, by the constitution of the -mind itself, from the first mo-
ment when the meaning of the proposition is apprehended ; and without
any necessity for verifying it by repeated trials, as is requisite in the case
of truths really ascertained by observation.
They can not, however, but allow that the truth of the axiom, Two
straight lines can not inclose a space, even if evident independently of ex-
perience, is also evident from experience. Whether the axiom needs con-
firmation or not, it receives confirmation in almost every instant of our
lives ; since we can not look at any two straight lines which intersect one
another, without seeing that from that point they continue to diverge more
and more. Experimental proof crowds in upon us in such endless profu-
sion, and without one instance in which there can be even a suspicion of
an exception to the rule, that we should soon have stronger ground for be-
lieving the axiom, even as an experimental truth, than we have for almost
any of the general truths which we confessedly learn from the evidence of
our senses. Independently of a priori evidence, we should certainly be-
lieve it with an intensity of conviction far greater than we accord to any
ordinary physical truth : and this too at a time of life much earlier than
that from which we date almost any part of our acquired knowledge, and
much too early to admit of our retaining any recollection of the history of
our intellectual operations at that period. Where then is the necessity for
assuming that our recognition of these truths has a difEei'ent origin from
the rest of our knowledge, when its existence is perfectly accounted for by
supposing its origin to be the same? when the causes which produce be-
lief in all other instances, exist in this instance, and in a degree of strength
as much superior to what exists in other cases, as the intensity of the be-
lief itself is superior? The burden of proof lies on the advocates of the
contrary opinion : it is for them to point out some fact, inconsistent with
the supposition that this part of our knowledge of nature is derived from
the same sources as every other part.*
* Some persons find themselves prevented from believing that the axiom, Two straight lines
can not inclose a space, could ever become known to us through experience, by a difficulty
which may be stated as follows : If the straight lines spoken of are those contemplated in the
definition — lines absolutely without breadth and absolutely straight — that such are incapable
of inclosing a space is not proved by experience, for lines such as these do not present them-
Belves in our experience. If, on the other hand, the lines meant are such straight lines as we
do meet with in experience, lines straight enough for practical purposes, but in reality slightly
zigzag, and with some, however trifling, breadth ; as applied to these lines the axiom is not
174 REASONING.
This, for instance, they would be able to do, if they could prove chrono-
logically that we had the conviction (at least practically) so early in infan-
cy as to be anterior to those impressions on the senses, upon which, on the
other theory, the conviction is founded. This, however, can not be proved:
the point being too far back to be within the reach of memory, and too ob-
scure for external observation. The advocates of the a priori theory are
obliged to have recourse to other arguments. These are reducible to two,
which I shall endeavor to state as clearly and as forcibly as possible.
§ 5. In the first place it is said, that if our assent to the proposition that
two straight lines can not inclose a space, were derived from the senses,
we could only be convinced of its truth by actual trial, that is, by seeing or
feeling the straight lines ; whereas, in fact, it is seen to be true by merely
thinking of them. That a stone thrown into water goes to the bottom,
may be perceived by our senses, but mere thinking of a stone thrown into
the water would never have led us to that conclusion : not so, however^
with the axioms relating to straight lines : if I could be made to conceive
what a straight line is, without having seen one, I should at once recognize
that two such lines can not inclose a space. Intuition is " imaginary look-
ing;"* but experience must be real looking: if we see a property of
straight lines to be true by merely fancying ourselves to be looking at
them, the ground of our belief can not be the senses, or experience ; it
must be something mental.
To this argument it might be added in the case of this particular axiom
(for the assertion would not be true of all axioms), that the evidence of it
from actual ocular inspection is not only unnecessary, but unattainable.
What says the axiom ? That two straight lines can not inclose a space ;
that after having once intersected, if they are prolonged to infinity they do
not meet, but continue to diverge from one another. How can this, in any
single case, be proved by actual observation ? We may follow the lines to
/ any distance we please; but we can not follow them to infinity : for aught
our senses can testify, they may, immediately beyond the farthest point to
which we have traced them, begin to approach, and at last meet. Unless,
therefore, we had some other proof of the impossibility than observation
affords us, we should have no ground for believing the axiom at all.
To these arguments, which I trust I can not be accused of understating,
a satisfactory answer will, I conceive, be found, if we advert to one of the
characteristic properties of geometrical forms — their capacity of being
painted in the imagination with a distinctness equal to reality : in other
words, the exact resemblance of our ideas of form to the sensations which
trae, for two of them may, and sometimes do, inclose a small portion of space. In neither
case, therefore, does experience prove the axiom.
Those who employ this argument to show that geometrical axioms can not be proved by
induction, show themselves unfamiliar with a common and perfectly valid mode of inductive
proof; proof by approximation. Though experience furnishes us with no lines so unim-
peachably straight that two of them are incapable of inclosing the smallest space, it presents
ns with gradations of lines possessing less and less either of breadth or of flexure, of which
series the straight line of the definition is the ideal limit. And observation shows that just as.
much, and as nearly, as the straight lines of experience approximate to having no breadth or
flexure, so much and so nearly does the space-inclosing power of any two of them approach
to zero. The inference that if they had no breadth or flexure at all, they would inclose no
space at all, is a correct inductive inference ft-JK thsso fasts, conformable' to one of the four
Inductive Methods hereinafter ehaiacterized, the Method of Concomitant Variations; of'
which the mathematical Doctrine of Limits presents the extreme case.
* Whewell's History of Scientific Ideas, i. , 140.
DEMONSTRATION, AND NECESSARY TRUTHS. 175
suggest them. This, in the first place, enables us to make (at least with a
little practice) mental pictures of all possible combinations of lines and an-
gles, which resemble the realities quite as well as any which we could make
on paper ; and in the next place, make those pictures just as fit subjects of
geometrical experimentation as the realities themselves ; inasmuch as pic-
tures, if sufficiently accurate, exhibit of course all the properties which
would be manifested by the realities at one given instant, and on simple
inspection : and in geometry we are concerned only with such properties,
and not with that which pictures could not exhibit, the mutual action of
bodies one upon another. The foundations of geometry would therefore
be laid in direct experience, even if the experiments (which in this case
consist merely in attentive contemplation) were practiced solely upon
what we call our ideas, that is, upon the diagrams in our minds, and not
upon outward objects. For in all systems of experimentation we take
some objects to serve as representatives of all which resemble them ; and
in the present case the conditions which qualify a real object to be the rep-
resentative of its class, are completely fulfilled by an object existing only
in our fancy. Without denying, therefore, the possibility of satisfying our-
selves that two straight lines can not inclose a space, by merely thinking
of straight lines without actually looking at them ; I contend, that we do
not believe this truth on the ground of the imaginary intuition simply, but
because we know that the imaginary lines exactly resemble real ones, and
that we may conclude from them to real ones with quite as much certainty
as we could conclude from one real line to another. The conclusion, there-
fore, is still an induction from observation. And we should not be author-
ized to substitute observation of the image in our mind, for observation
of the reality, if we had not learned by long-continued experience that the
properties of the reality are faithfully represented in the image; just as
we should be scientifically warranted in describing an animal which we
have never seen, from a picture made of it with a daguerreotype ; but not
until we had learned by ample experience, that observation of such a pic-
ture is precisely equivalent to observation of the original.
These considerations also remove the objection arising from the im-
possibility of ocularly following the lines in their prolongation to infinity.
For though, in order actually to see that two given lines never meet, it
would be necessary to follow them to infinity; yet without doing so we
may know that if they ever do meet, or if, after diverging from one anoth-
er, they begin again to approach, this must take place not at an infinite,
but at a finite distance. Supposing, therefore, such to be the case, we can
transport ourselves thi,ther in imagination, and can frame a mental image
of the appearance which one or both of the lines must present at that point,
which we may rely on as being precisely similar to the reality. Now,
whether we fix oui- contemplation upon this imaginary picture, or call to
mind the generalizations we have had occasion to make from former ocular
observation, we learn by the evidence of experience, that a line which, after
diverging from another straight line, begins to approach to it, produces
the impression on our senses which we describe by the expression, " a bent
line," not by the expression, " a straight line."*
* Dr. Whewell {Philosophy of Discovery, p. 289) thinks it unreasonable to contend that we
know by experience, that our idea of a line exactly resembles a real line. "It does not ap-
pear," he says, "how we can compare our ideas with the realities, since we know the realities
only by our ideas." We know the realities by our sensations. Dr. Whewell surely does not
hold the "doctrine of perception by means of ideas," which Reid gave himself so much trou-
ble to refute.
176 REASONING.
The preceding argument, which is, to my mind unanswerable, merges,
however, in a still more comprehensive one, which is stated most clearly
and conclusively by Professor Bain. The psychological reason why ax-
ioms, and indeed many propositions not ordinarily classed as such, may be
learned from the idea only without referring to the fact, is that in the proc-
€ss of acquiring the idea we have learned the fact. The proposition is
■assented to as soon as the terms are understood, because in learning to un-
derstand the terms we have acquired the experience which proves the propo-
sition to be true. " We required," says Mr. Bain,* " concrete experience in
the first instance, to attain to the notion of whole and part ; but the notion,
once arrived at, implies that the whole is greater. In fact, we could not
have the notion without ah experience tantamount to this conclusion
/When we have mastered the notion of straightness, we have also mastered
/ that aspect of it expressed by the affirmation that two straight lines can
wtiot inclose a space. No intuitive or innate powers or perceptions are
1 needed in such cases We can not have the full meaning of Straight-
fnoss, without going through a comparison of straight objects among them-
■ selves, and with their opposites, bent or crooked objects. The result of
this comparison is, inter alia, that straightness in two lines is seen to be
incompatible with inclosing a space ; the inclosure of space involves crook-
edness in at least one of the lines." And similarly, in the case of every
first principle,! " the same knowledge that makes it understood, suffices to
verify it." The more this observation is considered the more (I am con-
vinced) it will be felt to go to the Very root of the controversy.
§ 6. The first of the two arguments in support of the theory that axioms
are a priori truths, having, I think, been sufficiently answered ; I proceed
to the second, which is usually the most relied on. Axioms (it is asserted)
If Dr. Whewell doabts whether we compare our ideas with the corresponding sensations,
and assume that they resemble, let me ask on what evidence do we judge that a portrait of a
person not present is like the original. Surely because it is like our idea, or mental image of
the person, and because our idea is like the man himself.
Dr. "Whewell also says, that it does not appear why this resemblance of ideas to the sensa-
tions of which they are copies, should be spoken of as if it were a peculiarity of one class of
ideas, those of space. My reply is, that I do not so speak of it. The peculiarity I contend
for is only one of degree. All our ideas of sensation of course resemble the corresponding
sensations, but they do so with very different degrees of exactness and of reliability. No one,
I piesume, can recall in imagination a color or an odor with the same distinctness and ac-
curacy with which almost every one can mentally reproduce an image of a straight line or a
triangle. To the extent, however, of their capabilities of accuracy, our recollections of colors
or of odors may serve as subjects of experimentation, as well as those of lines and spaces, and
may yield conclusions which will be true of their external prototypes. A person in whom,
either from natural gjft or from cultivation,,the impressions of color were peculiarly vivid and
distinct, if asked which of two blue flowers was of the darkest tinge, though he might never
have compared the two, or even looked at them together, might be able to give a confident
answer on the faith of his distinct recollection of the colors ; that is, he might examine his
mental pictures, and find there a property of the outward objects. But in hardly any case
except that of simple geometrical forms, could this be done by mankind generally, with a de-
gree of assurance equal to that which is given by a contemplation of the objects themselves.
Persons differ most widely in the precision of their recollection, even of forms : one person,
when he has looked any one in the face for half a minute, can draw an accurate likeness of
him from memory ; another may have seen him every day for six months, and hardly know
whether hi? nose is long or short. But every body has a perfectly distinct mental image of a
straight line, a circle, or a rectangle. And every one concludes confidently from these mental
images to the corresponding outward things. The truth is, that we may, and continually do,
study nature in our recollections, when the objects themselves are absent ; and in the case of
geometrical forms we can perfectly, but in most other pases only imperfectly, trust our recol-
lections. * Logic, i., 222. t Ibid., 226.
DEMONSTRATION, AND NECESSARY TRUTHS. Ill
are conceived by U8 not only as true, but as universally and necessarily')
true. Now, experience can not possibly give to any proposition this char- j
acter. I may have seen snow a hundred times, and may have seen that it
was white, but this can not give me entire assurance even that all snow is
•white; much less that snow must be white. "However many instancesA^
■we may have observed of the truth of a proposition, there is nothing to i
assure us that the next case shall not be an exception to the rule. If it^
be strictly true that every ruminant animal yet known has cloven hoofs,
we still can not be sure that some creature will not hereafter be discov-
ered which has the first of these attributes, without having the other
Experience must always consist of a limited number of observations ; and-,
however numerous these may be, they can show nothing with regard to
the infinite number of cases in- which the experiment has not been made."^
Besides, Axioms are not only universal, they are also necessary. Now " ex-
perience can not offer the smallest ground for the necessity of a proposi-
tion. She can observe and record what has happened; but she can not
find, in any case, or in any accumulation of cases, any reason for what must ,
happen. She may see objects side by side; but she can not see a reason
why they must ever be side by side. She finds certain events to occur in
«uccession ; but the succession supplies, in its occurrence, no reason for its
recurrence. She contemplates external objects; but she can not detect any
internal bond, which indissolubly connects the future \yith the past, the pos-
sible with the real. To learn a proposition by experience, and to see it to
be necessarily true, are two altogether different processes of thought."*
And Dr. Whewell adds, " If any one does not clearly comprehend this dis-
tinction of necessary and contingent truths, he will not be able to go along
with us in our researches into the foundations of human knowledge ; nor,
indeed, to pursue with success any speculation on the subject."!
In the following passage, we are told what the distinction is, the non-
recognition of which incurs this denunciation. " Necessary truths are \
those in which we not only learn that the proposition is true, but see that j
it must be true ; in which the negation of the truth is not only false, but^y
impossible; in which we can not, even by an effort of imagination, or in '
a supposition, conceive the reverse of that which is asserted. That there
are such truths can not be doubted. We may take, for example, all rela-
tions of number. Three and' Two added together make Five. We can
not conceive it to be otherwise. We can not, by any freak of thought,
imagine Three and Two to make Seven."J
Although Dr. Whewell has natui-ally and properly employed a variety
of phrases to bring his meaning more forcibly home, he would, I presume,
allow that they are all equivalent; and that what he means by a necessary
truth, would be sufficiently defined, a proposition the negation of which is
not only false but inconceivable. I am unable to find in any of his expres-
sions, turn them what way you will, a meaning beyond this, and I do not
believe he would contend that they mean any thing more.
This, therefore, is the principle asserted : that propositions, the negation
of which is inconceivable, or in other words, which we can not figure to
ourselves as being false, must rest on evidence of a higher and more cogent
description than any which experience can afford.
- Now I can not but wonder that so much stress should be laid on the cir-
cumstance of inconceivableness, when there is such ample experience to
*mston/ of Scientific Ideas,!., 65-67. t Ibid., i., 60. t Ibid., 58, 59.
12
178 REASONING.
show, that our capacity or incapacity of conceiving a thing has very little
to do with the possibility of the thing in itself; but is in truth very much
an affair of accident, and depends on the past history and habits of our
ovrn minds. There is no more generally acknowledged fact in human na-
ture, than the extreme difficulty at first felt in conceiving any thing as pos-
sible, which is in contradiction to long established and familiar experience ;,
or even to old familiar habits of thought. And this difficulty is a necessary
result of the fundamental laws of the human mind. When we have oftea
seen and thought of two things together, and have never in any one in-
stance either seen or thought of them separately, there is by the primary
law of association an increasing difficulty, which may in the end become
insuperable, of conceiving the two things apart. This is most of all con-
spicuous in uneducated persons, who are in general utterly unable to sepa-
rate any two ideas which have once become firmly associated in their
minds; and if persons of cultivated intellect have any advantage on the
point, it is only because, having seen and heard and read more, and being
more accustomed to exercise their imagination, they have experienced their
sensations and thoughts in more varied combinations, and have been pre-
vented from forming many of these inseparable associations. But this ad-
vantage has necessarily its limits. The most practiced intellect is not ex-
empt from the universal laws of our conceptive faculty. If daily habit
presents to any one for a long period two facts in combination, and if he is.
not led during that period either by accident or by his voluntary mental
operations to think of them apart, he will probably in time become incapar
ble of doing so even by the strongest efEort ; and the supposition that the
two facts can be separated in nature, will at last present itself to his mind
with all the characters of an inconceivable phenomenon.* There are re-
markable instances of this in the history of science : instances in which the-
most instructed men rejected as impossible, because inconceivable, things:
which their posterity, by earlier practice and longer perseverance in the at-
tempt, found it quite easy to conceive, and which every body now knows-
to be true. There was a time when men of the most cultivated intellects,,
and the most emancipated from the dominion of early prejudice, could not
credit the existence of antipodes; were unable to conceive, in opposition
to old association, the force of gravity acting upward instead of downward..
The Cartesians long rejected the Newtonian doctrine of the gravitation of
all bodies toward one another, on the faith of a general proposition, the re-
verse of which seemed to them to be inconceivable — the proposition that a
body can not act where it is not. All the cumbrous machinery of imagi-
nary vortices, assumed without the smallest particle of evidence, appeared
to these philosophers a more rational mode of explaining the heavenly mo-
tions, than one which involved what seemed to them so great an absurdity.f
* "If all mankind had spoken one languhge, we can not doubt that there wonld have been
a powerful, perhaps a universal, school of philosophers, who would have believed in the in-
herent connection between names and things, who would have taken the sound man to be the
mode of agitating the air which is essentially communicative of the ideas of reason, cookery,
bipedality, etc." — De Morgan, Formal Logic, p. 246.
t It would be difficult to name a man more remarkable at once for the greatness and the
wide range of his mental accomplishments, than Leibnitz. Yet this eminent man gave as a
reason for rejecting Newton's scheme of the solar system, that God could not make a body re-
volve round a distant centre, unless either by some impelling mechanism, or by miracle;
" Tout ce qui n'est pas explicable," says he in a letter to the Abb^ Conti, " par la nature des
creatures, est miraculenx. II ne suffit pas de dire : Dieu a fait une telle loi de nature ; done
la chose est naturelle. II faut que la loi soit executable par les natures des creatures. Si.
DEMONSTRATION, AND NECESSARY TRUTHS. 1'79
And they no doubt found it as impossible to conceive that a body should
act upon the earth from the distance of the sun or moon, as we find it to
conceive an end to space or time, or two straight lines inclosing a space. -
Newton himself had not been able to realize the conception, or we should
not have had his hypothesis of a subtle ether, the occult cause of gravita-
tion ; and his writings prove, that though he deemed the particular nature
of the intermediate agency a matter of conjecture, the necessity of some
such agency appeared to him indubitable.
If, then, it be so natural to the human niind, even in a high state of cul-
ture, to be incapable of conceiving, and on that ground to believe impossi-
ble, what is afterward not only found to be conceivable but proved to be
true ; what wonder if in cases where the association is still older, more con-
firmed, and more familiar, and in which nothing ever occurs to shake our
conviction, or even suggest to us any conception at variance with the asso-
ciation, the acquired incapacity should continue, and be mistaken for a nat-
ural incapacity ? It is true, our experience of the varieties in nature ena-
bles us, within certain limits, to conceive other varieties analogous to them.
We can conceive the sun or moon falling ; for though we never saw them
fall, nor ever, perhaps, imagined them falling, we have seen so many other
things fall, that we have innumerable familiar analogies to assist the con-
ception ; which, after all, we should probably have some difficulty in fram-
ing, were we not well accustomed to see the sun and moon move (or ap-
pear to move), so that we are only called upon to conceive a slight change
in the direction of motion, a circumstance familiar to our experience. But
when experience affords no model on which to shape the new conception,
how is it possible for us to form it ? How, for example, can we imagine
an end to space or time? We never saw any object without something
beyond it, nor experienced any feeling without something following it.
When, therefore, we attempt to conceive the last point of space, we have
the idea irresistibly raised of other points beyond it. When we try to im-
agine the last instant of time, we can not help conceiving another instant
after it. Nor is there any necessity to assume, as is done by a modern
school of metaphysicians, a peculiar fundamental law of the mind to ac-
count for the feeling of infinity inherent in our conceptions of space and
time; that apparent infinity is sufficiently accounted for by simpler and
universally acknowledged laws.
Now, in the case of a geometrical axiom, such, for example, as that two
straight lines can not inclose a space — a truth which is testified to us by
our very earliest impressions of the external world — how is it possible
(whether those external impressions be or be not the ground of our belief)
that the reverse of the proposition coidd be otherwise than inconceivable
to us? What analogy have we, what similar order of facts in any other
branch of our experience, to facilitate to us the conception of two straight
lines inclosing a space ? Nor is even this all. I have already called atten-
tion to the peculiar property of our impressions of form, that the ideas or
mental images exactly resemble their prototypes, and adequately represent
them for the purposes of scientific observation. From this, and from the
intuitive character of the observation, which in this case reduces itself to
Dien donnait cette loi, par exemple, h, tin corps libre, de tourner k I'entour d'un certain centre,
ilfaudrait ou qu'il y joignit cTautres corps qui par leur impulsion Vobligeassent de rester tou-
jours dans son orbiie drculaire, ou qu'il mit un ange a ses trousses, ou enfin ilfaudrait qu'il y
eoncourut extraordinairement ; car naturellement il s'ecartera par la tangente." — Works of
Xeibnitz, ed. Dutens, iii., 446.
180 EEASONING.
simple inspection, we can not so much as call up in our imagination two
straight lines, in order to attempt to conceive them inclosing a space, with-
out by that very act repeating the scientific experiment which establishes
/ the contrary. Will it really be contended that the inconceivableness of the
I thing, in such circumstances, proves any thing against the experimental or-
\ igin of the conviction ? Is it not clear that in whichever mode our belief
in the proposition may have originated, the impossibility of our conceiving
the negative of it must, on either hypothesis, be the same ? As, then. Dr.
Whewell exhorts those who have any difficulty in recognizing the distinc-
tion held by him between necessary and contingent truths, to study geom-
etry— a condition which I can assure him I have conscientiously fulfilled —
I, in return, with equal confidence, exhort those who agree with him, to
study the general laws of association ; being convinced that nothing more
is requisite than a moderate familiarity with those laws, to dispel the illu-
sion which ascribes a peculiar necessity to our earliest inductions from ex-
perience, and measures the possibility of things in .themselves, by the hu-
man capacity of conceiving them.
I hope to be pardoned for adding, that Dr. Whewell himself has both
confirmed by his testimony the effect of habitual association in giving to
an experimental truth the appearance of a necessary one, and afforded a
striking instance of that remarkable law in his own person. In his Philos-
ophy of the Inductive Sciences he continually asserts, that propositions
which not only are not self-evident, but which we know to have been dis-
covered gradually, and by great efforts of genius and patience, have, when
once established, appeared so self-evident that, but for historical proof, it
would have been impossible to conceive that they had not been recognized
from the first by all persons in a sound state of their faculties. " We now
despise those who, in the Copernican controversy, could not conceive the
apparent motion of the sun on the heliocentric hypothesis ; or those who,
in opposition to Galileo, thought that a uniform force might be that which
generated a velocity proportional to the space; or those who held there
was something absurd in Newton's doctrine of the different refrangibility
of differently colored rays; or those who imagined that when elements
combine, their sensible qualities must be manifest in the compound ; or
those who were reluctant to give up the distinction of vegetables into herbs,
shrubs, and trees. We can not help thinking that men must have been
singularly dull of comprehension, to find a difficulty in admitting what is
to us so plain and simple. We have a latent persuasion that we in their
place should have been wiser and more clear-sighted ; that we should have
taken the right side, and given our assent at once to the truth. Yet in re-
ality such a persuasion is a mere delusion. The persons who, in such in-
stances as the above, were on the losing side, were very far, in most cases,
from being persons more prejudiced, or stupid, or narrow-minded, than the
greater part of mankind now are ; and the cause for which they fought
was far from being a manifestly bad one, till it had been so decided by the
result of the war So complete has been the victory of truth in most
of these instances, that at present we can hardly imagine the struggle to
have been necessary. The very essence of these triumphs is, that they lead
us to regard the views we reject as not only false but inconceivable."*
This last proposition is precisely what I contend lorT'SScT I ask no more,
in order to overthrow the whole theory of its author on the nature of the
• Novum Organum Renovatum, pp. 32, 33.
DEMONSTRATION, AND NECESSARY TRUTHS. 181
evidence of axioms. For what is that theory ? That the truth of axioms
can not have been learned from experience, because their falsity is incon- \
ceivable. But Dr. Whewell himself says, that we are continually led, by \
the natural progress of thought, to regard as inconceivable what our fore- \
fathers not only conceived but believed, nay even (he might have added) J
were unable to conceive the reverse of. He can not intend to justify this —
mode of thought : he can not mean to say, that we can be right in regard-
ing as inconceivable what others have conceived, and as self-evident what
to others did not appear evident at all. After so complete an admis- \
sion that inconceivableness is an accidental thing, not inherent in the phe- \
noraenon itself, but dependent on the mental history of the person who /
tries to conceive it, how can he ever call upon us to reject a proposition as
impossible on no other ground than its inconceivableness? Yet he not
only does so, but has unintentionally afforded some of the most remarkable
examples which can be cited of the very illusion which he has liimself so
clearly pointed out. I select as specimens, his remarks on the evidence of
the three laws of motion, and of the atomic theory.
With respect to the laws of motion, Dr. Whewell says : " No one can
doubt that, in historical fact, these laws were collected from experience.
That such is the case, is no matter of conjecture. We know the time, the
persons, the circumstances, belonging to each step of each discovery."*
After this testimony, to adduce evidence of the fact would be superfluous.
And not only were these laws by no means intuitively evident, but some
of them were originally paradoxes. The first law was especially so. That
a body, once in motion, would continue forever to move in the same direc-
tion with undiminished velocity unless acted upon by some new force, was
a proposition which mankind found for a long time the greatest difficulty
in crediting. It stood opposed to apparent experience of the most familiar
kind, which taught that it was the nature of motion to abate gradually,
and at last terminate of itself. Yet when once the contrary doctrine was
firmly established, mathematicians, as Dr. Whewell observes, speedily be-
gan to believe that laws, thus contradictory to first appearances, and which,
even after full proof had been obtained, it had required generations to ren-
der familiar to the minds of the scientific world, were under " a demonstra-
ble necessity, compelling them to be such as they are and no other;" and
he himself, though not venturing " absolutely to pronounce " that all these
laws " can be rigorously traced to an absolute necessity in the nature of
things,"f does actually so think of the law just mentioned ; of which he
says : " Though the discovery of the first law of motion was made, histor- N
ically speaking, by means of experiment, we have now attained a point of ^^
view in which we see that it might have been certainly known to be true,
independently of experience."! Can there be a more striking exemplifi-
cation than is here afforded, of the effect of association which we have de- ,
scribed ? Philosophers, for generations, have the most extraordinary diffi-
culty in putting certain ideas together ; they at last succeed in doing so ;
and after a s'ufficient repetition of the process, they first fancy a natural .^
bond between the ideas, then experience a growing difficulty, which at last,
by the continuation of the same progress, becomes an impossibility, of sev-
ering them from one another. If such be the progress of an experimental
conviction of which the date is of yesterday, and. which is in opposition to
first appearances, how must it fare with those which are conformable to
• Histon/ of Scientific Ideas, i., 264. t Ibid., i., 263. t Ibid., 240.
182 REASONING.
appearances familiar from the first dawn of intelligence, and of the conclu-
siveness of which, from the earliest records of human thought, no skeptic
has suggested even a momentary doubt?
The other instance which I shall quote is a truly astonishing one, and
may be called the reductio ad absurdum of the theory of incopceivableness.
Speaking of the laws of chemical composition. Dr. Whewell says:* "That
they could never have been clearly understood, and therefore never firmly
established, without laborious and exact experiments, is certain ; but yet
we may venture to say, that being once known, they possess an evidence
beyond that of mere experiment. For how in fact can we conceive combi-
nations, otherwise than as definite in kind and quality ? If we were to
suppose each element ready to combine with any other indifferently, and
indifferently in any quantity, we should have a world in which all would be
confusion and indefiniteness. There would be no fixed kinds of bodies.
Salts, and stones, and ores, would approach to and graduate into each other
by insensible degrees. Instead of this, we know that the world consists of
bodies distinguishable from each other by definite differences, capable of
being classified and named, and of having general propositions asserted
concerning them. And as we can not conceive a world in which this
should not be the case, it would appear that we can not conceive a state of
things in which the laws of the combination of elements should not be of
that definite and measured kind which we have above asserted."
That a philosopher of Dr. Whewell's eminence should gravely assert
that we can not conceive a world in which the simple elements should com-
bine in other than definite proportions; that by dint of meditating on a
scientific truth, the original discoverer of which was still living, he should
have rendered the association in his own mind between the idea of combi-
nation and that of constant proportions so familiar and intimate as to be
unable to conceive the one fact without, the other; is so signal an instance
of the mental law for which I am contending, that one word more in illus-
tration must be superfluous.
In the latest and most complete elaboration of his metaphysical system
(the Philosophy of Discovery), as well as in the earlier discourse on the
Fundamental Antithesis of Philosophy, reprinted as an appendix to that
work. Dr. Whewell, while very candidly admitting that his language was
open to misconception, disclaims having intended to say that mankind in
general can now perceive the law of definite proportions in chemical com-
bination to be a necessary truth. All he meant was that philosophical
chemists in a future generation may possibly see this. " Some truths may
be seen by intuition, but yet the intuition of them may be a rare and a dif-
ficult attainment."! ^"^^ he explains that the inconceivableness which, ac-
cording to his theory, is the test of axioms, " depends entirely upon the
'clearness of the Ideas which the axioms involve. So long as those ideas
are vague and indistinct, the contrary of an axiom may be assented to,
though it can not be distinctly conceived. It may be assented to, not be-
oause it is possible, but because we do not see clearly what is possible. To
a person who is only beginning to think geometrically, there may appear
nothing absurd in the assertion that two straight lines may inclose a space.
And in the same manner, to a person who is only beginning to think of
mechanical truths, it may not appear to be absurd, that in mechanical proc-
esses. Reaction should be greater or less than Action ; and so, again, to a
* Hist. Scientific Ideas, ii., 25, 26. f Phil, of Disc., p. 339.
DEMONSTRATION, AND NECESSARY TRUTHS. 183
person who has not thought steadily about Substance, it may not appear
inconceivable, that by chemical operations, we should generate new matter,
or destroy matter which already exists."* Necessary truths, therefore, are ,^
BOt those of which we can not conceive, but " those of which we can not \
distinctly conceive, the contrary."f So long as our ideas are indistinct al-- '
together, we do not know what is or is not capable of being distinctly
■conceived ; but, by the ever increasing distinctness with which scientific
men apprehend the general conceptions of science, they in time come to
perceive that there are certain laws of nature, which, though historically
-and as a matter of fact they were learned from experience, we can not,
now that we know them, distinctly conceive to be other than they are.
The account which I should give of this progress of the scientific mind
is somewhat different. After a general law of nature has been ascertained,
men's minds do not at first acquire a complete facility of familiarly repre-
senting to themselves the phenomena of nature in the character which that
law assigns to them. The habit which constitutes the scientific oast of
mind, that of conceiving facts of all descriptions conformably to the laws
which regulate them — phenomena of all descriptions according to the re-
lations which have been ascertained i-eally to exist between them ; this hab-
it, in the case of newly-discovered relations, comes only by degrees. So
Jong as it is not thoroughly formed, no necessary character is ascribed to
the new truth. But in time, the philosopher attains a state of mind in
which his mental picture of nature spontaneously represents to him all the
phenomena with which the new theory is concerned, in the exact light in
which the theory regards them : all images or conceptions derived from
any other theory, or from the confused view of the facts which is anterior
"to any theory, having entirely disappeared from his mind. The mode of
representing facts which results from the theory, has now become, to his
-faculties, the only natural mode of conceiving them. It is a known truth,
that a prolonged habit of arranging phenomena in certain groups, and ex-
plaining them by means of certain principles, makes any other arrangement
-or explanation of these facts be felt as unnatural : and it may at last be-
come as difficult to him to represent the facts to himself in any other mode,
■as it often was, originally, to represent them in that mode.
But, further (if the theory is true, as we are supposing it to be), any
•other mode in which he tries, or in which he was formerly accustomed,
to represent the phenomena, will be seen by him to be inconsistent with
the facts that suggested the new theory — facts which now form a part of
his mental picture of nature. And since a contradiction is always incon-
ceivable, his imagination rejects these false theories, and declares itself in-
capable of conceiving them. Their inconceivableness to him does not, how-_^
ever, result from any thing in the theories themselves, intrinsically and a \
jorjon repugnant to the human faculties; it results from the repugnanceX^
between them and a portion of the facts ; which facts as long as he did J
not know, or did not distinctly realize in his mental representations, the "
false theory did not appear other than conceivable; it becomes inconceiv-
able, merely from the fact that contradictory elements can not be combined
in the same conception. Although, then, his real reason for rejecting theo-
ries at variance with the true one, is no other than that they clash with his
experience, he easily falls into the belief, that he rejects them because they
«re inconceivable, and that he adopts the true theory because it is self-evi-
■dent, and does not need the Evidence of experience at all.
* Phil, of Disc., p. 338. t Ibid., p. 463.
184 REASONING.
This I take to be the real and snfEcient explanation of the paradoxical
truth, on which so much stress is laid by Dr. Whewell, that a scientifically
cultivated mind is actually, in virtue of that cultivation, unable to conceive
suppositions which a common man conceives without the smallest difficul-
ty. For there is nothing inconceivable in the suppositions themselves ; the
impossibility is in combining them with facts inconsistent with them, as
part of the same mental picture ; an obstacle of course only felt by those
who know the facts, and are able to perceive the inconsistency. As far as
the suppositions themselves are concerned, in the case of many of Dr. Whe-
well's necessary truths the negative of the axiom is, and probably will be
as long as the human race lasts, as easily conceivable as the affirmative.
There is no axiom (for example) to which Dr. Whewell ascribes a more
thorough character of necessity and self-evidence, than that of the inde-
structibility of matter. That this is a true law of nature I fully admit ;
but I imagine there is no human being to whom the opposite supposition
is inconceivable — who has any difficulty in imagining a portion of matter
annihilated : inasmuch as its apparent annihilation, in no respect distin-
guishable from real by our unassisted senses, takes place every time that
water dries up, or fuel is consumed. Again, the law that bodies combine
chemically in definite proportions is undeniably true ; but few besides Dr.
Whewell have reached the point which he seems personally to have arrived
at (though he only dares prophesy similar success to the multitude after
the lapse of generations), that of being unable to conceive a world in which
the elements are ready to combine with one another " indifferently in any
quantity ;" nor is it likely that we shall ever rise to this sublime height of
inability, so long as all the mechanical mixtures in our planet, whether sol-
id, liquid, or aeriform, exhibit to our daily observation the very phenomenon
declared to be inconceivable.
According to Dr. Whewell, these and similar laws of nature can not be
drawn from experience, inasmuch as they are, on the contrary, assumed in
the interpretation of experience. Our inability to " add to or diminish the
quantity of matter in the world," is a truth which " neither is nor can be
derived from experience ; for the experiments which we make to verify it
presuppose its truth When men began to use the balance in chem-
ical analysis, they did not prove by trial, but took for granted, as self-evi-
dent, that the weight of the whole must be found in the aggregate weight
of the elements."* True, it is assumed ; but, I apprehend, no otherwise
than as all experimental inquiry assumes provisionally some theory or hy-
pothesis, which is to be finally held true or not, according as the experi-
ments decide. The hypothesis chosen for this purpose will naturally be
one which groups together some considerable number of facts already
known. The proposition that the material of the world, as estimated by
weight, is neither increased nor diminished by any of the processes of na-
ture or art, had many appearances in its favor to begin with. It expressed
truly a great number of familiar facts. There were other facts which it
had the appearance of conflicting with, and which made its truth, as a
universal law of nature, at first doubtful. Because it was doubtful, exper-
iments were devised to verify it. Men assumed its truth hypothetically,
and proceeded to try whether, on more careful examination, the phenomena
which apparently pointed to a different conclusion, would not be found to
be consistent with it. This turned out to be the case ; and from that time
* Phil, of Disc, pp. 472, 473.
DEMONSTRATION, AND NECESSARY TRUTHS. 185
the doctrine took its place as a universal truth, but as one proved to hQ_
such by experience. That the theory itself preceded the proof of its truth
— that it had to be conceived before it could be proved, and in order that
it might be proved — does not imply that it was self-evident, and did not
need proof. Otherwise all the true theories in the sciences are necessary
and self-evident ; for no one knows better than Dr. Whewell that they all
began by being assumed, for the purpose of connecting them by deduc-
tions with those facts of experience on which, as evidence, they now con-
fessedly rest.* .
* The Quarterly Review for June, 1841, contained an article of great ability on Dr. Whe-
•well's two great works (since acknowledged and reprinted in Sir John Herschel's Essays)
which maintains, on the subject of axioms, the doctrine advanced in the text, that they are x
generaliziitions from experience, and supports that opinion by a line of argument strikingly
coinciding with mine. When I state that the whole of the present chapter (except the last ,
four pages, added in the fifth edition) was written before I had seen the article (the greater
part, indeed, before it was published), it is not my object to occupy the reader's attention with
a matter so unimportant as the degree of originality which may or may not belong to any por-
tion of my own speculations, but to obtain for an opinion which is opposed to reigning doc-
trines, the recommendation derived from a striking concurrence of sentiment between two
inquirers entirely independent of one another. I embrace the opportunity of citing from a
writer of the extensive Acquirements in physical and metaphysical knowledge and the capacity
of systematic thought which the article evinces, passages so remarkably in unison with my
own views as the following :
"The truths of geometry are summed up and embodied in its definitions and axioms
Xet us turn to the axioms, and what do we find ? A string of propositions concerning mag-
nitude in the abstract, which are equally true of space, time, force, number, and every other
magnitude susceptible of aggregation and subdivision. Such propositions, where they are
not mere definitions, as some of them are, carry their inductive origin on the face of their
enunciation Those which declare that two straight lines can not inclose a space, and
that two straight lines which cut one another can not both be parallel to a third, are in reality
the only ones which expi-ess characteristic properties of space, and these it will be worth while
to consider more nearly. Now the only clear notion we can form of straightness is uniform-
ity of direction, for space in its ultimate analysis is nothing but an assemblage of distances
and directions. And (not to dwell on the notion of continued contemplation, i. e., mental ex-
perience, as included in the very idea of uniformity ; nor on that of transfer of the contem-
plating being from point to point, and of experience, during such transfer, of the homogeneity
of the interval passed over) we can not even propose the proposition in an intelligible form to
any one whose experience ever since he was born has not assured him of the fact. The unity
of direction, or that we can not march from a given point by more than one path direct to the
same object, is matter of practical experience long before it can by possibility become matter
of abstract thought. We can not attempt mentally to exemplify the conditions of the assertion
in an imaginary case opposed to it, without violating our habitual recollection of this experi-
ence, and defacing our mental picture of space as grounded on it. What but experience, we
may ask, can possibly assure us of the homogeneity of the parts of distance, time, force, and
measurable aggregates in general, on which the truth of the other axioms depends ? As re-
gards the latter axiom, after what has been said it must be clear that the very same course of
remarks equally applies to its case, and that its truth is quite as much forced on the mind as
that of the former by daily and hourly experience, including always, be it observed, in
<mr notion of experience, that which is gained by contemplation of the inward picture which the
mind forms to itself in any proposed case, or which it arbitrarily selects as an example — such
^picture, in virtue of the extreme simplicity of these primary relations, being called up by the
imagination with as much vividness and clearness as could be done by any external impression,
which is the only meaning we can attach to the word intuition, as applied to such relations. "
And again, of the axioms of mechanics : " As we admit no such propositions, other than
as truths inductively collected from observation, even in geometry itself, it can hardly be ex-
pected that, in a science of obviously contingent relations, we should acquiesce in a contrary
view. Let us take one of these axioms and examine its evidence : for instance, that equal
forces perpendicularly appUed at the opposite ends of equal arms of a straight lever will bal-
ance each other. • What but experience, we may ask, in the first place, can possibly inform us
that a force so applied will have any tendency to turn the lever on its centre at all ? or that
force can be so transmitted along a rigid line perpendicular to its direction, as to act elsewhere
in space than along its own line of action ? Surely this is so far from being self-evident that
186 REASONING.
it has even a paradoxical appearance, which is only to be removed by giving our lever thick-
ness, material composition, and molecular powers. Again, we conclude, that the two forces,
being equal and applied under precisely similar circumstances, must, if they exert any effort
at all to turn the lever, exert equal and opposite eftbrts : but what a priori reasoning can pos-
sibly assure us that they do act under precisely similar circumstances ? that points which dif-
fer in place are similarly circumstanced as regards the exertion of force? that universal space
may not have relations to universal force — or, at all events, that the organization of the ma-
terial universe may not be such as to place that portion of space occupied by it in such rela-
tions to the forces exerted in it, as may invalidate the absolute similarity of circumstances as-
. sumed ? Or we may argue, what have we to do with the notion of angular movement in the
lever at all ? The case^is one of rest, and of quiescent destruction of force by force. Now
how is this destruction effected? Assuredly by the counter-pressure which supports the ful-
crum. But would not this destruction equally arise, and by the same amount of counteract-
ing force, if each force simply pressed its own half of the lever against the fulcrum ? And.
what can assure us that it is not so, except removal of one or other force, and consequent tilt-
ing of the lever? The other fundamental axiom of statics, that the pressure on the point of
support is the sum of the weights is merely a scientific transformation and more refined.
mode of stating a coarse and obvious result of universal experience, viz. , that the weight of a
rigid body is the same, handle it or suspend it in what position or by what point we will, and
that whatever sustains it sustains its total weight. Assuredly, as Mr. Whewell justly remarks,
' No one probably ever made a trial for the purpose of showing that the pressure on the sup-
port is equal to the sum of the weights.' But it is precisely because in every action
of his life from earliest infancy he has been continually making the trial, and seeing it made
by every other living being about him, that he never dreams of staking its result on one addi-
tional attempt made with scientific accuracy. This would be as if a man should resolve Uy
decide by experiment whether his eyes were useful for the purpose of seeing, by hermetically
sealing himself up for half an hour in a metal case."
On the "paradox of universal propositions obtained by experience," the same writer says :
"If there be necessary and universal truths expressible in propositions of axiomatic simplicity
and obviousness, and having for their subject-matter the elements of all our experience and
all our knowledge, surely these are the truths which, if experience suggest to us any truths at
all, it ought to suggest most readily, clearly, and unceasingly. If it were a truth, universal,
and necessary, that a net is spread over the whole surface of every planetary globe, we should,
not travel far on our own without getting entangled in its meshes, and making the necessity
of some means of extrication an axiom of locomotion There is, therefoi'e, nothing par-
adoxical, but the reverse, in our being led by observation to a recognition of such truths, as
general propositions, co-extensive at least with all human experience. That they pervade all
the objects of experience, must insure their continual suggestion bt/ experience; that they are
true, must insure that consistency of suggestion, that iteration of uncontradicted assertion,
which commands implicit assent, and removes all occasion of exception ; that they are simple,
and admit of no misunderstanding, must secure their admission by every mind."
" A truth, necessary and univeisal, relative to any object of our knowledge, must verify it-
self in every instance where that object is before our contemplation, and if at the same time it
be simple and intelligible, its verification must be obvious. The sentiment of such a truth
can not, therefore, but be present to our minds whenever that object is contemplated, and must
therefore make apart of the mental picture or idea of that object which we may on any occa-
sion summon before our imagination All propositions, therefore, become not only untrue
but inconceivable, if axioms be violated in their enunciation."
Another eminent mathematician had previously sanctioned by his authority the doctrine of
the origin of geometrical axioms in experience. "Geometry is thus founded likewise on;
observation ; but of a kind so familiar and obvious, that the primary notions which it fur-
nishes might seem intuitive." — Sir John Leslie, quoted by Sir William Hamilton, Discourses,,
etc., p. 272.
DEMONSTBATION, AND NECESSARY TRUTHS. 187
CHAPTER VI.
THE SAME SUBJECT CONTINUED.
§ 1. Ik the examination which formed the subject of the last chapter,
into the nature of the evidence of those deductive sciences which are com-
monly represented to be systems of necessary truth, we have been led to
the following conclusions. The results of those sciences are indeed nec-
essary, in the sense of necessarily following from certain first principles,
commonly called axioms and definitions; that is, of being certainly true
if those axioms and definitions are so ; for the word necessity, even in this
acceptation of it, means no more than certainty. But their claim to the
character of necessity in any sense beyond this, as implying an evidence
independent of and superior to observation and experience, must depend
on the previous establishment of such a claim in favor of the definitions
and axioms themselves. With regard to axioms, we found that, consid-
ered as experimental truths, they rest on superabundant and obvious ev-
idence. We inquired, whether, since this is the case, it be imperative to
suppose any other evidence of those truths than experimental evidence, any
other origin for our belief of them than an experimental origin. We de-
cided, that the burden of proof lies with those who maintain the afEi-ma-
tive, and we examined, at considerable length, such arguments as they have
produced. The examination having led to the rejection of those arguments,
we have thought ourselves warranted in concluding that axioms are but a
class, the most universal class, of inductions from experience; the simplest
and easiest cases of generalization fromths jacts furnished to us by our
senses or by our liitBrntrhCOlisciousness.
While the axioms of demonstrative sciences tlins appeared to be exper-
imental truths, the definitions, as they are incorrectly called, in those sci- /
ences, were found by us to be generalizations from experience which are/
not even, accurately speaking, truths ; being propositions in whioh, while
we assert of some kind of object, some property or properties which ob-
servation shows to belong to it, we at the same time deny that it possesses
any other properties, though in truth other properties do in every individ-
nai instance accompany, and in almost all instances modify, the property
thus exclusively predicated. The denial, therefore, is a mere fiction, or sup-
position, made for the purpose of excluding the consideration of those mod-
ifying circumstances, when their influence is of too trifling amount to be
worth considering, or adjourning it, when important -to a more convenient
moment. ,
From these considerations it would appear that Deductive or Demon- ^
strative Sciences are all, without exception. Inductive Sciences ; that theiw-'
evidence is that of experience ; but that they are also, in virtue of the pe-
culiar character of one indispensable portion of the general formulae ac-
cording to which their inductions are made. Hypothetical Sciences. Their
conclusions are only true on certain suppositions, which are, or ought to
be, approximations to the truth, but are seldom, if ever, exactly true ; and
to this hypothetical character is to be ascribed the peculiar certainty, which^
is supposed to be inherent in demonstration.
188 REASONING.
What we have now asserted, however, can not be received as universally
true of Deductive or Demonstrative Sciences, until verified by being ap-
plied to the most remarkable of all those sciences, that of Numbers ; the
theory of the Calculus ; Arithmetic and Algebra. It is harder to believe
of the doctrines of this science than of any other, either that they are not
truths a priori, but experimental truths, or that their peculiar certainty is
owing to their being not absolute but only conditional truths. This, there-
fore, is a case which merits examination apart ; and the more so, because
on this subject we have a double set of doctrines to contend with ; that of
the a priori philosophers on one side; and on the other, a theory the most
. opposite to theirs, which was at one time very generally received, and is
still far from being altogether exploded, among metaphysicians.
§ 2. This theory attempts to solve the difficulty apparently inherent in
the case, by representing the propositions of the science of numbers as
merely verbal, and its processes as simple transformations of language, sub--
/'stitntions of one expression for another. The proposition, Two and one is
( equal to three, according to these writers, is not a truth, is not the assei'tion
V of a really existing fact, but a definition of the word three ; a statement
that mankind have agreed to use the name three as a sign exactly equiva-
lent to two and one ; to call by the former name whatever is called by the
other more clumsy phrase. According to this doctrine, the longest process
in algebra is but a succession of changes in terminology, by which equiva-
lent expressions are substituted one for another ; a series of translations of
the same fact, from one into another language ; though how, after such a
series of translations, the fact itself comes out changed (as when we de-
monstrate a new geometrical theorem by algebra), they have not explain-
ed ; and it is a difiiculty which is fatal to their theory.
It must be acknowledged that there are peculiarities in the processes of
arithmetic and algebra which render the theory in question very plausible,
and have not unnaturally made those sciences the stronghold of Nominal-
ism. The doctrine that we can discover facts, detect the hidden processes
of nature, by an artful manipulation of language, is so contrary to common
sense, that a person must have made some advances in philosophy to be-
lieve it : m^n fly to so paradoxical a belief to avoid, as they think, some
even greater difficulty, which the vulgar do not see. What has led many
to believe' that reasoning is a mere verbal process, is, that no other theory
seemed reconcilable with the nature of the Science of Numbers. For we
do not carry any ideas along with us when we use the symbols of arithme-
tic or of algebra. In a geometrical demonstration we have a mental dia-
gram, if not one on paper ; AB, AC, are present to our imagination as lines,
intersecting other lines, forming an angle with one another, and the like;
but not so a and h. These may represent lines or any other magnitudes,
but those magnitudes are never thought of; nothing is realized in our im-
agination but a and h. The ideas which, on the particular occasion, they
happen to represent, are banished from the mind during every intermediate
part of the pi'ocess, between the beginning, when the pi'emises are trans-
lated from things into signs, and the end, wtien the conclusion is translated
back from signs into things. Nothing, then, being in the reasoner's mind
but the symbols, what can seem more inadmissible than to contend that the
reasoning process has to do with any thing more? We seem to have come
■'o one of Bacon's Prerogative Instances ; an exp&rimentum crucis on the
nature of reasoning itself.
DEMONSTRATION, AND NECESSARY TRUTHS. ]89
Nevertheless, it will appear on consideration, that this apparently so de*
cisive instance is no instance at all ; that there is in every step of an arith-
metical or algebraical calculation a real induction, a real inference of facts
from facts; and that what disguises the induction is simply its compre-
hensive nature, and the consequent extreme generality of the language.
All numbers must be numbers of something : there are no such things as
numbers in the abstract. Ten must mean ten bodies, or ten sounds, or ten
beatings of the pulse. But though numbers must be numbers of some- ,
thing, they may be numbers of any thing. Propositions, therefore, con-''
cerning numbers, have the remarkable peculiarity that they are proposi-
tions concerning all things whatever; all objects, all existences of every
kind, known to our experience. All things possess quantity ; consist of
parts which can be numbered ; and in that character possess all the prop-
erties which are called properties of numbers. That half of four is two,
must be true whatever the word four represents, whether four hours, four
miles, or four pounds weight. We need only conceive a thing divided into
four equal parts (and all things may be conceived as so divided), to be able
to predicate of it every property of the number four, that is, every arith-
metical proposition in which the number four stands on one side of the
equation. Algebra extends the generalization still farther : every number
represents that particular number of all things without distinction, but ev-
ery algebraical symbol does more, it represents all nuinbers without dis-
tinction. As soon as we conceive a thing divided into equal parts, without
knowing into what number of parts, we may call it a or x, and apply to it,
without danger of error, every algebraical formula in the books. The
proposition, 2 (a -f 5) = 2 or -|- 2 S, is a truth co-extensive with all nature.
Since then algebraical truths are true of all things whatever, and not, like
those of geometry, true of lines only or of angles only, it is no wonder that
the symbols should not excite in our minds ideas of any things in particu-
lar. When we demonstrate the forty-seventh proposition of Euclid, it is
not necessary that the words should raise in us an image of all right-angled
triangles, but only of some one right-angled triangle : so in algebra we
need not, under the symbol «, picture to ourselves all things whatever, but
only some one thing ; why not, then, the letter itself ? The mere written
characters, a, h, x, y, z, serve as well for representatives of Things in general,
as any more complex and apparently more concrete conception. That we
are conscious of them, however, in their character of things, and not of mere
signs, is evident from the fact that our whole process of reasoning is car-
ried on by predicating of them the properties of things. In resolving an
algebraic equation, by what rules do we proceed ? By applying at each
step to a, b, and x, the proposition that equals added to equals make equals ;
that equals taken from equals leave equals ; and other propositions founded
on these two. These are not properties of language, or of signs as such,
but of magnitudes, which is as much as to say, of all things. The infer-
ences, therefore, which are successively drawn, are inferences concerning ,
things, not symbols; though as any Things whatever will serve the turn,-^
there is no necessity for keeping the idea of the Thing at all distinct, and
consequently the process of thought may, in this case, be allowed without
danger to do what all processes of thought, when they have been performed
often, will do if permitted, namely, to become entirely mechanical. Hence
the general language of algebra comes to be used familiarly without excit-
ing ideas, as all other general language is prone to do from mere habit,
though iu no other case than this can it be done with complete safety.
190 REASONING.
But when we look back to see from whence the probative force of the
process is derived, we find that at every single step, unless we suppose our-
selves to be thinking and talking of the things, and not the mere symbols,
the evidence fails.
There is another circumstance, which, still more than that which we have
now mentioned, gives plausibility to the notion that the propositions of
arithmetic and algebra are merely verbal. That is, that when considered
as propositions respecting Things, they all have the appearance of being
identical propositions. The assertion. Two and one is equal to three, con-
sidered as an assertion respecting objects, as for instance, " Two pebbles
and one pebble are equal to three pebbles," does not affirm equality be-
tween two collections of pebbles, but absolute identity. It affirms that if
we put one pebble to two pebbles, those very pebbles are three. The ob-
jects, therefore, being, the very same, and the mei-e assertion that " objects
are themselves " being insignificant, it seems but natural to consider the
proposition, Two and one is equal to three, as asserting mere identity of
signification between the two names.
This, however, though it looks so plausible, will not bear examination.
The expression " two pebbles and one pebble," and the expression " three
pebbles," stand indeed for the same aggregation of objects, but they by no
means stand for the same physical fact. They are names of the same ob-
jects, but of those objects in two diffei-ent states : though they (denote the
same things, their connotation is different. Three pebbles in two separate
parcels, and three pebbles in one parcel, do not make the same impression
on our senses ; and the assertion that the very same pebbles may by an al-
teration of place and arrangement be made to produce either the one set of
sensations or the other, though a very familiar proposition, is not an iden-
tical one. It is a truth known to us by early and constant experience : an
inductive truth ; and such truths are the foundation of the science of Num-
ber. The fundamental truths of that science all rest on the evidence of
sense; they are proved by showing to our eyes and our fingers that any
given number of objects — ten balls, for example — may by separation and
re-arrangement exhibit to our senses all the different sets of numbers the
sums of which is equal to ten. All the improved methods of teaching
arithmetic to children proceed on a knowledge of this fact. All who wish
to carry the child's mind along with them in learning arithmetic ; all who
wish to teach numbers, and not mere ciphers — now teach it through the ev-
idence of the senses, in the manner we have described.
We may, if we please, call the proposition, " Three is two and one," a
definition of the number three, and assert that arithmetic, as it has been
asserted that geometry, is a science founded on definitions. But they are
definitions in the geometrical sense, not the logical ; asserting not the mean-
ing of a term only, but along with it an observed matter of fact. The
proposition, "A circle is a figure bounded by a line which has all its points
' equally distant from a point within it," is called the definition of a circle ;
but the proposition from which so many consequences follow, and which
is really a first principle in geometry, is, that figures answering to this de-
scription exist. And thus we may call "Three is two and one "a defini-
tion of three; but the calculations which depend on that proposition do
not follow from the definition itself, but from an arithmetical theorem pre-
supposed in it, namely, that collections of objects exist, which while they
impress the senses thus, V, may be separated into two parts, thus, o » o-
This proposition being granted, we term all such parcels Threes, after
DEMONSTRATION, AND NECESSARY TRUTHS. 191
■which the enunciation of the above-mentioned physical fact will serve also
for a definition of the word Three.
The Science of Number is thus no exception to the conclusion we pre-
viously arrived at, that the processes even of deductive sciences are alto-
gether inductive, and that their first principles are generalizations from ex-
perience. It remains to be examined whether this science resembles geoni-
■etry in the further circumstance, that some of its inductions are not exactly
true ; and that the peculiar certainty ascribed to it, on account of which its
propositions are called Necessary Truths, is fictitious and hypothetical, be-
ing true in no other sense than that those propositions legitimately follow
from the hypothesis of the truth of premises which are avowedly mere ap-
proximations to truth.
§ 3. The inductions of arithmetic are of two sorts : first, those which we
have just expounded, such as One and one are two. Two and one are three,
■etc., which may be called the definitions of the various numbers, in the im-
proper or geometrical sense of the word Definition ; and secondly, the two
following axioms : The sums of equals are equal, The differences of equals
are equal. These two are sufficient ; for the corresponding propositions re-
specting unequals may be proved from these by a reductio ad absurdum.
These axioms, and likewise the so-called definitions, are, as has already
been said, results of induction ; true of all objects whatever, and, as it may
seem, exactly true, without the hypothetical assumption of unqualified truth
where an approximation to it is all that exists. The conclusions, therefore,
it will naturally be inferred, are exactly true, and the science of number is
an exception to other demonstrative sciences in this, that the categorical
certainty which is predicable of its demonstrations is independent of all
hypothesis.
On more accurate investigation, however, it will be found that, even in
this case, there is one hypothetical element in the ratiocination. In all
propositions concerning numbers, a condition is implied, without which
none of them would be true ; and that condition is an assumption which
may be false. The condition is, that 1=1 ; that all the numbers are num-
bers of the same or of equal units. Let this be doubtful, and not one of
the propositions of arithmetic will hold true. How can we know that one
pound and one pound make two pounds, if one of the pounds may be troy,
■axiA. the other avoirdupois? They may not make two pounds of either, or
■of any weight. How can we know that a forty-horse power is always equal
to itself, unless we assume that all horses are of equal strength ? It is cer-
tain that 1 is always equal in numher to 1 ; and where the mere number of
objects, or of the parts of an object, without supposing them to be equiv-
alent in any other respect, is all that is material, the conclusions of arith-
metic, so far as they go to that alone, are true without mixture of hypoth-
■esis. There are such cases in statistics ; as, for instance, an inquiry into
the amount of the population of any country. It is indifferent to that in-
quiry whether they are grown people or children, strong or weak, tall or
short; the only thing we want to ascertain is their number. But when-
ever, from equality or inequality of number, equality or inequality in any
other .rgspect is to be inferred, arithmetic carried into such inquiries be-
comes as hypothetical a science as geometry. All units must be assumed
to be equal in that other respect; and this is never accurately true, for one
:actual pound weight is not exactly equal to another, nor one measured mile's
length to another ; a nicer balance, or more accurate measuring instruments,
-would alwavs detect some difference.
\
192 REASONING.
What is commonly called mathematical certainty, therefore, wMch com-
prises the twofold conception of unconditional truth and perfect accuracy,
lis not an attribute of all mathematical truths, but of those only which re-
bate to pure Number, as distinguished from Quantity in the more enlarged
^nse; and only so long as we abstain from supposing that the numbers
(are a precise index to actual quantities. The certainty usually ascribed to
the conclusions of geometry, and even to those of mechanics, is nothing
whatever but certainty of inference. We can have full assurance of par*
ticular results under particular suppositions, but we can not have the same
assurance that these suppositions are accurately true, nor that they include
all the data which may exercise an influence over the result in any given
instance.
< § 4. It appears, therefore, that the method of all Deductive Sciences is
Jiypothetioal. They proceed by tracing the consequences of certain as-
isumptions ; leaving for separate consideration whether the assumptions
y^e true or not, and if not exactly true, whether they are a sufficiently near
•'approximation to the truth. The reason is obvious. Since it is only in
questions of pure number that the assumptions are exactly true, and even
there only so long as no conclusions -except purely numerical ones are to
be founded on them ; it must, in all other cases of deductive investigation,
form a part of the inquiry, to determine how much the assumptions want
of being exactly true in the case in hand. This is generally a matter of
observation, to be repeated in every fresh case ; or if it has to be settled
by argument instead of observation, may require in every different case
different evidence, and present every degree of difficulty, from the lowest
to the highest. But the other part of the process — namely, to determine
■what else may be concluded if we find, and in proportion as we find, the
assumptions to be true — may be performed ont^e for all, and the results
held ready to be employed as the occasions turn up for use. We thus do
all beforehand that can be so- done, and leave the least possible work to be
performed when cases arise and press for a decision. This inquiry into the
inferences which can be drawn from assumptions, is what properly consti-
tutes Demonstrative Science.
It is of course quite as practicable to arrive at new conclusions from:
facts assumed, as from facts observed ; from fictitious, as from real, induc-
tions. Deduction, as we have seen, consists of a series of inferences in this
form — a is a mark of b, b of c, c of d, therefore a is a mark of d, which
last may be a truth inaccessible to direct observation. In like manner it
is allowable to say, suppose that a were a mark of h, b of c, and c of d, a
would be a mark of d, which last conclusion was not thought of by those
-who laid down the premises. A system of propositions as complicated as
geometry might be deduced from assumptions which are false; as was
done by Ptolemy, Descartes, and others, in their attempts to explain syn-
thetically the phenomena of the solar system on the supposition that the-
apparent motions of the heavenly bodies were the real motions, or were
produced in some way more or less different from the true one. Some-
times the same thing is knowingly done, for the purpose of showing the-
falsity of the assumption ; which is called a reductio ad absurdijim. In.
such cases, the reasoning is as follows : a is a mark of b, and b oi c; now
if c were also a mark of d, a would be a mark of d; but d is known to be-
a mark of the absence of a ; consequently a would be a mark of its owa.
absence, which is a contradiction ; therefore c is not a mark of d.
THEORIES CONCERNING AXIOMS. 19S
§ 5. It has even been held by some writers, that all ratiocination rests
in the last resort on a reductio ad ahsurdum; since the way to enforce as-
sent to it, in case of obscurity, would be to show that if the conclusion be
denied we must deny some one at least of the premises, which, as they are
all supposed true, would be a contradiction. And in accordance with this,
many have thought that the peculiar nature of the evidence of ratiocina-
tion consisted in the impossibility of admitting the premises and rejecting
the conclusion without a contradiction in terms. This theory, however, is
inadmissible as an explanation of the grounds on which ratiocination itself
rests. If any one denies the conclusion notwithstanding his admission of
the premises, he is not involved in any direct and express contradiction un-
til he is compelled to deny some premise; and he can only be forced to do
this by a reductio ad absurdum, that is, by another ratiocination : now, if
he denies the validity of the reasoning process itself, he can no more be
forced to assent to the second syllogism than to the first. In truth, there-
fore, no one is ever forced to a contradiction in terms : he can only be
forced to a contradiction (or rather an infringement) of the fundamental
maxim of ratiocination, namely, that whatever has a mark, has what it is
a mark of; or (in the case of universal propositions), that whatever "is a
mark of any thing, is a mark of whatever else that thing is a mark of. For
in the case of every correct argument, as soon as thrown into the syllogis-
tic form, it is evident without the aid of any other syllogism, that he who,
admitting the premises, fails to draw the conclusion, does not conform to
the above axiom.
We have now proceeded as far in the theory of Deduction as we can ad-
vance in the present stage of our inquiry. Any further insight into the
subject requires that the foundation shall have been laid of the philosophic
theory of Induction itself ; in which theory that of Deduction, as a mode
of Induction, which we have now shown it to be, will assume spontaneous-
ly the place which belongs to it, and will receive its share of whatever light
may be thrown upon the great intellectual operation of which it forms so
important a part.
CHAPTER VII.
EXAMINATION OF SOME OPINIONS OPPOSED TO THE PRECEDING DOCTRINES.
§ 1. Polemical discussion is foreign to the plan of this work. But an
opinion which stands in need of much illustration, can often receive it most
effectually, and least tediously, in the form of a defense against objections.
And on subjects concerning which speculative minds ai-e still divided, a
writer does but half his duty by stating his own doctrine, if he does not
also examine, and to the best of his ability judge, those of other thinkers.^
In the dissertation which Mr. Herbert Spencer has prefixed to his, in
many respects, highly philosophical treatise on the Mind,* he criticises some
of the doctrines of the two preceding chapters, and propounds a theory of
his own on the subject of first principles. Mr. Spencer agrees with me in
considering axioms to be " simply our earliest inductions from experience."
But he differs from me " widely as to the worth of the test of inconceiva-
* Principles of Psychology.
13
194 REASONING.
thleness." He thinks that it is the ultimate test of all beliefs. He arrives
at this conclusion by two steps. First, we never can have any stronger
ground for believing any thing, than that the belief of it " invariably exists."
Whenever any fact or proposition is invariably believed ; that is, if I un-
derstand Mr. Spencer rightly, believed by all persons, and by one's self at all
times ; it is entitled to be received as one of the primitive truths, or orig-
/inal premises of our knowledge. Secondly, the criterion by which we de-
/ <!ide whether any thing is invariably believed to be true, is our inability to
[ /'conceive it as false. " The inconceivability of its negation is the test by
(which we ascertain whether a given belief invariably exists or not." " For
^r primary beliefs, the fact of invariable existence, tested by an abortive
effort to cause their non-existence, is the only i-eason assignable." He
•thinks this the sole ground of our belief in our own sensations. If I believe
.that I feel cold, I only receive this as true because I can not conceive that
U am not feeling cold. " While the proposition remains true,TEe'negation
of it remains inconceivable." There are numerous other beliefs which Mr.
Spencer considers to rest on the same basis ; being chiefly those, or a part
of those, which the metaphysicians of the Reid and Stewart school con-
sider as truths of immediate intuition. That there exists a material world ;
that this is the very world which we directly and immediately perceive,
and not merely the hidden cause of our perceptions ; that Space, Time,
Force, Extension, Figure, are not modes of our consciousness, but objective
realities ; are regarded by Mr. Spencer as truths known by the inconceiva-
bleness of their negatives. We can not, he says, by any effort, conceive
these objects of thought as mere states of our mind ; as not having an ex-
istence external to us. Their real existence is, therefore, as certain as our
sensations themselves. The truths which are the subject of direct knowl-
edge, being, according to this doctrine, known to be truths only by the in-
conceivability of their negation ; and the truths which are not the object
of direct knowledge, being known as inferences from those which are ; and
those inferences being believed to follow from the premises, only because
we can not conceive them not to follow; inconceivability is thus the ulti-
mate ground of all assured beliefs.
.Thus far, there is no very wide difference between Mr. Spencer's doctrine
and the ordinary one of philosophers of the intuitive school, from Descartes
1 to Dr. Whewell; but at this point Mr. Spencer diverges from them. For
i he does not, like them, set up the test of inconceivability as infallible. On
the contrary, he holds that it may be fallacious, not from any fault in the
i test itself, but because " men have mistaken for inconceivable things, some
j things which were not inconceivable." And he himself, in this very book,
denies not a few propositions usually regarded as among the most marked
examples of truths whose negations are inconceivable. But occasional fail-
ure, he says, is incident to all tests. If such failure vitiates " the test of in-
conceivableness," it " must similarly vitiate all tests whatever. We con-
sider an inference logically drawn from established premises to be true.
Yet in millions of cases men have been wrong in the inferences they have
thought thus drawn. Do we therefore argue that it is absurd to consider
an inference true on no other ground than that it is logically drawn from
•established premises ? No : we say that though men may have taken for
logical inferences, inferences that were not logical, there nevertheless are
logical inferences, and that we are justified in assuming the truth of what
seem to us such, until better instructed. Similarly, though men may have
thought some things inconceivable which were not so, there may still be in-
THEORIES CONCERNING AXIOMS. 195
oonceivable things ; and the inability to conceive the negation of a thing,
may still be our best warrant for believing it Though occasional-
ly it may prove an imperfect test, yet, as our most certain beliefs are capar
ble of no better, to doubt any one belief because we have no higher guar-
antee for it, is really to doubt all beliefs." Mr. Spencer's doctrine, there-
fore, does not erect the curable, but only the incurable limitations of the
human conceptive faculty, into laws of the outward universe.
§ 2. The doctrine, that " a belief which is proved by the inconceivable-
■ness of its negation to invariably exist, is true," Mr. Spencer enforces by
two arguments, one of which may be distinguished as positive, and the
•other as negative.
The positive argument is, that every such belief represents the aggregattJ
•of all past experience. " Conceding the entire truth of " the " position/
that during any phase of human progress, the ability or inability to form
-a specific conception wholly depends on the experiences men have had;
and that, by a widening of their experiences, they may, by and by, be en-
abled to conceive things before inconceivable to them, it may still be argued
that as, at any time, the best warrant men can have for a belief is the per-
fect agreement of all pre-existing experience in support of it, it follows that,
at any time, the inconceivableness of its negation is the deepest test any
belief admits of. Objective facts are ever impressing themselves upon
us; our experience is a register of these objective facts; and the incon-
oeivableness of a thing implies that it is wholly at variance with the regis- 1
ter. Even were this all, it is not clear how, if every truth is primarily in-
•ductive, any better test of truth could exist. But it must be remembered
that while many of these facts, impressing themselves upon us, are occa-
sional ; while others again are very general ; some are universal and un-
changing. These universal and unchanging facts are, by the hypothesis,
■certain to establish beliefs of which the negations are inconceivable ; while
the others are not certain to do this ; and if they do, subsequent facts will
reverse their action. Hence if, after an immense accumulation of experi-
ences, there remain beliefs of which the negations are still inconceivable,
most, if not all of them, must correspond to universal objective facts. If
there be .... certain absolute uniformities in nature ; if these uniform-
ities produce, as they must, absolute uniformities in our experience ; and <
if these absolute uniformities in our experience disable us from con- 1
ceiving the negations of them ; then answering to each absolute uniformi- i
ty in nature which we can cognize, there must exist in us a belief of which /
the negation is inconceivable, and which is absolutely true. In this wide'
range of cases subjective inconceivableness must correspond to objective"]
impossibility. Further experience will produce correspondence where ifr
may not yet exist ; and we may expect the correspondence to become ulti-
mately complete. In nearly all cases this test of inconceivableness must be
valid now " (I wish I could think we were so nearly arrived at omnis-
cience) ; " and where it is not, it still expresses the net result of our experiA
«nce up to the present time ; which is the most that any test can do." >
To this I answer, first, that it is by no means true that the inconceivabUi--
ty, by us, of the negative of a proposition proves all, or even any, " pre-exist-
ing experience " to be in favor of the affirmative. There may have been
no such pre-existing experiences, but only a mistaken supposition of expe-
rience. How did the inconceivability of antipodes prove that experience
had given any testimony against their possibility ? How did the incapaci-
r
190 KEASONING.
\ ty men felt of conceiving sunset otherwise than as a motion of the surij
; represent any " net result " of experience in support of its being the sun
and not the earth that moves ? It is not experience that is represented, it
is only a superficial semblance of experience. The only thing proved with
regard to real expei-ience, is the negative fact, that men have not had it
of the kind which would have made the inconceivable pi'oposition conceiv-
able.
I Next : Even if it were true that inconceivableness represents the net re-
sult of all past experience, why should we stop at the representative when
we can get at the thing represented ? If our incapacity to conceive the
negation of a given supposition is proof of its truth, because provuig that
our experience has hitherto been uniform in its favor, the real evidence for
the supposition is not the inconceivableness, but the uniformity of experi-
ence. Now this, which is the substantial and only proof, is directly access-
ible. We are not obliged to presume it from an incidental consequence.
If all past experience is in favor of a belief, let this be stated, and the be-
lief openly rested on that ground : after which the question arises, what
that fact may be worth as evidence of its truth ? For uniformity of expe-
rience is evidence in very different degrees : in some cases it is strong evi-
dence, in others weak, in others it scarcely amounts to evidence at all.
That all metals sink in water, was a uniform experience, from the origin
of the human race to the discovery of potassium in the present century
by Sir Humphry Davy. That all swans are white, was a uniform experi-
ence down to the discovery of Australia. In the few^^cases in which uni-
formity of experience does amount to the strongest possible proof, as with
^ such propositions as these. Two straight lines can not inclose a space. Ev-
ery event has a cause, it is not because their negations are inconceivable,,
which is not always the fact; but because the experience, which has been
thus uniform, pervades all nature. It will be shown in the following Book
that none of the conclusions either of induction or of deduction can be
considered certain, except as far as their truth is shown to be inseparably
, bound up with truths of this class.
\ I maintain then, first, that uniformity of past experience is very far from
\being universally a criterion of truth. But secondly, inconceivableness is
Still further from being a test even of that test. Uniformity of contrary
experience is only one of many causes of inconceivability. Tradition
handed down from a period of more limited knowledge, is one of the com-
monest. The mere familiarity of one mode of production of a phenome-
non often suffices to make every other mode appear inconceivable. What-
ever connects two ideas by a strong association may, and continually does,,
render their separation in thought impossible ; as Mr. Spencer, in other
parts of his speculations, frequently recognizes. It was not for want of ex-
perience that the Cartesians were unable to conceive that one body could
produce motion in another without contact. They had as much experience
of other modes of producing motion as they had of that mode. The plan-
ets had revolved, and heavy bodies had fallen, every hour of their lives.
But they fancied these phenomena to be produced by a hidden machinery
, which they did not see, because without it they were unable to conceive
\ what they did see. The inconceivableness, instead of representing their
1 experience, dominated and overrode their experience. Without dwelling
further on what I have termed the positive argument of Mr. Spencer in
support of his criterion of truth, I pass to his negative argument, on which.
he lays more stress.
THEORIES CONCERNING AXIOMS. 197
§ 3. The negative argument is, that, whether inconceivability be good j
evidence or bad, no stronger evidence is to be obtained. That what is in- /
conceivable can not be true, is postulated in every act of thought. It is i
the foundation of all our original premises. Still more it is assumed in all |
conclusions from those premises. The invariability of belief, tested by the
inconceivableness of its negation, " is our sole warrant for eveiy demon-
stration. Logic is simply a systematization of the process by which we in-
directly obtain this warrant for beliefs that do not directly possess it. To
gain the strongest conviction possible respecting any complex fact, we ei-
ther analytically descend from it by successive steps, each of which we un-
consciously test by the inconceivableness of its negation, until we reach
6ome axiom or truth which we have similarly tested; or we synthetically
ascend from such axiom or truth by such steps. In either case we connect
some isolated belief, with a belief which invariably exists, by a series of
intermediate beliefs which invariably exist." The following passage suras
■up the theory : " "When we perceive that the negation of the belief is in-
conceivable, we have all possible warrant for asserting the invariability of
its existence : and in asserting this, we express alike our logical justifica- I
tion of it, and the inexorable necessity we are under of holding it '
We have seen that this is the assumption on which every conclusion what- >
€ver ultimately rests. We have no other guarantee for the reality of con- 1
sciousness, of sensations, of personal existence ; we have no other guaran-
tee for any axiom ; we have no other guarantee for any step in a demon-
stration. Hence, as being taken for granted in every act of the under-
standing, it must be regarded as the Universal Postulate." But as this
postulate, which we are under an " inexorable necessity " of holding true, is
sometimes false; as "beliefs that once were shown by the inconceivable-
ness of their negations to invariably exist, have since been found untrue,"
and as " beliefs that now possess this character may some day share the
same fate ;" the canon of belief laid down by Mr. Spencer is, that " the
most certain conclusion " is that " which involves the postulate the fewest \
times." Reasoning, therefore, never ought to prevail against one of the '• '■
immediate beliefs (the belief in Matter, in the outward reality of Extension, i
Space, and the like), because each of these involves the postulate only once ;
while an argument, besides involving it in the premises, involves it again in •
every step of the ratiocination, no one of the successive acts of inference |
being recognized as valid except because we can not conceive the conclu-
sion not to follow from the premises.
It will be convenient to take the last part of this argument first. In ev-
ery reas"oning, according to Mr. Spencer, the assumption of the postulate is
renewed at every step. At each inference we judge that the conclusion
follows from the premises, our sole warrant for that judgment being that
we can not conceive it not to follow. Consequently if the postulate is fal-
lible, the conclusions of reasoning are more vitiated by that uncertainty
tlian direct intuitions ; and the disproportion is greater, the more numerous
the steps of the argument.
To test this doctrine, let us first suppose an argument consisting only of
a single step, which would be represented by one syllogism. This argu-
ment does rest on an assumption, and we have seen in the prepeding chap-
ters what the assumption is. It is, that whatever has a mark, has what it^
is a mark of. The evidence of this axiom I shall not consider at present ;*
* Mr. Spencer is mistaken in supposing me to claim any peculiar " necessity " for this ax- -
iom as compared with others. I have corrected the expressions which led him into that mis-
apprehension of my meaning.
198 REASONING.
let us suppose it (with Mr. Spencei-) to be the inoonceivableness of its re-
verse.
Let us now add a second step to the argument: we require, what? An-
other assumption ? No : the same assumption a second time ; and so ovt'
to a third, and a fourth. I coniess I do not see how, on Mr. Spencer's own
principles, the repetition of the assumption at all weakens the force of the^
argument. If it were necessary the second time to assume some other ax-
iom, the argument would no doubt be weakened, since it would be necessary
to its validity that both axioms should be true, and it might happen that
one was true and not the other: making two chances of error instead of
one. But since it is the same axiom, if it is true once it is true every
time ; and if the argument, being of a hundred links, assumed the axiom a
hundred times, these hundred assumptions would make but one chance of
error among them all. It is satisfactory that we are not obliged to sup-
pose the deductions of pure mathematics to be among the most uncertaitt
of argumentative processes, which on Mr. Spencer's theory they could
hardly fail to be, since they are the longest. But the number of steps inr
\ an argument does not subtract from its reliableness, if no new premises, oi
an uncertain character, are taken up by the way.*
To speak next of the premises. Our assurance of their truth, whether
they be generalities or individual facts, is grounded, in Mr. Spencer's opin-
ion, on the inconceivableness of their being false. It is necessary to advert
to a double meaning of the word inconceivable, which Mr. Spencer is aware
* Mr. Spencer, in recently returning to the subject (Principles of Psychology, new edition,,
chap. xii. : " The Test of Eelative Validity "),. makes two answers to the preceding remarks..
One is :
"Were an argument formed by repeating the same proposition over and over again, it
would be true that any intrinsic fallibility of the postulate would not make the conclusioi»
more untrustworthy than the first step. But an argument consists of unlike propositions.
Now, since Mr. Mill's criticism on the Universal Postulate is that in some cases, which he
■ names, it has proved to be an untrustworthy test ; it follows that in any argument consisting;
of heterogeneous propositions, there is a risk, increasing as the number of propositions in-
creases, that some one of them belongs to this class of cases, and is wrongly accepted because'
of the inconceivableness of its negation."
No doubt ; but this supposes new premises to be taken in. The point we are discussing is-
■the fallibility not of the premises, but of the reasoning, as distinguished from the premises.
Now the validity of the reasoning depends always upon the same axiom, repeated (in thought)
"over and over again," viz., that whatever has a mark, has what it is a mark of. Even,
therefore, on the assumption that this axiom rests ultimately on the Universal Postulate, and
that, the Postulate not being wholly trustworthy, the axiom may be one of the cases of its
failure ; all the risk there is of this is incurred at the very first step of the reasoning, and isi
not added to, however long may be the series of subsequent steps.
A I am here arguing, of course, from Mr. Spencer's point of view. Erom my own the case is-
/ still clearer ; for, in my view, the truth that whatever has a mark has what it is a mark of, is-
I wholly trustworthy, and derives none of its evidence from so very untrustworthy a test as the
inconceivability of the negative.
y , ■ Mr. Spencer's second answer is valid up to a certain point ; it is, that every prolongation of
^he process involves additional chances of casual error, from carelessness in the reasoning
/operation. This is an important consideration in the private speculations of an individual
/reasoner; and even with respect to mankind at large, it must be admitted that, though mere
/ oversights in the syllogistic process, like errors of addition in an account, are special to th&
/ individual, and seldom escape detection, confusion of thought produced (for example) by am-
( biguous terms has led whole nations or ages to accept fallacious reasoning as valid. But this-
very fact points^o causes of error so much more dangerous than the mere length of the proc-
ess, as quite to vitiate the doctrine that the "test of the relative validities of conflicting con-
clusions" is the number of times the fundamental postulate is involved. On the contrary, the.
subjects on which the trains of reasoning are longest, and the assumption, therefore, oftenest
repeated, are in general those which are best fortified against the really formidable causes of
fallacy ; as in the example :ilready given of mathematics.
THEORIES CONCERNING AXIOMS. 19»
of, and would sincerely disclaim founding an argument upon, but from
which his case derives no little advantage notwithstanding. By inconceiv- \
ableness is sometimes meant, inability to form or get rid of an idea ; some- j
times, inability to form or get rid of a belief. The former meaning is the '
most conformable to the analogy of language; for a conception always
means an idea, and never a belief. The wrong meaning of " inconceivable "
is, however, fully as frequent in philosophical discussion as the right mean-
ing, and the intuitive school of metaphysicians could not well do without
either. To illustrate the difference, we will take two contrasted examples.
The early physical speculators considered antipodes incredible, because in-
conceivable. But antipodes were not inconceivable in the primitive sense
of the word. An idea of them could be formed without difficulty : they
could be completely pictured to the mental eye. What was difficult, and,,
as it then seemed, impossible, was to apprehend them as believable. The
idea could be put together, of men sticking on by their feet to the under
side of the earth ; but the belief would follow, that they must fall off. An-\
tipodes were not unimaginable, but they were unbelievable; )
On the other hand, when I endeavor to conceive an end to extension, the-
two ideas refuse to come together. When I attempt to form a conception
of the last point of space, I can not help figuring to myself a vast space
beyond that last point. The combination is, under the conditions of our -
experience, unimaginable. This double meaning of inconceivable it is very j
important to bear in mind, for the argument from inconceivableness almost
always turns on the alternate substitution of each of those meanings for
the other.
In which of these two senses does Mr. Spencer employ the term, when
he makes it a test of the truth of a proposition that its negation is incon-
ceivable ? Until Mr. Spencer expressly stated the contrary, I inferred from
the course of his argument, that he meant unbelievable. He has, however,,
in a paper published in the fifth number of the Fortnightly Meview, dis-
claimed this meaning, and declared that by an inconceivable proposition
he means, now and always, " one of which the terms can not, by any effort,
be brought before consciousness in that relation which the proposition as-
serts between them — a proposition. of which the subject and predicate offer
an insurmountable resistance to union in thought." We now, therefore,,
know positively that Mr. Spencer always endeavors to use the word incon-
ceivable in this, its proper, sense : but it may yet be questioned whether
his endeavor is always successful ; whether the other, and popular use of
the word, does not sometimes creep in with its associations, and prevent,
him from maintaining a clear separation between the two. When, for
example, he says, that when I feel cold, I can not conceive that I am not
feeling cold, this expression can not be translated into "I can not con-
ceive myself not feeling cold," for it is evident that I can: the word ,^
conceive, therefore, is here used to express the recognition of a matter of ',
fact — the perception of truth or falsehood ; which I apprehend to be ex-
actly the meaning of an act of belief, as distinguished from simple con-
ception. Again, Mr. Spencer calls the attempt to conceive something
which is inconceivable " an abortive effort to cause the non-existence,'"
not of a conception or mental representation, but of a belief. There is.
need, therefore, to revise a considerable part of Mr. Spencer's language, if
it is to be kept always consistent with his definition of inconceivability.
But in truth the point is of little importance ; since inconceivability, in
Mr. Spencer's theory, is only a test of truth, inasmuch as it is a test of
200 REASONING.
believability. The ihconceivableness of a supposition is the extreme case
of its unbelievability. This is the very foundation of Mr. Spencer's doc-
trine. The invariability of the belief is with him the real guarantee.
The attempt to conceive the negative is made in order to test the inevita-
bleness of the belief. It should be called, an attempt to believe the nega-
tive. When Mr. Spencer says that while looking at the sun a man can not
oonceive that he is looking into darkness, he should have said that a man
<jan not believe that he is doing so. For it is surely possible, in broad day-
light, to imagine one's self looking into darkness.* As Mr. Spencer him-
self says, speaking of the belief of our own existence, " That he might not
I exist, he can conceive well enough ; but that he does not exist, he finds it
impossible to conceive," i. e., to believe. So that the statement resolves it-
.self into this : That I exist, and that I have sensations, I believe, because I
•can not believe otherwise. And in this case every one will admit that the
impossibility is real. Any one's present sensations, or other states of sub-
jective consciousness, that one person inevitably believes. They ai-e facts
known ^er se: it is impossible to ascend beyond them. Their negative is
really unbelievable, and therefore there is never any question about believ-
ing it. Mr. Spencer's theory is not needed for these truths.
But according to Mr. Spencer there are other beliefs, relating to other
things than our own subjective feelings, for which we have the same guar-
• antee — which are, in a similar manner, invariable and necessary. With re-
/eai-d to these other beliefs, they can not be necessary, since they do not al-
ways exist. There have been, and are, many persons who do not believe
the reality of an external world, still less the reality of extension and figure
as the forms of that external world ; who do not believe that space and time
/ have an existence independent of the mind — nor any other of Mr. Spencer's
\ / objective intuitions. The negations of these alleged invariable beliefs are
'J- not unbelievable, for they are believed. It may be maintained, without ob-
vious error, that we can not imagine tangible objects as mere states of our
own and other people's consciousness; that the perception of them irresist-
ibly suggests to us the idea of something external to ourselves : and I am
not in a condition to say that this is not the fact (though I do not think
any one is entitled to afiirm it of any person besides himself). But many
thinkers have believed, whether they could conceive it or not, that what we
represent to ourselves as material objects, are mere modifications of con-
sciousness ; complex feelings of touch and of muscular action. Mr. Spencer
may think the inference correct from the unimaginable to the unbelievable,
because he holds that belief itself is but the persistence of an idea, and that
what we can succeed in imagining we can not at the moment help appre-
hending as believable. But of what consequence is it what we apprehend
at the mome'nt, if the moment is in contradiction to the permanent state of
our mind ? A person who has been frightened when an infant by stories
of ghosts, though he disbelieves them in after years (and perhaps never be-
lieved them), may be unable all his life to be in a dark place, in circum-
stances stimulating to the imagination, without mental discomposure. The
idea of ghosts, with all its attendant terrors, is irresistibly called up in his
mind by the outward circumstances. ' Mr. Spencer may say, that while he
* Mr. Spencer makes a distinction between conceiving myself looking into darkness, and
conceiving that I am then and there looking into darkness. To me it seems that this change
of the expression to the form / am, just marks the transition from conception to belief, and
that the phrase " to conceive that / am," or "that any thing is," is not consistent with using
the word conceive in its rigorous sense.
THEORIES CONCEENING AXIOMS. 201
is under the influence of this terror he does not disbelieve in ghosts, but
has a temporary and uncontrollable belief in them. Be it so ; but allowing
it to be so, which would it be truest to say of this man on the whole — that
he believes in ghosts, or that he does not believe in them ? Assuredly that
he does not believe in them. The case is similar with those who disbelieve
a material world. Though they can not get rid of the idea ; though while
looking at a solid object they can not help having the conception, and there-
fore, according to Mr. Spencer's metaphysics, the momentary belief, of its-
externality ; even at that moment they would sincerely deny holding that
belief : and it would be incorrect to call them other than disbelievers of the
doctrine. The belief therefore is not invariable; and the test of inconceiv-
ableness fails in the only cases to which there could ever be any occasion to-
apply it.
That a thing may be perfectly believable, and yet may not have become *
conceivable, and that we may habitually believe one side of an alternative,, >
and conceive only in the other, is familiarly exemplified in the state of mind
of educated persons respecting sunrise and sunset. All educated persons
either know by investigation, or believe on the authority of science, that
it is the earth and not the sun which moves : but there are probably few
who habitually conceive the phenomenon otherwise than as the ascent or
descent of the sun. Assuredly no one can do so without a prolonged trial ;,
and it is probably not easier now than in the first generation after Coper-
nicus. Mr. Spencer does not say, " In looking at sunrise it is impossible
not to conceive that it is the sun which moves, therefore this is what eveiy
body believes, and we have all the evidence for it that we can have for any
truth." Yet this would be an exact parallel to his doctrine about the belief
in matter.
The existence of matter, and other Noumena, as distinguished from the-
phenomenal world, remains a question of argument, as it was before ; and
the very general, but neither necessary nor universal, belief in them, standi
as a psychological phenomenon to be explained, either on the hypothesis of
its truth, or on some other. The belief is not a conclusive proof of its own
truth, unless there are no such things as idola tribiis^ but being a fact, it
calls on antagonists to show, from what except the real existence of the
thing believed, so general and apparently spontaneous a belief can have
originated. And its opponents have never hesitated to accept this chal-
lenge.* The amount of their success in meeting it will probably deter-
mine the ultimate verdict of philosophers on the question.
§ 4. In the revision, or rather reconstruction, of his "Principles of Psy-
chology," as one of the stages or platforms in the imposing structure of
his System of Philosophy, Mr. Spencer has resumed what he justly termsf
the " amicable controversy that has been long pending between us ;" ex-
pressing at the same time a regret, which I cordially share, that " this
lengthened exposition of a single point of difference, unaccompanied by
an exposition of the numerous points of concurrence, unavoidably produces
an appearance of dissent very far greater than that which exists." I be-
lieve, with Mr. Spencer, that the difference between us, if measured by our
conclusions, is " superficial rather than substantial ;" and the value I attach
to so great an amount of agreement, in the field of analytic psychology,.
* I have myself accepted the contest, and fought it oat on this battle-ground, in the eleventh,
chapter of An Examination of Sir William Hamilton's Philosophy.
t Chap. xi.
■202 REASONING.
-with a thinker of his force and depth, is such as I can hardly overstate.
But I also agree with him that the difference which exists in our premises
is one of " profound importance, philosophically considered ;" and not to
be dismissed while any part of the case of either of us has not been fully
■examined and discussed.
In his present statement of the Universal Postulate, Mr. Spencer has ex-
changed his former expression, " beliefs which invariably exist," for the
following : " cognitions of which the predicates invariably exist along with
their subjects." And he says that " an abortive effort to conceive the ne-
gation of a proposition, shows that the cognition expressed is one of which
the predicate invariably exists along with its subject ; and the discovery
that the predicate invariably exists along with its subject, is the discovery
that this cognition is one we are compelled to accept." Both these prem-
ises of Mr. Spencer's syllogism I am able to assent to, but in different senses
■of the middle term. If the invariable existence of the predicate along
with its subject, is to be understood in the most obvious meaning, as an
existence in actual Nature, or in other words, in our objective, or sensa-
tional, experience, I of course admit that this, once ascertained, compels us
to accept the proposition : but then I do not admit that the failure of an at-
tempt to conceive the negative, proves the predicate to be always co-exist-
■ent with the subject in actual Nature. If, on the other hand (which I believe
to be Mr. Spencer's meaning) the invariable existence of the predicate along
■with the subject is to be understood only of our conceptive faculty, i. e.,
that the one is inseparable from the other in our thoughts ; then, indeed,
the inability to separate the two ideas proves their inseparable conjunc-
tion, here and now, in the mind which has failed in the attempt ; but this
inseparability in thought does not prove a corresponding inseparability in
fact ; nor even in the thoughts of other people, or of the same person in a
possible future.
" That some propositions have been wrongly accepted as true, because
their negations were supposed inconceivable when they were not," does
not, in Mr. Spencer's^ opinion, " disprove the validity of the test ;" not only
because any test whatever "is liable to yield untrue results, either.from in-
capacity or from carelessness in those who use it," but because the propo-
sitions in question " were complex propositions, not to be established by a
test applicable to propositions no further decomposable." " A test legiti-
mately applicable to a simple proposition, the subject and predicate of which
are in direct relation, can not be legitimately applied to a complex proposi-
tion, the subject and predicate of which are indirectly related through the
, many simple propositions implied." " That things which are equal to the
same thing are equal to one another, is a fact which can be known by di-
rect comparison of actual or ideal relations But that the square of
Ithe hypothenuse of a right-angled triangle equals the sum of the squares
of the other two sides, can not be known immediately by comparison of
two states of consciousness : here the truth can be reached only mediately,
through a sei-ies of pimple judgments respecting the likenesses or unlike-
nesses of certam relations?' Moreover, even when the proposition admits
of being tested by immediate consciousness, people often neglect to do it.
A school-boy, in adding up a column of figures, will say " 35 and 9 are 46,"
■though this is contrary to the verdict which consciousness gives when 35
and 9 are really called up before it ; but this is not done. And not only
school-boys, but men and thinkers, do not always " distinctly translate into
their equivalent states of consciousness the words they use."
THEORIES CONCERNING AXIOMS. 203
It is but just to give Mr. Spencer's doctrine the benefit of the limitation
le claims — viz., that it is only applicable to propositions which are assented "
to on simple inspection, without any intervening media of proof. But this
limitation does not exclude some of the most marked instances of proposi-
tions now known to be false or groundless, but whose negative was once
iound inconceivable : such as, that in sunrise and sunset it is the sun which
moves ; that gravitation may exist without an intervening medium ; and
•even the case of antipodes. The distinction drawn by Mr. Spencer is real ;,
but, in the case of the propositions classed by him as complex, conscious-
ness, until the media of proof are supplied, gives no verdict at all: it nei-
ther declares the equality of the square of the hypothenuse with the sum
■of the squares of the sides to be inconceivable, nor their inequality to be
inconceivable. But in all the three cases which I have just cit^d, the in-^'
conceivability seems to be apprehended directly ; no train of argument was .
needed, as in the case of the square of the hypothenuse, to obtain the ver-
dict of consciousness on the point. Neither is any of the three a case like
that of the school-boy's mistake, in which the mind was never really brought
into contact with the proposition. They are cases in which one of two op-
posite predicates, mero adspectu, seemed to be incompatible with the sub-
ject, and the other, therefore, to be proved always to exist with it.*
As now limited by Mr. Spencer, the ultimate cognitions fit to be submit-
ted to his test are only those of so imiversal and elementary a character as
to be represented in the earliest and most unvarying experience, or appar-
ent experience, of all mankind. In such cases the inconceivability of -the
negative, if real, is accounted for by the experience : and why (I have ask-
ed) should the truth be tested by the inconceivability, when we can go fur-
ther back for proof — namely, to the experience itself ? To this Mr. Spen-
cer answers, that the experiences can not be all recalled to mind, and if r^-
-called, would be of unmanageable multitude. To test a proposition by ex-*
perience seems to him to mean that " before accepting as certain the prop-
osition that any rectilineal figure must have as many angles as it has sides,"
I have " to think of every triangle, square, pentagon, hexagon, etc., which I j
have ever seen, and to verify the asserted relation in each case." I can
only say, with surprise, that I do not understand this to be the meaning of
an appeal to experience. It is enough to know that one has been seeing 'N
the fact all one's life, and has never remarked any instance to the contrary, )
and that other people, with every opportunity of observation, unanimously/
declare the same thing. It is true, even this experience may be insufficient,
and so it might be even if I could recall to mind every instance of it ; bdt
• In one of the three cases, Mr. Spencer, to my no small surprise, thinks that the belief of
mankind "can not be rightly said to have undergone" the change I allege. Mr. Spencer
himself still thinks we are unable to conceive gravitation acting through empty space. " If
an astronomer avowed that he could conceive gravitative force as exercised through space ab-
solutely void, my private opinion would be that he mistook the nature of conception. Con-
ception implies representation. Here the elements of the representation are the two bodies
«ai an agency by which either affects the other. To conceive this agency is to represent it
in some terms derived from our experiences — that is, from our sensations. As this agency
gives us no sensations, we are obliged (if we try to conceive it) to use symbols idealized from
our sensations — imponderable units forming a medium.".
If Mr. Spencer means that the action of gravitation gives us no sensations, the assertion is
one than which I have not seen, in the writings of philosophers, many more startling. What
•other sensation do we need than the sensation of one body moving toward another? "The
elements of the representation " are not two bodies and an " agency," but two bodies and an
effect ; viz., the fact of their approaching one atiother. If we are able to conceive a vacuum,
is there any difficulty in conceiving a body falling to the earth through it ?
204 EEASONING.
its insufficiency, instead of being brought to light, is disguised, if instead of
sifting the experience itself, I appeal to a test which bears no relation to
the sufficiency of the experience, but, at the most, only to its familiarity.
These remarks do not lose their force even if we believe, with Mr. Spencer,,
that mental tendencies originally derived from experience impress them-
selves permanently on the cerebral structure and are transmitted by inher-
itance, so that modes of thinking which are acquired by the race become
innate and a priori in the individual, thus representing, in Mr. Spencer's
opinion, the experience of his progenitors, in addition to his own. All that
would follow from this is, that a conviction might be really innate, i. e., prior
to individual experience, and yet not be true, since the inherited tendency
to accept it may have been originally the result of other causes than its
truth.
Mr. Spencer would have a much stronger case, if he could really show-
that the evidence of Reasoning rests on the Postulate, or, in other words^
that we believe that a conclusion follows from pi'emises only because we
can not conceive it not to follow. But this statement seems to me to be
of the same kind as one I have previously commented on, viz., that I believe
I see light, because I can not, while the sensation remains, conceive that I
am looking into darkness. Both these statements seem to me incompatible
with the meaning (as very rightly limited by Mr. Spencer) of the verb to
conceive. To say that when I apprehend that A is B and that B is C, I
can not conceive that A is not C, is to my mind merely to say that I am
compelled to believe that A is C. If to conceive be taken in its proper
meaning, viz., to form a mental representation, I may be able to conceive A
as not being C. After assenting, with full understanding, to the Coperni-
can proof that it is the earth and not the sun that moves, I not only can
conceive, or represent to myself, sunset as a motion of the sun, but almost
every one finds this conception of sunset easier to form, than that which
they nevertheless know to be the true one.
§ 6. Sir William Hamilton holds as I do, that inconceivability is no criteri-
on of impossibility. " There is no ground for inferring a certain fact to be
impossible, merely from our inability to conceive its possibility." " Things
there are which may, nay must, be true, of which the understauding is
wholly unable to construe to itself the possibility."* Sir William Hamil-
ton is, however, a firm believer in the a priori character of many axioms,
and of the sciences deduced from them; and is so far from considering
those axioms to rest on the evidence of experience, that he declares certain
of them to be true even of Noumena — of the Unconditioned — of which it
is one of the principal aims of his philosophy to prove that the nature of
our faculties debars us from having any knowledge. The axioms to which
he attributes this exceptional emancipation from the limits which confine
all our other possibilities of knowledge ; the chinks through which, as he
represents, one ray of light finds its way to us from behind the curtain
which veils from us the mysterious world of Things in themselves— are
the two principles, which he terms, after the school-men, the Principle of
Contradiction, and the Principle of Excluded Middle : the first, that twO'
contradictory propositions can not both be true ; the second, that they can
not both be false. Armed with these logical weapons, we may boldly face
Things in themselves, and tender to them the double alternative, sure that
* Discussions, etc., 2d ed., p. 624.
TIIEOEIES CONCERNING AXIOMS. 205
they must absolutely elect one or the other side, though we may be forever
precluded from discovering which. To take his favorite example, we can
not conceive the infinite divisibility of matter, and we can not conceive a
minimum, or end to divisibility : yet one or the other must be true.
As I have hitherto said nothing of the two axioms in question, those of
Contradiction and of Excluded Middle, it is not unseasonable to consider
them here. The former asserts that an affirmative proposition and the cor-
responding negative proposition can not both be true ; which has generally
been held to be intuitively evident. Sir William Hamilton and the Ger-
mans consider it to be the statement in words of a form or law of our
thinking faculty. Other philosophers, not less deserving of consideration,
deem it to be an identical proposition ; an assertion involved in the mean-
ing of terms ; a mode of defining Negation, and the word Not.
I am able- to go one step with these last. An affirmative assertion and
its negative are not two independent assertions, connected with each other
only as mutually incompatible. That if the negative be true, the affirmative
must be false, really is a mere identical proposition ; for the negative prop-
position asserts nothing but the falsity of the affirmative, and has no other
'sense or meaning whatever. The Principium Contradictionis should there-
fore put off the ambitious phraseology which gives it the air of a funda-
mental antithesis pervading nature, and should be enunciated in the simpler
form, that the same proposition can not at the same time be false and true.
But I can go no further with the Nominalists ; for I can not look upon this \
last as a merely verbal proposition. I consider it to be, like other axioms, !
one of our first and most familiar generalizations from experience. The
original foundation of it I take to be, that Belief and Disbelief are two dif-
ferent mental states, excluding one another. This we know by the simplest
observation of our own minds. And if we carry our observation outward,
we also find that light and darkness, sound and silence, motion and quies-
cence, equality and inequality, preceding and following, succession and si-
multaneousness, any positive phenomenon whatever and its negative, are
distinct phenomena, pointedly contrasted, and the one always absent where
the other is present. I consider the maxim in question to be a generaliza-
tion from all these facts.
In like manner as the Principle of Contradiction (that one of two contra-
dictories must be false) means that an assertion can not be both true and
false, so the Principle of Excluded Middle, or that one of two contradic-
tories must be true, means that an assertion must be either true or false :
either the affirmative is true, or otherwise the negative is true, which means
that the affirmative is false. I can not help thinking this principle a sur-
prising specimen of a so-called necessity of Thought, since it is not even
true, unless with a large qualification. A proposition must be either true
or false, provided that the predicate be one which can in any intelligible
sense be attributed to the subject; (and as this is always assumed to be the
case in treatises on logic, the axiom is always laid down there as of absolute
truth). "Abracadabra is a second intention" is neither true nor false. Be-
tween the true and the false there is a third possibility, the Unmeaning t--
and this alternative is fatal to Sir William Hamilton's extension of the max-
im to Noumena. That Matter must either have a minimum of divisibility
or be infinitely divisible, is more than we can ever know. For in the first
place. Matter, in any other than the phenomenal sense of the term, may not
exist : and it will scarcely be said that a nonentity must be either infinite-
ly or finitely divisible. In the second place, though matter, considered as
206 EEASONING.
thii occult cause of our sensations, do really exist, yet what we call divisi.
bility may be an attribute only of our sensations of sight and touch, and
not of their uncognizable cause. Divisibility may not be predicable at all,
in any intelligible sense, of Things in themselves, nor therefore of Matter
in itself ; and the assumed necessity of being either infinitely or finitely di-
■- visible, may be an inapplicable alternative.
On this question I am happy to have the full concurrence of Mr. Herbert
Spencer, from whose paper in the FortnighUy Review I extract the follow-
ing passage. The germ of an idea identical with that of Mr. Spencer may
be found in the present chapter, on a preceding page ; but in Mr. Spencer
it is not an undeveloped thought, but a philosophical theory.
" When remembering a certain thing as in a certain place, the place and
the thing are mentally represented together ; while to think of the non-ex-
istence of the thing in that place implies a consciousness in which the place
is represented, but not the thing. Similarly, if instead of thinking of an
object as colorless, we think of its having color, the change consists in the
addition to the concept of an element that was before absent from it — the
object can not be thought of first as red and then as not red, without one,
component of the thought being totally expelled from the mind by another.
The law of the Excluded Middle, then, is simply a generalization of the uni-
versal experience that some mental states are directly destructive of other
states. It formulates a certain absolutely constant law, that the appearance
of any positive mode of consciousness can not occur without excluding a
correlative negative mode ; and that the negative mode can not occur with-
out excluding the correlative positive mode : the antithesis of positive and
negative being, indeed, merely an expression of this experience. Hence it
follows that if consciousness is not in one of the two modes it must be in
the other."*
I must here close this supplementary chapter, and with it the Second
Book. The theory of Induction, in the most comprehensive sense of the
term, will form the subject of the Third.
* Professor Bain {Logic, i., 16) identifies the Principle of Contradiction with his Law of
Relativity, viz., that "every thing that can be thought of, every affirmation that can be made,
has an opposite or counter notion or affirmation ;" a proposition which is one of the general
results of the whole body of human experience. For further considerations respecting the
axioms of Contradiction and Excluded Middle, see the twenty-first chapter of An Examina-
tion of Sir William Hamilton's Philosophy,
BOOK III.
OP INDUCTION.
" According to the doctrine now stated, the highest, or rather the only proper object of
physics, is to ascertain those established conjunctions of successive events, which constitute
the order of the universe ; to record the phenomena which it exhibits to our observations, or
which it discloses to our experiments ; and to refer these phenomena to their general laws."
— D. Stevfakt, Elements of' the Philosophy of the Human Mind, vol. ii., chap, iv., sect. 1.
"In such cases the inductive and deductive methods of inquiry may be said to go hand in
hand, the one verifying the conclusions deduced by the other ; and the combination of experi-
ment and theory, which may thus be brought to bear in such cases, forms an engine of dis-
covery infinitely more powerful than either taken separately. This state of any department
of science is perhaps of all others the most interesting, and that which promises the most to
research." — Sir J. Hebschel, Discourse on the Study of Natural Philosophy.
CHAPTER I.
PKELIMINAET OBSBEVATIONS ON INDUCTION IN GENERAL.
§ 1. The portion of the present inquiry upon which we are now about
to enter, may be considered as the principal, both from its surpassing in
intricacy all the other branches, and because it relates to a process which
has been shown in the preceding Book to be that in which the investiga-
tion of nature essentially consists. We have found that all Inference, con-
sequently all Proof, and all discovery of truths not self-evident, consists of
inductions, and the interpretation of inductions : that all our knowledge,
not intuitive, comes to us exclusively from that source. What Induction
is, therefore, and what conditions render it legitimate, can not but be deem-
ed the main question of the science of logic — the question which includes
all others. It is, however, one which professed writers on logic have al-
most entirely passed over. The generalities of the subject have not been
altogether neglected by metaphysicians ; but, for want of sufficient ac-
quaintance with the processes by which science has actually succeeded in
establishing general truths, their analysis of the inductive operation, even
when unexceptionable as to correctness, has not been specific enough to be
made the foundation of practical rules, which might be for induction itself
what the rules of the syllogism are for the interpretation of induction :
while those by whom physical science has been carried to its present state
of improvement — and who, to arrive at a complete theory of the process,
needed only to generalize, and adapt to all varieties of problems, the meth-
ods which they themselves employed in their habitual pursuits — never un-
til very lately made any serious attempt to philosophize on the subject, nor
regarded the mode in which they arrived at their conclusions as deserving
of study, independently of the conclusions themselves.
208 INDUCTION.
§ 2. For the purposes of the present inquiry, Induction may be defined,
the bperation of discovering and proving general pi-opositions. It is true
that (as already shown) the process of indirectly ascertaining individual
facts, is as truly inductive as that by which we establish general truths.
But it is not a different kind of induction ; it is a form of the very same
process : since, on the one hand, generals are but collections of particulars,
definite in kind but indefinite in number ; and on the other hand, whenever
the evidence which we derive from observation of known cases justifies ua
in drawing an inference respecting even one unknown case, we should on
the same evidence be justified in drawing a similar inference with respect
to a whole class of cases. The inference either does not hold at all, or it
holds in all cases of a certain description ; in all cases which, in certain de-
finable respects, resemble those we have observed.
If these remarks are just ; if the principles and rules of inference are the
same whether we infer general propositions or individual facts ; it follows
that a complete logic of the sciences would be also a complete logic of prac-
tical business and common life. Since there is no case of legitimate infer-
ence from experience, in which the conclusion may not legitimately be a
general proposition ; an analysis of the process by which general truths are
arrived at, is virtually an analysis of all induction whatever. Whether we
are inquiring into a scientific pi-inciple or into an individual fact, and wheth-
er we proceed by experiment or by ratiocination, every step in the train of
inferences is essentially inductive, and the legitimacy of the induction de-
pends in both cases on the same conditions.
True it is that in the case of the practical inquirer, who is endeavoring
to ascertain facts not for the purposes of science but for those of business,
such, for instance,as the advocate or the judge, the chief diificulty is one in
which the principles of induction will afford him no assistance. It lies not
in making his inductions, but in the selection of them ; in choosing froin
among all general propositions ascertained to be true, those which furnish
marks by which he may trace whether the given subject possesses or not
the predicate in question. In arguing a doubtful, question of fact before
a jury, the general propositions or principles to which the advocate ap-
peals are mostly, in themselves, sufficiently trite, and assented to as soon as
stated : his skill lies in bringing his case under those propositions or princi-
ples ; in calling to mind such of the known or received maxims of probabil-
ity as admit of application to the case in hand, and selecting from among
them those best adapted to his object. Success is here dependent on nat-
tiral or acquired sagacity, aided by knowledge of the particular subject, and
of subjects allied with it. Invention, though it can be cultivated, can not
be reduced to rule ; there is no science which will enable a man to bethink
himself of that which will suit his purpose.
But when he has thought of something, science can tell him whether
that which he has thought of will suit his purpose or not. The inquirer
or arguer must be guided by his own knowledge and sagacity in the choice
of the inductions out of which he will construct his argument. But the
validity of the argument when constructed, depends on principles, and must
be tried by tests which are the same for all descriptions of inquiries,
whether the result be to give A an estate, or to enrich science with a new
general truth. In the one case and in the other, the senses, or testimony,
must decide on the individual facts ; the rules of the syllogism will deter-
mine whether, those facts being supposed correct, the case really falls with-,
in the formulae of the different inductions under which it has been succes-
INDUCTION IN GENERAL. 209
sively brought; and. finally, the legitimacy of -tbe^inductidns 'tliemselvea
must be decided by other rules, and these it is now our purpose to investi-
gate. If this third part of the operation be, in many of the questions of
practical life, not the most, but the least arduous portion of it, we have
seen that this is also the case in some great departments of the field of sci-
ence; in all those which are principally deductive, and most of all in math-
ematics ; where the inductions themselves are few in number, and so obvi-
ous and elementary that they seem to stand in no need of the evidence of
sxperience, while to combine them so as to prove a given theorem or solve
a problem, may call for the utmost powers of invention and contrivance
with which our species is gifted.
If the identity of the logical processes which prove particular facts and
those which establish general scientific truths, required any additional con-
firmation, it would be sufficient to consider that in many branches of sci-
€nce, single facts have to be proved, as well as principles ; facts as com-
pletely individual as any that are debated in a court of justice; but which
are proved in the same manner as the other truths of the science, and with-
out disturbing in any degree the homogeneity of its method. A remark-
able example of this is afforded by astronomy. The individual facts on
which that science grounds its most important deductions, such facts as
the magnitudes of the bodies of the solar system, their distances from one
another, the figure of the earth, and its rotation, are scarcely any of them
accessible to our means of direct observation : they are proved indirectly,
by the aid of inductions founded on other facts which we can more easily
reach. For example, the distance of the moon from the earth was deter-
mined by a very circuitous process. The share which dii-ect observation
had in the work consisted in ascertaining, at one and the same instant, the
zenith distances of. the moon, as seen from two points very remote from
one another on the earth's surface. The ascertainment of these angular
distances ascertained their supplements ; and since the angle at the earth's
centre subtended by the distance between the two places of observation
was dedncible by spherical trigonometry from the latitude and longi-
tude of those places, the angle at the moon subtended by the same line
became the fourth angle of a quadrilateral of which the other three
angles were known. The four angles being thus ascertained, and two
sides of the quadrilateral being radii of the earth; the two remaining
sides and the diagonal, or, in other words, the moon's distance from the
two places of observation and from the centre of the earth, could be as-
certained, at least in terms of the earth's radius, from elementary theo-
rems of geometry. At each step in this demonstration a new induction
is taken in, represented in the aggregate of its results by a general propo-
sition.
Not only is the process by which an individual astronomical fact was
thus ascertained, exactly similar to those by which the same science estab-
lishes its general truths, but also (as we have shown to be the case in all
legitimate reasoning) a general proposition might have been concluded in-
stead of a single fact. In strictness, indeed, the result of the reasoning is
a general proposition ; a theorem respecting the distance, not of the moon
in particular, but of any inaccessible object ; showing in what relation that
distance stands to certain other quantities. And although the moon is al-
most the only heavenly body the distance of which from the earth can real-
ly be thus ascertained, this is merely owing to the accidental circumstances
of the other heavenly bodies, which render them incapable of affording such
14
210 INDUCTION.
data as the application of the theorem requires ; for the theorem itself is.
as true of them as it is of the moon.*
We shall fall into no error, then, if in treating of Induction, we limit our
attention to the establishment of general propositions. The principles and
rules of Induction as directed to this end, are the principles and rules of
all Induction ; and the logic of Science is the universal Logic, applicable to
all inquiries in which man can engage.
CHAPTER II.
OF INDUCTIONS IMPEOPEELT SO CALLED.
§ 1. Induction, then, is that operation of the mind, by which we infer
that what we know to be true in a particular case or cases, will be true in
all cases which resemble the former in certain assignable respects. In other
words. Induction is the process by which we conclude that what is true of
certain individuals of a class is true of the whole class, or that what is true
at certain times will be true in similar circumstances at all times.
This definition excludes from the meaning of the term Induction, various
logical operations, to which it is not unusual to apply that name.
Induction, as above defined, is a process of inference ; it proceeds from
the known to the unknown ; and any operation involving no inference, any
process in which what seems the conclusion is no wider than the premises
from which it is drawn, does not fall within the meaning of the term. Yet
* Dr. Whewell thinks it improper to apply the term Induction to any operation not termi-
nating in the establishment of a general truth. Induction, he says (Philosophy of Discovery,
p. 245), "is not the same thing as experience and observation. Induction is experience or
observation consciously loolced at in a general form. This consciousness and generality are
necessary parts of that knowledge which is science." And he objects (p. 241) to the mode in
which the word Induction is employed in this work, as an undue extension of that term "not
only to the cases in which the general induction is consciously applied to a particular in-
stance, but to the cases in which the particular instance is dealt with by means of experience
in that rude sense in which experience can be asserted of brutes, and in which of course w&
can in no way imagine that the law is possessed or understood as a, general proposition."
This use of the term he deems a ' ' confusion of knowledge with practical tendencies. "
I disclaim, as strongly as Dr. Whewell can do, the application of such terms as induction,,
inference, or reasoning, to operations performed by mere instinct, that is, from an animal im-
pulse, without the exertion of any intelligence. But I perceive no ground for confining the
use of those terms to cases in which the inference is drawn in the forms and with the precau-
tions required by scientific propriety. To the idea of Science, an express recognition and
distinct apprehension of general laws as such, is essential : but nine-tenths of the conclusions
drawn from experience in the course of practical life, are drawn without any such recognition ;
they are direct inferences from known cases, to a case supposed to be similar. I have endeav-
ored to show that this is not only as legitimate an operation, but substantially the same oper-
ation, as that of ascending from known cases to a general proposition ; except that the latter
process has one great security for correctness which the former does not possess. In science,
the inference must necessarily pass through the intermediate stage of a general proposition,
because Science wants its conclusions for record, and not for instantaneous use. But the in-
ferences drawn for the guidance of practical affairs, by persons who would often be quite in-
capable of expressing in unexceptionable terms the corresponding generalizations, may and
frequently do exhibit intellectual powers quite equal to any which have ever been displayed
in science ; and if these inferences are not inductive, what are they ? The limitation imposed
on the terra by Dr. Whewell seems perfectly arbitrary ; neither justified by any fundamental
distinction between what he includes and what he desires to exclude, nor sanctioned by usage,
at least from the time of Keid and Stewart, the principal legislators (as far as the English-
language is concerned) of modern metaphysical terminology.
INDUCTIONS IMPROPERLY SO CALLED. 211
in the common books of Logic we find this laid down as the most perfect,
indeed the only quite perfect, form of induction. In those books, every
process which sets out from a less general and terminates in a more gen-
eral expression — which admits of being stated in the form, " This and that
A are B, therefore every A is B " — is called an induction, whether any
thing be really concluded or not : and the induction is asserted not to be
perfect, unless every single individual of the class A is included in the
antecedent, or premise : that is, unless what we affirm of the class has
already been ascertained to be true of every individual in it, so that the
nominal conclusion is not I'eally a conclusion, but a mere re-assertion of the
premises. If we were to say. All the planets shine by the sun's light, from
observation of each separate planet, or All the Apostles were Jews, because
this is true of Peter, Paul, John, and every other apostle — these, and such
as these, would, in the phraseology in question, be called perfect, and the
only perfect, Inductions. This, however, is a totally different kind of in-
duction from ours ; it is not an inference from facts known to facts un-
known, but a mere short-hand registration of facts known. The two sim-
ulated arguments which we have quoted, are not generalizations ; the prop-
ositions purporting to be conclusions from them, are not really general
propositions. A general proposition is one in which the predicate is af-
firmed or denied of an unlimited number of individuals ; namely, all, wheth-
er few or many, existing or capable of existing, which possess the proper-
ties connoted by the subject of the proposition. " All men are mortal " does
not mean all now living, but all men past, present, and to come. When the
signification of the term is limited so as to render it a name not for any
and every individual falling under a certain general description, but only
for each of a number of individuals, designated as such, and as it were
counted off individually, the proposition, though it may be general in its
language, is no general proposition, but merely that number of singular
propositions, written in an abridged character. The operation may be very
useful, as most forms of abridged notation are ; but it is no part of the in-
vestigation of truth, though often bearing an important part in the prepa-
ration of the materials for that investigation.
As we may sum up a definite number of singular propositions in one
proposition, which will be apparently, but not really, general, so we may
sum up a definite number of general propositions in one proposition, which
will be apparently, but not really, more general. If by a separate induc-
tion applied to every distinct species of animals, it has been established
that each possesses a nervous system, and we affirm thereupon that all an-
imals have a nervous system ; this looks like a generalization, though as
the conclusion merely affirms of all what has already been affirmed of each,
it seems to tell us nothing but what we knew before. A distinction, how-
ever, must be made. If in concluding that all animals have a nervous sys-
tem, we mean the same thing and no more as if we had said " all known
animals," the proposition is not general, and the process by which it is ar-
rived at is not induction. But if our meaning is that the observations
made of the various species of animals have discovered to ns a law of an-
imal nature, and that we are in a condition to say that a nervous system
will be found even in animals yet undiscovered, this indeed is an induc-
tion ; but in this case the general proposition contains more than the sum
of the special propositions from which it is inferred. The distinction is
still more forcibly brought out when we consider, that if this real general-
ization be legitimate at all, its legitinnacy probably does not require that
212 INDUCTION.
we should have examined without exception every known species. It is
the number and nature of the instances, and not their being the whole of
those which happen to be known, that makes them sufficient evidence to
prove a general law : while the more limited assertion, which stops at all
known animals, can not be made unless we have rigorously verified it in
every species. In like manner (to return to a former example) we might
have inferred, not that all the planets, but that all planets, shine by reflect-
ed light : the former is no induction ; the latter is an induction, and a bad
one, being disproved by the case of double stars — self-luminous bodies
which are properly planets, since they revolve round a centre.
§ 2. There are several processes used in mathematics which require to
be, distinguished from Induction, being not unfrequently called by that
name, and being so far similar to Induction properly so called, that the
propositions they lead to are really general propositions. For example,
when we have proved with respect to the circle, that a straight line can
not meet it in more than two points, and when the same thing has been
successively pi-oved of the ellipse, the parabola, and the hyperbola, it may
be laid down as a universal property of the sections of the cone. The
distinction drawn in the two previous examples can have no place here,
there being no difference between all known sections of the cone and all
sections, since a cone demonstrably can not be intersected by a plane ex-
cept in one of these four lines. It would be difficult, therefore, to refuse
to the proposition arrived at, the name of a generalization, since there is
no room for. any generalization beyond it. But there is no induction, be-
cause there is no inference : the conclusion is a mere summing up of what
was asserted in the various propositions from which it is drawn. A case
somewhat, though not altogether, similar, is the proof of a geometrical theo-
rem by means of a diagram. Whether the diagram be on paper or only
in the imagination, the demonstration (as formerly observed*) does not
prove directly the general theorem ; it proves only that the conclusion,
whifih the theorem asserts generally, is true of the particular triangle or
circle exhibited in the diagram ; but since we perceive that in the same
way in which we have proved it of that circle, it might also be proved of
any other circle, we gather up into one general expression all the singular
propositions susceptible of being thus proved, and embody them in a uni-
versal proposition. Having shown that the three angles of the triangle
ABC are together equal to two right angles, we conclude that this is true
of every other triangle, not because it is true of ABC, but for the same
reason which proved it to be true of ABC. If this were to be called In-
duction, an appropriate name for it would be, induction by parity of rea-
soning. But the term can not properly belong to it; the characteristic
quality of Induction is wanting, since the truth obtained, though really
general, is not believed on the evidence of particular instances. We do not
conclude that all triangles have the property because some triangles have,
but from the ulterior demonstrative evidence which was the ground of our
conviction in the particular instances.
There are nevertheless, in mathematics, some examples of so-called In-
duction, in which the conclusion does bear the appearance of a generaliza-
tion grounded on some of the particular cases included in it. A mathe-
matician, when he has calculated a sufficient number of the terms of an al-
* Supra, p. 145.
INDUCTIONS IMPROPERLY SO CALLED. 213
gebraical or arithmetical series to have ascertained what is called the law
of the series, does not hesitate to fill up any number of the succeeding terms
without repeating the calculations. But I apprehend he only does so when
it is apparent from a priori considerations (which might be exhibited in
the form of demonstration) that the mode of formation of the subsequent
terms, each from that which preceded it, must be similar to the formation
of the terms which have been already calculated. And when the attempt
has been hazarded without the sanction of such general considerations, there
are instances on record in which it has led to false results.
It is said that Newton discovered the binomial theorem by induction ;
by raising a binomial successively to a certain number of powers, and
comparing those powers with one another until he detected the relation in
which the algebraic formula of each power stands to the exponent of that
power, and to the two terms of the binomial. The fact is not improbable :
but a mathematician like Newton, who seemed to arrive per saltum at
principles and conclusions that ordinary mathematicians only reached by a
succession of steps, certainly could not have performed the comparison in
question without being led by it to the a priori ground of the law ; since
any one who understands sufficiently the nature of multiplication to ven-
ture upon multiplying several lines of symbols at one operation, can not
but perceive that in raising a binomial to a power, the co-efficients must
depend on the laws of permutation and combination : and as soon as this
is recognized, the theorem is demonstrated. Indeed, when once it was seen
that the law prevailed in a few of the lower powers, its identity with the
law of permutation would at once suggest the considerations which prove
it to obtain universally. Even, therefore, such cases as these, are but ex-
amples of wliat I have called Induction by parity of reasoning, that is, not
really Induction, because not involving inference of a general proposition
from particular instances.
§ 3. There remains a third improper use of the term Induction, which it
is of real importance to clear up, because the theory of Induction has been,
in no ordinary degree, confused by it, and because the confusion is exem-
plified in the most recent and elaborate treatise on the inductive philosophy
which exists in our language. The error in question is that of confound-
ing a mere description, by general terms, of a set of observed phenomena,
with an induction from them.
Suppose that a phenomenon consists of parts, and that these parts are
only capable of being observed separately, and as it were piecemeal.
When the observations have been made, there is a convenience (amounting
for many purposes to a necessity) in obtaining a representation of the phe-
nomenon as a whole, by combining, or as we may say, piecing these de-
tached fragments together. A navigator sailing in the midst of the ocean
discovers land : he can not at first, or by any one observation, determine
whether it is a continent or an island ; but he coasts along it, and after a
few days finds himself to have sailed completely round it : he then pro-
nounces it an island. Now there was no .particular time or place of ob-
servation at which he could perceive that this land was entirely surrounded
by water : he ascertained the fact by a succession of partial observations,
and then selected a general expression which summed up in two or three
words the whole of what he so observed. But is there any thing of the
nature of an induction in this process ? Did he infer any thing that had
not been observed, from something else which had ? Certainly not. He
214 INDUCTION.
had observed the whole of what the proposition asserts. That the land ia
question is an island, is not an inference from the partial facts which the
navigator saw in the course of his circumnavigation ; it is the facts them-
selves ; it is a summary of those facts ; the description of a complex fact,
to which those simpler ones are as the parts of a whole.
Now there is, I conceive, no difference in kind between this simple op-
eration, and that by which Kepler ascertained the nature of the planetary
orbits : and Kepler's operation, all at least that was characteristic in it, was
not more an inductive act than that of our supposed navigator.
The object of Kepler was to determine the real path described by each
of the planets, or let us say by the planet Mars (since it was of that body
that he first established the two of his three laws which did not require a
comparison of planets). To do this there was no other mode than that of
direct observation : and all which observation could do was to ascertain a
gi'eat number of the successive places of the planet ; or rather, of its ap-
parent places. That the planet occupied successively all these positions, or
at all events, positions which produced the same impressions on the eye,
and that it passed from one of these to another insensibly, and without any
apparent breach of continuity ; thus much the senses, with the aid of the
proper instruments, could ascertain. What Kepler did more than this, was
to find what sort of a curve these different points would make, supposing
them to be all joined together. He expressed the whole series of the ob-
served places of Mars by what Dr. Whewell calls the general conception of
an ellipse. This operation was far from being as easy as that of the navi-
gator who expressed the series of his observations on successive points of
the coast by the general conception of an island. But it is the very same
sort of operation; and if the one is not an induction but a description, this
must also be true of the other.
The only real induction concerned in the case, consisted in inferring that
because the observed places of Mars were cori-ectly represented by points
in an imaginary ellipse, therefore Mars would continue to revolve in that
same ellipse ; and in concluding (before the gap had been filled up by fur-
ther observations) that the positions of the planet during the time which
intervened between two observations, must have coincided with the inter-
mediate points of the curve. For these were facts which had not been di-
rectly observed. They were inferences from the observations; facts in-
ferred, as distinguished from facts seen. But these inferences were so far
from being a part of Kepler's philosophical operation, that they had been
drawn long before he was born. Astronomers had long known that the
planets periodically returned to the same places. "When this had been as-
certained, there was no induction left for Kepler to make, nor did he make
any further induction. He merely applied his new conception to the facts
inferred, as he did to the facts observed. Knowing already that the plan-
ets continued to move in the same paths ; when he found that an ellipse
correctly represented the past path, he knew that it would represent the
future path. In finding a compendious expression for the one set of facts,
he found one for the other : but he found the expression only, not the in-
ference ; nor did he (which is the true test of a general truth) add any
thing to the power of prediction already possessed.
§ 4. The descriptive operation which enables a number of details to be
summed up in a single proposition. Dr. Whewell, by an aptly chosen ex-
pression, has termed the Colligation of Facts. In most of his observations
INDUCTIONS IMPROPERLY SO CALLED. 215
concerning that mental process I fully agree, and would gladly transfer all
that portion of his book into my own pages. I only think him mistaken
in setting up this kind of operation, which according to the old and received
meaning of the term, is not induction at all, as the type of induction gener-
ally ; and laying down, throughout his work, as principles of induction, the
principles of mere colligation.
Dr. Whewell maintains that the general proposition which binds togeth-
er the particular facts, and makes them, as it were, one fact, is not the mere
sum of those facts, but something more, since there is introduced a concep-
tion of the mind, which did not exist in the facts themselves. " The par-
ticular facts," says he,* " arc not merely brought together, but there is a
new element added to the combination by the very act of thought by which
they are combined When the Greeks, after long observing the mo-
tions of the planets, saw that these motions might be rightly considered as
produced by the motion of one wheel revolving in the inside of another
wheel, these wheels were creations of their minds, added to the facts which
they perceived by sense. And even if the wheels were no longer supposed
to be material, but were reduced to mere geometrical spheres or circles, they
were not the less products of the mind alone — something additional to the
iacts observed. The same is the case in all other discoveries. The facts
are known, but they are insulated and unconnected, till the discoverer sup-
,plies from his own store a principle of connection. The pearls are there,
tbut they will not hang together till some one provides the string."
Let me first remark that Di-. Whewell, in this passage, blends together,
iudiscriminately, examples of both the processes which I am endeavoring
to distinguish from one another. When the Greeks abandoned the suppo-
sition that the planetary motions were produced by the revolution of mate-
rial wheels, and fell back upon the idea of " mere geometrical spheres or
-circles," there was more in this change of opinion than the mere substitu-
tion of an ideal curve for a physical one. There was the abandonment of
-a theory, and the replacement of it by a mere description. No one would
think of calling the doctrine of material wheels a mere description. That
■doctrine was an attempt to point out the force by which the planets were
acted upon, and compelled to move in their orbits. But when, by a great
step in philosophy, the materiality of the wheels was discarded, and the ge-
ometrical forms alone retained, the attempt to account for the motions was
given up, and what was left of the theory was a mere description of the
orbits. The assertion that the planets were carried round by wheels re-
volving in the inside of other wheels, gave place to the proposition, that
they moved in the same lines which would be traced by bodies so carried :
which was a mere mode of representing the sum of the observed facts ; as
Kepler's was another and a better mode of representing the same observa-
tions.
It is true that for these simply descriptive operations, as well as for the
•erroneous inductive one, a conception of the mind was required. The con-
ception of an ellipse must have presented itself to Kepler's mind, before he
could identify the planetary orbits with it. According to Dr. Whewell,
the conception was something added to the facts. He expresses himself
■&S if Kepler had put something into the facts by his mode of conceiving
them. But Kepler did no such thing. The ellipse was in the facts before
£!epler recognized it; just as the island was an island before it had been
. * Novum Organum Renovatum, pp. 72, 73.
216 INDUCTION.
Bailed round. Kepler did not put what he had conceived into the facts,
but saw it in them. A conception implies, and corresponds to, something
conceived : and though the conception itself is not in the facts, but in our
mind, yet if it is to convey any knowledge relating to them, it must be a con-
ception of something which really is in the facts, some property which they
actually possess, and which they would manifest to our senses, if our senses
were able to take cognizance of it. If, for instance, the planet left behind
it in space a visible track, and if the observer were in a fixed position at
such a distance from the plane of the orbit as would enable him to see the
whole of it at once, he would see it to. be an ellipse; and if gifted with ap-
propriate instruments and powers of locomotion, he could prove it to be
such by measuring its different dimensions. Nay, further: if the track
were visible, and he were so placed that he could see all parts of it in suc-
cession, but not all of them at once, he might be able, by piecing together
his successive observations, to discover both that it was an ellipse and that
the planet moved in it. The case would then exactly resemble that of the
navigator who discovers the land to be an island by sailing round it. If
the path was visible, no one I think would dispute that to identify it with
an ellipse is to describe it : and I can not see why any difference should be
made by its not being directly an object of sense, when every point in it is
as exactly, ascertained as if it were so.
Subject to the indispensable condition which has just been stated, I do
not conceive that the part which conceptions have in the operation of
studying facts, has ever been- overlooked or undervalued. No one ever dis'
puted that in order to reason about any thing we must have a conception
of it; or that when we include a multitude of things under a general ex-
pression, there is implied in the expression a conception of something com-
mon to those things. But it by no means follows that the conception is
necessarily pre-existent, or constructed by the mind out of its own mate-
rials. If the facts are rightly classed under the conception, it is because
there is in the facts themselves something of which the conception is itself
a copy ; and which if we can not directly perceive, it is because of the lim-
ited power of our organs, and not because the thing itself is not there.
The conception itself is often obtained by abstraction from the very facts
which, in Dr. Whewell's language, it is afterward called in to connect.
This he himself admits, when he observes (which he does on several occa-
sions), how great a service would be rendered to the science of physiology
by the philosopher " who should establish a precise, tenable, and consistent
conception of life."* Such a conception can only be abstracted from the
phenomena of life itself ; from the very facts which it is put in requisition
to connect. In other cases, no doubt, instead of collecting the conception
from the Very phenomena which we are attempting to colligate, we select
it from among those which have been previously collected by abstraction
from other facts. In the instance of Kepler's laws, the latter was the
case. The facts being out of the reach of being observed, in any such
manner as would have enabled the senses to identify directly the path of
the planet, the conception requisite for framing a general description of
that path could not be collected by abstraction from the observations
themselves ; the mind had to supply hypothetically, from among the con-
ceptions it had obtained from other portions of its experience, some one
which would correctly represent the series of the observed facts. It had
♦ Novum Organum Renovatum, p. 32.
INDUCTIONS IMPROPERLY SO CALLED. 211
to frame a supposition respecting the general course of the phenomenon,
and ask itself, If this be the general description, what will the details be ?
and then compare these with the details actually observed. If they agreed,
the hypothesis would serve for a description of the phenomenon : if not, it
was necessarily abandoned, and another tried. It is such a case as this
which gives rise to the docti'ine that the mind, in framing the descriptions,
adds something of its own which it does not find in the facts.
Yet it is a fact surely, that the planet does describe an ellipse ; and a fact
which we could see, if we had adequate visual organs and a suitable posi-
tion. Not having these advantages, but possessing the conception of an el-
lipse, or (to express the meaning in less technical language) knowing what
an ellipse was, Kepler tried whether the observed places of the planet were
consistent with such a path. He found they were so ; and he, consequent-
ly, asserted as a fact that the planet moved in an ellipse. But this fact,
which Kepler did not add to, but found in, the motions of the planet, name-
ly, that it occupied in succession the various points in the circumference of
a given ellipse, was the very fact, the separate parts of which had been sep-
arately observed ; it was the sum of the different observations.
Having stated this fundamental difference between my opinion and that
of Dr. Whewell, I must add, that his account of the manner in which a
conception is selected, suitable to express the facts, appears to me perfectly
just. The experience of all thinkers will, 1 believe, testify that the process
is tentative; that it consists of a succession of guesses; many being reject-
ed, until one at last occurs fit to be chosen. We know from Kepler him-
self that before hitting upon the " conception " of an ellipse, he tried nine-
teen other imaginary paths, which, finding them inconsistent with the ob-
servations, he was obliged to reject. But as Dr. Whewell truly says, the
successful hypothesis, though a guess, ought generally to be called, not a
lucky, but a skillful guess. The guesses which serve to give mental unity
and wholeness to a chaos of scattered particulars, are accidents which rare-
ly occur to any minds but those abounding in knowledge and disciplined in
intellectual combinations.
How far this tentative method, so indispensable as a means to the colli-
gation of facts for purposes of description, admits of application to Induc-
tion itself, and what functions belong to it in that department, will be con-
sidered in the chapter of the present Book which relates to Hypotheses.
On the present occasion we have chiefly to distinguish this process of Col-
ligation from Induction properly so called ; and that the distinction may be
made clearer, it is well to advert 'to a curious and interesting remark, which
is as strikingly true of the former operation, as it appears to me unequivo-
cally false of the latter.
In different stages of the progress of knowledge, philosophers have em-
ployed, for the colligation of the same order of facts, different conceptions.
The early rude observations of the heavenly bodies, in which minute pre-
cision was neither attained nor sought, presented nothing inconsistent with
the representation of the path of a planet as an exact circle, having the earth
for its centre. As observations increased in accuracy, facts were disclosed
which were not reconcilable with this simple supposition : for the colliga-
tion of those additional facts, the supposition was varied ; and varied again
and again as facts became more numerous and precise. The earth was re-
moved fi-om the centre to some other point within the circle; the planet
was supposed to revolve in a smaller circle called an epicycle, round an im-
aginary point which revolved in a circle round the earth : in proportion as
218 INDUCTION.
observation elicited fresh facts contradictory to these representations, other
epicycles and other eccentrics were added, producing additional complica-
tion ; until at last Kepler swept all these circles away, and substituted the
conception of an exact ellipse. Even this is found not to represent with,
complete correctness the accurate observations of the present day, which,
disclose many slight deviations from an orbit exactly elliptical. Now Dr.
Whewell has remarked that these successive general expressions, though,
apparently so conflicting, were all correct : they all answered the purpose
I of colligation ; they all enabled the mind to represent to itself with facility,
and by a simultaneous glance, the whole body of facts at the time ascer-
tained : each in its turn served as a correct description of the phenomena,,
so far as the senses had up to that time taken cognizance of them. If a.
necessity afterward arose for discarding one of these general descriptions
of the planet's orbit, and framing a different imaginary line, by which to-
express the series of observed positions, it was because a number of new
facts had now been added, which it was necessary to combine with the old
facts into one general description. But this did not affect the correctness-
of the former expression, considered as a general statement of the only facts,
which it was intended to represent. And so true is this, that, as is well re-
marked by M. Comte, these ancient generalizations, even the rudest and
most imperfect of them, that of uniform movement in a circle, are so far
from being entirely false, that they are even now habitually employed by
astronomers when only a rough appi'oximation to correctness is required..
" L'astronomie moderne, en detruisant sans retour les hypotheses primi-
tives, envisagees comme lois reelles du monde, a soigneusement maintena
leur valeur positive et permanente, la propri^te de representer commod^-
ment les phenom^nes quand il s'agit d'une premiere 6bauche. Nos res-
sources k cet 6gard sont raeme bien plus etendues, precis^ment k cause
que nous ne nous faisons aucune illusion sur la realitd des hypotheses; ce
qui nous permet d'employer sans scrupule, en chaque cas, celle que nous^
jugeons la plus avantageuse."*
Dr. Whewell's remark, therefore, is philosophically correct. Successive^
expressions for the colligation of observed facts, or, in other words, succes-
sive descriptions of a phenomenon as a whole, which has been observed
only in parts, may, though conflicting, be all correct as far as they go. But
it would surely be absurd to assert this of conflicting inductions.
The scientific study of facts may be undertaken for three different pur-
poses: the simple description of the facts; their explanation; or their pre-
diction : meaning by prediction, the determination of the conditions under
which similar facts may be expected again to occur. To the first of these
three operations the name of Induction does not properly belong : to the
other two it does. Now, Dr. Whewell's observation is true of the first
alone. Considered as a mere description, the circular theory of the heaven-
ly motions represents perfectly well their general features : and by adding
epicycles without limit, those motions, even as now known to us, might be
expressed with any degree of accuracy that might be required. The ellip-
tical theory, as a mere description, would have a great advantage in point
of simplicity, and in the consequent facility of conceiving it and reasoning,
about it ; but it would not really be more true than the other. Different
descriptions, therefore, may be all true : but not, surely, different explana-
tions. The doctrine that the heavenly bodies moved by a virtue \nherent
* Cours de Philosophic Positive, vol. ii., p. 202.
INDUCTIONS IMPROPEKLY SO CALLED. 219
in their celestial nature; the doctrine that they were moved by impact
(which led to the hypothesis of vortices as the only impelling force capable
of whirling bodies in circles), and the Newtonian doctrine, that they are
moved by the composition of a centripetal with an original projectile
force ; all these are explanations, collected by real induction from supposed
parallel cases ; and they were all successively I'eceived by philosophers, as
scientific truths on the subject of the heavenly bodies. Can it be said of
these, as was said of the different descriptions, that they are all true as far
as they go ? Is it not clear that only one can be true in any degree, and
the other two must be altogether false ? So much for explanations : let us
now compare different predictions : the first, that eclipses will occur when
one planet or satellite is so situated as to cast its shadow upon another;
the second, that they will occur when some great calamity is impending
over mankind. Do these two doctrines only differ in the degree of their
truth, as expressing real facts with unequal degrees of accuracy ? Assur-
edly the one is true, and the other absolutely false.*
* Dr. Whewell, in his reply, contests the distinction here drawn, and maintains, that not
only different descriptions, but diiferent explanations of a phenomenon, may all be true^ Of
the three theories respecting the motions of the heavenly bodies, he says (Philosophy of Dis-
covery, f. 231): "Undoubtedly all these explanations may be true and consistent with each
other, and would be so if each had been followed out so as to show in what manner it could
be made consistent with the facts. And this was, in reality, in a great measure done. The
doctrine that the heavenly bodies were moved by vortices was successfully modified, so that
it came to coincide in its results with the doctrine of an inverse-quadratic centripetal force.
When this point was reached, the vortex was merely a machinery, well or ill devised,
for producing such a centripeta.1 force, and therefore did not contradict the doctrine of a cen-
tripetal force. Newton himself does not appear to have been averse to explaining gravity by
impulse. So little is it true that if one theory be true the other must be false. The attempt
to explain gravity by the impulse of streams of particles flowing through the universe in all
directions, which I have mentioned in the Philosophy, is so far from being inconsistent with
the Newtonian theory, that it is founded entirely upon it. And even with regard to the doc-
trine, that the heavenly bodies move by an inherent virtue ; if this doctrine had been main-
tained in any such way that it was brought to agree with the facts, the inherent virtue must
have had its laws determined ; and then it would have been found that the virtue had a refer-
ence to the central body ; and so, the ' inherent virtue ' must have coincided in its effect with
the Newtonian force ; and then, the two explanations would agree, except so far as the word
'inherent' was concerned. And if such a part of an earlier theory as this word inherent in-
dicates, is found to be untenable, it is of course rejected in the transition to later and more
exact theories, in Inductions of this kind, as well as in what Mr. Mill calls Descriptions.
There is, therefore, still no validity discoverable in the distinction which Mr. Mill attempts to
draw between descriptions like Kepler's law of elliptical orbits, and other examples of induc-
tion."
If the doctrine of vortices had meant, not that vortices existed, but only that the planets
moved in the same manner as if they had been whirled by vortices ; if the hypothesis had been
merely a mode of representing the facts, not an attempt to account for them ; if,, in short, it
had been only a Description ; it would, no doubt, have been reconcDable with the Newtonian
theory. The vortices, however, were not a mere aid to conceiving the motions of the plan-
ets, but a supposed physical agent, actively impelling them ; a material fact, which might be
true or not true, but could not be both true and not true. According to Descartes's theory it
was true, according to Newton's it was not true. Dr. Whewell probably means that since the
phrases, centripetal and projectile force, do not declare the nature hut only the direction of
the forees, the Newtonian theory does not absolutely contradict any hypothesis which may be
framed respecting the mode of their production. 'The Newtonian theory, regarded as a mere
description of the planetary motions, does not ; but the Newtonian theory as an explanation
of them does. Tor in what does the explanation consist? In ascribing those motions to a
general law which obtains between all particles of matter, and in identifying this with the law
by which bodies fall to the ground. If the planets are kept in their orbits by a force which
draws the particles composing them toward every other particle of matter in the solar system,
they are not kept in those Orbits by the impulsive force of certain streams of matter which
whirl them round. The one explanation absolutely excludes the other. Either the planets
are not moved by vortices, or they do not move by a law common to all matter. It is im-
220 INDUCTION.
In every way, therefore, it is evident that to explain induction as the
colligation of facts by means of appropriate conceptions, that is, concep-
tions which will really express them, is to confound mere description of the
observed facts with inference from those facts, and ascribe to the latter
what is a characteristic property of the former.
There is, however, between Colligation and Induction, a real correlation,
•which it is important to conceive correctly. Colligation is not always in-
duction ; but induction is always colligation. The assertion that the plan-
ets move in ellipses, was but a mode of representing observed facts ; it was
but a colligation ; while the assertion that they are drawn, or tend, toward
the sun, was the statement of a new fact, inferred by induction. But the
induction, once made, accomplishes the purposes of colligation likewise. It
brings the same facts, which Kepler had connected by his conception of an
ellipse, under the additional conception of bodies acted upon by a central
force, and serves, therefore, as a new bond of connection for those facts ; a
new principle for their classification.
Further, the descriptions which are improperly confounded with induc-
tion, are nevertheless a necessary preparation for induction ; no less neces-
sary than correct observation of the facts themselves. Without the pre-
vious colligation of detached observations by means of one general concep-
tion, we could never have obtained any basis for an induction, except in
the case of phenomena of very limited compass. We should not be able
possible that both opinions can be true. As well might it be said that there is no contradic-
tion between the assertions, that a man died because somebody killed him, and that he died a
natural death.
So, again, the theory that the planets move by a virtue inherent in their celestial nature, is
incompatible with either of the two others : either that of their being moved by vortices, or
that which regards them as moving by a property which they have in common with the earth
and all terrestrial bodies. Dr. Whewell says that the theory of an inherent virtue agrees with
Newton's when the word inherent is left out, which of course it would be (he says) if " found
to be untenable. " But leave that out, and where is the theory ? The word inherent is the
theory. When that is omitted, there remains nothing except that the heavenly bodies move
"by a virtue," i. e., by a power of some sort; or by virtue of their celestial nature, which di- '
rectly contradicts the doctrine that terrestrial bodies fall by the same law.
If Dr. Whewell is not yet satisfied, any other subject will serve equally well to test his doc-
trine. He will hardly say that there is no contradiction between the emission theory and the
undulatory theory of light ; or that there can be both one and two electricities ; or that the
hypothesis of the production of the higher organic forms by development from the lower, and
the supposition of separate and successive acts of creation, are quite reconcilable ; or that
the theory that volcanoes are fed from a central fire, and the doctrines which ascribe them to
chemical action at a comparatively small depth below the earth's surface, are consistent with
one another, and all true as far as they go.
If different explanations of the same fact can not both be true, still less, surely, can differ-
ent predictions. Dr. Whewell quarrels (on what ground it is not necessary here to consider)
with the example I had chosen on this point, and thinks an objection to an illustration a suf-
ficient answer to a theory. Examples not liable to his objection are easily found, if the prop-
osition that conflicting predictions can not both be true, can be made clearer by any examples.
Suppose the phenomenon to be a newly-discovered comet, and that one astronomer predicts
its return once in every 300 years— another once in every 400: can they both be right?
When Columbus predicted that by sailing constantly westward he should in time return to
the point from which he set out, while others asserted that he could never do so except by
turning back, were both he and his opponents true prophets ? Were the predictions which
foretold the wonders of railways and steamships, and those which averred that the Atlantic
could never be crossed by steam navigation, nor a railway train propelled ten miles an hour,
both (in Dr. Whewell's words) " true, and consistent with one another?"
Dr. Whewell sees no distinction between holding contradictory opinions on a question of
fact, and merely employing different analogies to facilitate the conception of the same fact.
The case of different Inductions belongs to the former class, that of different Descriptions to
the latter.
INDUCTIONS IMPEOPEELT SO CALLED. 221
to affirm any predicates at all, of a subject incapable of being observed
otherwise than piecemeal : much less could we extend those predicates by
induction to other similar subjects. Induction, therefore, always presup-
poses, not only that the necessary observations are made with the necessary
accuracy, but also that the results of these observations are, so far as prac-
ticable, connected together by general descriptions, enabling the mind to
represent to itself as wholes whatever phenomena are capable of being so
represented.
§ 5. Dr. Whewell has replied at some length to the preceding observa-
tions, restating his opinions, but without (as far as I can perceive) adding
any thing material to his former arguments. Since, however, mine have
not had the good fortune to make any impression upon him, I will subjoin
a few remarks, tending to show more clearly in what our difference of
opinion consists, as well as, in some measure, to account for it.
Nearly all the definitions of induction, by writers of authority, make it
consist in drawing inferences from known cases to unknown ; affirming of
a class, a predicate which has been found true of some cases belonging to
the class ; concluding because some things have a certain property, that
other things which resemble them have the same property — or because a
thing has manifested a property at a certain time, that it has and will have
that property at other times.
It will scarcely be contended that Kepler's operation was an Induction
in this sense of the term. The statement, that Mars moves in an elliptical
orbit, was no generalization from individual cases to a class of cases. Nei-
ther was it an extension to all time, of what had been found true at some
particular time. The whole amount of generalization which the case ad-
mitted of, was already completed, or might have been so. Long before
the elliptic theory was thought of, it had been ascertained that the planets
returned periodically to the same apparent places ; the series of these
places was, or might have been, completely determined, and the apparent
course of each planet marked out on the celestial globe in an uninterrupted
line. Kepler did not extend an observed truth to other cases than those in
which it had been observed : he did not widen the subject of the proposi-
tion which expressed the observed facts. The alteration he made was in
the predicate. Instead of saying, the successive places of Mars are so and
so, he summed them up in the statement, that the successive places of Mars
are points in an ellipse. It is true, this statement, as Dr. Whewell says,
was not the sum of the observations merely ; it was the sum of the obser-
vations seen under a new point of view* But it was not the sum of more
than the observations, as a real induction is. It took in no cases but those
which had been actually observed, or which could have been inferred from
the observations before the new point of view presented itself. There was
not that transition from known cases to unknown, which constitutes Induc-
tion in the original and acknowledged meaning of the term.
Old definitions, it is true, can not prevail against new knowledge : and if
the Keplerian operation, as a logical process, be really identical with what
takes place in acknowledged induction, the definition of induction ought to
be so widened as to take it in ; since scientific language ought to adapt it-
self to the true relations which subsist between the things it is employed
to designate. Here then it is that I am at issue with Dr. Whewell. He
* Phil. ofDiscm., p. 256.
222 INDUCTION.
does think the operations identical. He allows of no logical process in any
case of induction, other than what there was in Kepler's case, namely,
guessing until a guess is found which tallies with the facts ; and accord-
ingly, as we shall see hereafter, he rejects all canons of induction, because
it is not by means of them that we guess. Dr. Whewell's theory of the
logic of science would be very perfect if it did not pass over altogether the
question of Proof. But in my apprehension there is such a thing as proof,
and inductions differ altogether from descriptions in their relation to that
element. Induction is proof ; it is inferring something unobserved from
something observed: it requires, therefore, an appropriate test of proof;
and to provide that test, is the special purpose of inductive logic. When,
on the contrary, we merely collate known observations, and, in Dr. Whe-
well's phraseology, connect them by means of a new conception ; if the
conception does serve to connect the observations, we have all we want.
As the proposition in which it is embodied pretends to no other truth than
what it may share with many other modes of representing the same facts,
to be consistent with the facts is all it requires : it neither needs nor ad-
mits of proof ; though it may serve to prove other things, inasmuch as, by
placing the facts in mental connection with other facts, not previously seen
to resemble them, it assimilates the case to another class of phenomena,
concerning which real Inductions have already been made. Thus Kepler's
so-called law brought the orbit of Mars into the class ellipse, and by doing
so, proved all the properties of an ellipse to be true of the orbit : but in this
proof Kepler's law supplied the minor premise, and not (as is the case with
real Inductions) the major.
Dr. Whewell calls nothing Induction where there is not a new mental
conception introduced, and every thing induction where there is. But this
is to confound two very different things. Invention and Proof. The intro-
duction of a new conception belongs to Invention : and invention may be
required in any operation, but is the essence of none. A new conception
may be introduced for descriptive purposes, and so it may for inductive
purposes. But it is so far from constituting induction, that induction does
not necessarily stand in need of it. Most inductions require no conception
but what was present in every one of the particular instances on which the
induction is grounded. That all men are mortal is surely an inductive
conclusion ; yet no new conception is introduced by it. Whoever knows
that any man has died, has all the conceptions involved in the inductive
generalization. But Dr. Whewell considers the process of invention which
consists in framing a new conception consistent with the facts, to be not
merely a necessary part of all induction, but the whole of it.
The mental operation which extracts from a number of detached obser-
vations certain general characters in which the observed phenomena resem-
ble one another, or resemble other known facts, is what Bacon, Locke, and
most subsequent metaphysicians, have understood by the word Abstrac-
tion. A general expression •obtained by abstraction, connecting known
facts by means of common characters, but without concluding from them
to unknown, may, I think, with strict logical correctness, be termed a De-
scription ; nor do I know in what other way things can ever be described.
My position, however, does not depend on the employment of that partic-
ular word ; I am quite content to use Dr. Whewell's term Colligation, or
the more general phrases, " mode of representing, or of expressing, phe-
nomena :" provided it be clearly seen that the process is not Induction, but
Something radically different.
GROUND OF INDUCTION. 223
What more may usefully be said on the subject of Colligation, or of the
correlative expression invented by Dr. Whewell, the Explication of Con-
oeptions, and generally on the subject of ideas and mental representations
as connected with the study of facts, will find a more appropriate place in
the Fourth Book, on the Operations Subsidiary to Induction : to which I
must refer the reader for the removal of any difficulty which the present
discussion may have left.
CHAPTER III.
OP THE GROUND OF INDUCTION.
§ 1. Induction properly so called, as distinguished from those mental
•operations, sometimes, though improperly, designated by the name, which I
have attempted in the preceding chapter to characterize, may, then, be sum-
marily defined as Generalization from Experience. It consists in inferring u
from some individual instances in which a phenomenon is observed to oc-
cur, that it occurs in all instances of a certain class ; namely, in all which
resemble the former, in what are regarded as the material circumstances^
In what way the material circumstances are to be distinguished from
those which are immaterial, or why some of the circumstances are material
and others not so, we are not yet ready to point out. We must first ob-'
serve, that there is a principle implied in the very statement of what Induc-
tion is; an assumption with regard to the course of nature and the order
•of the universe; namely, that there are such things in nature as parallel
•cases ; that what happens once, will, under a sufficient degree of similarity
of circumstances, happen again, and not only again, but as often as the
same circumstances recur. This, I say, is an assumption, involved in every
case of induction. And, if we consult the actual course of nature, we find
that the assumption is warranted. The universe, so far as known to us, is
so constituted, that whatever is true in any one case, is true in all cases of
a certain description ; the only difficulty is, to find what description.
This universal fact, which is our warrant for all inferences from experi-
«nce, has been described by different philosophers in different forms of lan-
guage: that the course of nature is uniform; that the universe is governed
by general laws ; and the like. One of the most usual of these modes of
expression, but also one of the most inadequate, is that which has been
brought into familiar use by the metaphysicians of the school of Reid
and Stewart. The disposition of the human mind to generalize from ex-
perience— a propensity considered by these philosophers as an instinct of
our nature — they usually describe under some such name as " our intuitive
conviction that the future will resemble the past." Now it has been well
pointed out by Mr. Bailey,* that (whether the tendency be or not an orig-
inal and ultimate element of our nature). Time, in its modifications of past,
present, and future, has no concern either with the belief itself, or with the
grounds of it. We believe that fire will burn to-morrow, because it burned
to-day and yesterday; but we believe, on precisely the same grounds, that
it burned before we were born, and that it burns this very day in Cochin-
•China. It is not from the past to the future, as past and future, that we
* Essays on the Pursuit of Truth,
224 INDUCTION.
infer, but from the known to the unknown ; from facts observed to facts
unobserved ; from what we have perceived, or been directly conscious of,
to what has not come within our experience. In this last predicament i^
the whole region of the future ; but also the vastly greater portion of the
present and of the past.
// Whatever be the most proper mode of expressing it, the proposition that
the course of nature is uniform, is the fundamental principle, or general ax-
iom, of Induction. I/It would yet be a great error to offer this large gener-
alization as any explanation of the inductive process. On the contrary, lAf
hold it to be itself an instance of induction, and induction by no means of
the most obvious kind. Far from being the first induction we make, it is
one of the last, or at all events one of those which are latest in attaining
strict philosophical accuracy. As a general maxim, indeed, it has scarcely
entered into the minds of any but philosophers ; nor even by them, as we
shall have many opportunities of remarking, have its extent and limits been
always very justly conceived. The truth is, that this great generalization
is itself founded on prior generalizations. The obscurer laws of nature
were discovered by means of it, but the more obvious ones must have
been understood and assented to as general truths before it was ever heard
of. "We should never have thought of affirming that all phenomena take
place according to general laws, if we had not first arrived, in the case of a
great multitude of phenomena, at some knowledge of the laws themselves ;
which could be done no otherwise than by induction. In what sense, then,
can a principle, which is so far from being our earliest induction, be re-
garded as our warrant for all the others ? In the only sense, in which (as
we have already seen) the general propositions which we place at the head
of our reasonings when we throw them into syllogisms, ever really contrib-
ute to their validity. As Archbishop Whately remarks, every induction is
a syllogism with the major premise suppressed ; or (as I prefer expressing
3'lt*). every induction may be thrown into the form of a syllogism, by supply-
*ing a major premise. If this be actually done, the principle which we are
now considering, that of the uniformity of the course of nature, will appear
•as the ultimate major premise of all inductions, and will, therefore, stand to
all inductions in the relation in which, as has been shown at so much length,
the major proposition of a syllogism always stands to the conclusion ; not
contributing at all to prove it, but being a necessary condition of its being
proved; since no conclusion is proved, for which there can not be found a
true major premise.*
^ * In the first edition a note was appended at this place, containing some criticism on Arch-
bishop Whately's mode of conceiving the relation between Syllogism and Induction. In a
subsequent issue of his Logic, the Archbishop made a reply to the criticism, which induced
me to cancel part of the note, incorporating the remainder in the text. In a still later edi-
tion, the Archbishop observes in a tone of something like disapprobation, that the objections,
"doubtless from their being fully answered and found untenable, were silently suppressed,"
and that hence he might appear to some of his readers to be combating a shadow. On this
latter point, the Archbishop need give himself no uneasiness. His readers, I make bold to
say, will fully credit his mere affirmation that the objections have actually been made.
But as he seems to think that what he terms the suppression of the objections ought not to
have been made "silently," I now break that silence, and state exactly what it is that I sup-
pressed, and why. I suppressed that alone which might be regarded as personal criticism on
the Archbishop. I had imputed to him the having omitted to ask himself a particular ques-
tion. I found that he had asked himself the question, and could give it an answer consistent
with his own theory. I had also, within the compass of a parenthesis, hazarded some re-
marks on certain general characteristics of Archbishop Whately as a philosopher. These re-
marks, though their tone, I hope, was neither disrespectful nor arrogant, I felt, on reconsider-
ation, that I was hardly entitled to make j least of all, when the instance which I liad re-
GROUND OP INDUCTION. 225
The statement, that the uniformity of the course of nature is the ulti-
mate major premise in all cases of induction, may be thought to require
some explanation. The immediate major premise in every inductive argu-
ment, it certainly is not. Of that. Archbishop Whately's must be held to
be the correct account. The induction, « John, Peter, etc., are mortal, there-
fore all mankind are mortal," may, as he justly says, be thrown into a syl-
logism by prefixing as a major premise (what is at any rate a necessary
condition of the validity of the argument), namely, that what is true of
John, Peter, etc., is true of all mankind. But how came we by this ma-
jor premise ? It is not self-evident ; nay, in all cases of unwarranted gen-
eralization, it is not true. How, then, is it arrived at ? Necessarily either
by induction or ratiocination ; and if by induction, the process, like all oth-
er inductive arguments, may be thrown into the form of a syllogism. This
previous syllogism it is, therefore, necessary to construct. There is, in the
long run, only one possible construction. The real proof that what is true
of John, Peter, etc., is true of all mankind, can only be, that a different sup-
position would be inconsistent with the uniformity which we know to exist
in the course of nature. Whether there would be this inconsistency or not,
may be a matter of long and delicate inquiry ; but unless there would, we
have no suflBcient ground for the major of the inductive syllogism. It
hence appears, that if we throw the whole course of any inductive argu-
ment into a series of syllogisms, we shall arrive by more or fewer steps at
an ultimate syllogism, which will have for its major premise the principle,
or axiom, of the uniformity of the course of nature.*
It was not to be expected that in the case of this axiom, any more than
of other axioms, there should be unanimity among thinkers with respect to
the grounds on which it is to be received as true. I have already stated.^^
that I regard it as itself a generalization from experience. Others hold it f-
to be a principle which, antecedently to any verification by experience, we
garded as an illustration of them, failed, as I now saw, to bear them out. The real matter at
the bottom of the whole dispute, the different view we take of the function of the major prem-
ise, remains exactly where it was ; and so far was I from thinking that my opinion had
been fully "answered" and was' "untenable," that in the same edition in which I canceled
the note, I not only enforced the opinion by further arguments, but answered (though without
naming him) those of the Archbishop.
Por not having made this statement before, I do not think it needful to apologize. It would
be attaching very great importance to one's smallest sayings, to think a formal retractation req-
uisite every time that one falls into an eiTor. Nor is Archbishop Whately's well-earned fame
of so tender a quality as to require that in withdrawing a slight criticism on him I should have
been bound to offer a public amende for having made it.
* But though it is a condition of the validity of every induction that there be uniformity in
the course of nature, it is not a necessary condition that the uniformity should pervade all na-
ture. It is enough that it pervades the particular class of phenomena to which the induction
relates. An induction concerning the motions of the planets, or the properties of the magnet,
would not be vitiated though we were to suppose that wind and weather are the sport of
chance, provided it be assumed that astronomical and magnetic phenomena are under the
dominion of general laws. Otherwise the early experience of mankind would have rested on
a very weak foundation ; for in the infancy of science it could not be known that all phe-
nomena are regular in their course.
Neither would it be correct to say that every induction by which we infer any truth, implies
the general fact of uniformity as foreknown, even in reference to the kind of phenomena con-
cerned. It implies, either that this general fact is already known, or that we may now know
it : as the conclusion, the Duke of Wellington is mortal, drawn from the instances A, B, and
C, implies either that we have already concluded all men to be mortal, or that we are now en-
titled to do so from the same evidence. A vast amount of confusion and paralogism respect-
ing the grounds of Induction would be dispelled bj keeping in view these simple consider-
ations.
15
•226 INDUCTION.
are compelled by the constitution of our thinking faculty to assume as true.
Having so recently, and at so much length, combated a similar doctrine as
applied to the axioms of mathematics, by arguments which are in a great
measure applicable to the present case, I shall defer the more particular
discussion of this controverted point in regard to the fundamental axiom
of induction, until a more advanced period of our inquiry.* At present it
is of more importance to understand thoroughly the import of the axiom
itself. For the proposition, that the course of nature is uniform, possesses
rather the brevity suitable to popular, than the precision requisite in phil-
osophical language : its terms require to be explained, and a stricter than
their ordinary signification given to them, before the truth of the assertion
can be admitted.
§ 2. Every person's consciousness assures him that he does not always
«xpect uniformity in the course of events; he does not always believe that
the unknown will be similar to the known, that the future will resemble the
past. Nobody believes that the succession of rain and fine weather will be
the same in every future year as in the present. Nobody expects to have
the same dreams repeated every night. On the contrary, every body men-
tions it as something extraordinary, if the course of nature is constant, and
resembles itself, in these particulars. To look for constancy where con-
stancy is not to be expected, as for instance that a day which has once
brought good fortune will always be a fortunate day, is justly accounted
superstition.
The course of nature, in truth, is not only uniform, it is also infinitely va-
rious. Some phenomena are always seen to recur in the very same combi-
nations in which we met with them at first ; others seem altogether caprir
cious ; while some, which we had been accustomed to regard as bound
down exclusively to a particular set of combinations, we unexpectedly find
detached from some of the elements with which we had hitherto found
them conjoined, and united to others of quite a contrary description. To
an inhabitant of Central Africa, fifty years ago, no fact probably appeared
to rest on more imiform experience than this, that all human beings are
black. To Europeans, not many years ago, the proposition. All swans are
white, appeared an equally unequivocal instance of uniformity in the course
of nature. Further experience has proved to both that they were mistaken;
but they had to wait fifty centuries for this experience. During that long
time, mankind believed in a uniformity of the course of nature where no
such uniformity really existed.
According to the notion which the ancients entertained of induction, the
foregoing were cases of as legitimate inference as any inductions whatever.
In these two instances, in which, the conclusion being false, the ground of
inference must have been insufficient, there was, nevertheless, as much
ground for it as this conception of induction admitted of. The induction
of the ancients has been well described by Bacon, under the name of " In-
ductio per enumerationem simplicem, ubi nou reperitur instantia contradic-
toria." It consists in ascribing the character of general truths to all prop-
ositions which are true in every instance that we happen to know ot This
is the kind of induction which is natural to the mind when unaccustomed
to scientific methods. The tendency, which some call an instinct, and
which others account for by association, to infer the future from the-^ast,
* Infra, chap. xxi.
GROUND OF INDUCTION. 227
*he known from the unknown, is simply a habit of expecting that what has
been found true once or several times, and never yet found false, will be
found true again. Whether the instances are few or many, conclusive or
inconclusive, does not much affect the matter : these are considerations
which occur only on reflection ; the unprompted tendency of the mind is to
generalize its experience, provided this points all in one direction ; provided
■no other experience of a conflicting character comes unsought. The notion
-of seeking it, of experimenting for it, of interrogating nature (to use Ba-
boon's expression) is of much later growth. The observation of nature, by
-uncultivated intellects, is purely passive : they accept the facts which pre-
sent themselves, without taking the trouble of searching for more : it is a >i
-superior mind only which asks itself what facts are needed to enable it to
«ome to a safe conclusion, and then looks out for these. ^
,^But though we have always a propensity to generalize from unvarying
experience, we are not always warranted in doing so. Before we can be
at liberty to conclude that something is universally true because we have
never known an instance to the contrary, we must have reason to believe
that if there were in nature any instances to the contrary, we should have
known of tliem.^ This assurance, in the great majority of cases, we can not
have, or can have only in a very moderate degree. The possibility of hav-
ing it, is the foundation on which we shall see hereafter that induction by
simple enumeration may in some remarkable cases amount practically to
^^f^epf.* No such assurance, however, can be had, on any of the ordinary
.subjects of scientific inquiry. Popular notions are usually founded on in-
duction by simple enumeration ; in science it carries us but a little way.
We are forced to begin with it ; we must often rely on it provisionally, in
the absence of means of more searching investigation. But, for the accu-'
rate study of nature, we require a surer and a more potent instrument.
It was, above all, by pointing out the insufliciency of this rude and loose
■conception of Induction, that Bacon merited the title so generally awarded
to him, of Founder of the Inductive Philosophy. The value of his own con-
tributions to a more philosophical theory of the subject has certainly been
exaggerated. Although (along with some fundamental errors) his writings
contain, more or less fully developed, several of the most important princi-
ples of the Inductive Method, physical investigation has now far outgrown
the Baconian conception of Induction. Moral and political inquiry, indeed,
are as yet far behind that conception. The current and appi-oved modes
of reasoning on these subjects are still of the same vicious description
against which Bacon protested ; the method almost exclusively employed
by those professing to treat such matters inductively, is the very inductio
per enumerationem simplicem which he condemns ; and the experience
which we hear so confidently appealed to by all sects, parties, and interests,
is still, in his own emphatic words, mera palpatio.
§ 3. In order to a better understanding of the problem which the logi-
cian must solve if he would establish a scientific theory of Induction, let us
compare a few cases of incorrect inductions with others which are acknowl-
edged to be legitimate. Some, we know, which were believed for centuries
to be correct, were nevertheless incorrect. That all swans are white, can
not have been a good induction, since the conclusion has turned out errone-
ous. The experience, however, on which the conclusion rested, was genu-
* Infra, chap, xxi., xxii.
228 INDUCTION.
ine. From the earliest records, the testimony of the inhabitants of the
known world was unanimous on the point. The uniform experience, there-
fore, of the inhabitants of the known world, agreeing in a common result,
without one known instance of deviation from that result, is not always
sufficient to establish a general conclusion.
But let us now turn to an instance apparently not very dissimilar to this.
Mankind were wrong, it seems, in concluding that all swans were white :
are we also wrong, when we conclude that all men's heads grow above their
shoulders, and never below, in spite of the conflicting testimony of the natu-
ralist Pliny ? As there were black swans, though civilized people had exist-
ed for three thousand years on the earth without meeting with them, may
there not also be " men whose heads do grow beneath their shoulders," not-
withstanding a rather less perfect unanimity of negative testimony from
observers ? Most persons would answer 'No ; it was more credible that a
bird should vary in its color, than that men should vary in the relative po-
sition of their principal organs. And there is no doubt that in so- saying
they would be right: but to say why they are right, would be impossible,,
without entering more deeply than is usually done, into the true theory of
Induction.
Again, there are cases in which we reckon with the most unfailing confi-
dence upon uniformity, and other cases in which we do not count upon it
at all. In some we feel complete assurance that the future will resemble the
past, the unknown be precisely similar to the known. In others, however
invariable may be the result obtained from the instances which have been
obsprved, we draw from them no more than a very feeble presumption that
the like result will hold in all other cases. That a straight line is the short-
est distance between two points, we do not doubt to be true even in the re-
gion of the fixed stars.* When a chemist announces the existence and
properties of a newly-discovered substance, if we confide in his accuracy,
we feel assured that the conclusions he has arrived at will hold universally,
though the induction be founded but on a single instance. We do not
withhold our assent, waiting for a repetition of the experiment : or if we
do, it is from a doubt whether the one experiment was properlyMhade, not .
whether if properly made it would be conclusive. Here, then, is a general
law of nature, inferred without hesitation from a single instance; a uni-
versal proposition from a singular one. Now mark another case, and con-
trast it with this. Not all the instances which have been observed since
the beginning of the world, in support of the general proposition that all
crows are black, would be deemed a sufiicient presumption of the truth of
the proposition, to outweigh the testimony of one unexceptionable witness
who should affirm that in some region of the earth not fully explored, he
had caught and examined a crow, and had found it to be gray.
Why is a single instance, in some oases, sufficient for a complete induc-
tion, while in others, myriads of concurring instances, without a single ex-
ception known or presumed, go such a very little way toward establishing
a universal proposition ? Whoever can answer this question knows more
of the philosophy of logic than the wisest of the ancients, and has solved
the problem of induction.
* In strictness, wherever the present constitution of space exists ; which we have ample
reason to believe that it does in the region of the fixed stars.
LAWS OF NATURE. 229
CHAPTER IV.
OP LAWS OF NATURE.
§ 1; In the contemplation of that uniformity in the course of nature,
which is assumed in every inference" from experience, one of the first ob-
servations that present themselves is, that the uniformity in question is not
properly uniformity, but uniformities. The_general regalarity results from
the no-exiatenne of partial regularities. The (30urse oi'^nature in general is
constant, because the course of each of the various phenomena that com- ,
pose it is so. .4^^fi3lain-fact-invajdabLyjOccurajvhfinev£r:.cfiitaiii-^ ^"^ "4
stances are jBliesent^and does not qcour„wlieii_thfi3L-are absent^, the like is ^/.^^.^.-im^k!
true_of_anothep-faet ; -ahdTso on._ From these separate threads of j;onnec-
tion betwppn partfi of thp grpnt .^ole_HhicL!ffifiJifirm_nature,^gerjfiral lis-
6ueof_caiiiiectiQn.unavoidably_\veaves itself, by which the whole is held to-
getEer! If A is always accompanied by D, B by E, and C by F, it follows
that A B is accompanied by D E, A C by D F, B C by E F, and finally A
B C by D E F ; and thus the general character of regularity is produced,
which, along with and in the midst of infinite diversity, pervades all nature.
The first point, therefore, to be noted in regard to what is called the uni- *-■
formity of the course of nature, is, that it is itself a complex fact, com^
pounded of all the separate uniformities which exist in respect to single
phenomena. These various uniformities, when ascertained by what is re-
garded as a sufiicient induction, we call, in common parlance. Laws of Na- <'
ture. Scientifically speaking, that title is employed in a more restricted
sense, to designate the uniformities when reduced to their most simple ex-
pression. Thus in the illustration already employed, there were seven uni-
formities ; all of which, if considered suflBciently certain, would, in the more
lax application of the term, be called laws of nature. But of the seven,
three alone are properly distinct and independent: these being presup-
posed, the others follow of course. The first three, therefore, according to
the stricter acceptation, are called laws of nature ; the remainder not ; be-
cause they are in truth mere cases of the first three ; virtually included in
them ; said, therefore, to result from them : whoeveraffirms those three has
already affirmed all the rest.
To substitute real examples for symbolical ones, the following are three
uniformities, or call them laws of nature : the law that air has weight, the
law that pressure on a fluid is propagated equally in all directions, and the
law that pressure in one direction, not opposed by equal pressure in the
contrary direction, produces motion, which does not cease until equilibrium
is restored. From these three uniformities we should be able to predict
another uniformity, namely, the rise of the mercury in the Torricellia,n
tube. This, in the stricter use of the phrase, is not a law of nature. It is
the result of laws of nature. It is a case of each and every one of the
three laws : and is the only occurrence by which they could all be fulfilled.
If the mercury were not sustained in the barometer, and sustained at such
a height that the column of mercury were equal in weight to a column of
the atmosphere of the same diameter ; here would be a case, either of the
v(
V
230 INDUCTION.
^ jair not pressing upon the surface of the mercury with the force which is:
j. ^called its weight, or of the downward pressure on the mercury not being-
^ y propagated equally in an upward direction, or of a body pressed in one di-
v^ , rection and not in the direction opposite, either not moving in the direction
'x^-' in which it is pressed, or stopping before it had attained equilibrium. If
V '^ ~-Vwe knew, therefore, the three simple laws, but had never tried the Torricel-
f •> Han experiment, we might deduce its result from those laws. The known
■ i i / ■weight of the air, combined with the position of the apparatus, would
y .^t yl^ring the mercury within the first of the three inductions ; the first induc-
'' f' jV tion would bring it within the second, and the second within the third, in
yf y the manner which we characterized in treating of Ratiocination. We should '
p thus come to know the more complex uniformity, independently of specific:
/ „ experience, through our knowledge of the simpler ones from which it results;.
Nj J though, for reasons which will appear hereafter, verification by specific ex-
^ perience would still be desirable, and might possibly be indispensable.
Complex uniformities which, like this, are mere cases of simpler ones,.
and have, therefore, been virtually affirmed in affirming those, may with
propriety be called laws, but can scarcely, in the strictness of scientific-
speech, be termed Laws of Nature. .. It is the custom in science, whereverK^
regularity of any kind can be traced, to call the geileral proposition whion
expresses the nature of that regularity, a law^ as when, in mathematics,,
we speak of the law of decrease of the successive terms of a converging
/series. But the expression law of nature has generally been employed
^ with a sort of tacit reference to the original sense of the word law, namely,
the expression of the will of a superior. When, therefore, it appeared that
' j-any of the uniformities which were observed in nature, would result spon-
^ '-'taneously from certain other uniformities, no separate act of creative will
>v^ being supposed necessary for the production of the derivative uniformities,.
^v'J^hese have not usually been spoken of as laws of nature. According to
\vs5^ J. one mode of expression, the question, What are the laws of nature? may
V (5 be stated thus : What are the fewest and simplest assumptions, which be-
i^J- V, «;rv> ing granted, the whole existing order of nature would result ?< Another
J xj ^mode of stating it would be thus : What are the fewest general proposi-
X I ,f tions from which all the uniformities which exist in the universe might be
^ "£ deductively inferred?!^
I V n^ Every great advance which marks an epoch in the progress of science,
.^y J has consisted in a step made toward the solution of this problem. Even a
tO. simple colligation of inductions already made, without any fresh extension
j\/ of the inductive inference, is already an advance in that direction. When
. ^ Kepler expressed the regularity which exists in the observed motions of
/^ the heavenly bodies, by the three general propositions called his laws, he,
^ / in so doing, pointed out three simple suppositions which, instead of a much
^ greater number, would suffice to construct the whole scheme of the heav-
>j enly motions, so far as it was known up to that time. A similar and still
greater step was made when these laws, which at first did not seem to be
included in any more general truths, were discovered to be cases of the
three laws of motion, as obtaining among bodies which mutually tend to-
ward one another with a certain force, and have had a certain instantaneoa*
impulse originally impressed upon them. After this great discovery, Kep-
ler's three propositions, though still called laws, would hardly, by any per-
son accustomed to use language with precision, be termed laws of nature :
that phrase would be reserved for the simpler and more general laws inta
which Newton is said to have resolved them.
/
LAWS OF NATUEE. 231
' According to this language, every well-grounded inductive generaliza- '
tion is either a law of nature, or a result of laws of nature, capable, if those-
laws are known, of being predicted from them. -^ And the problem of In- '
ductive Logic may be summed up in two questions : how to ascertain the-
laws of nature ; and how, after having ascertained them, to follow them
into their results. On the other hand, we must not suffer ourselves to im-
agine that this mode of statement amounts to a real analysis, or to any
thing but a mere verbal transformation of the problem ; for the expression,.
Laws of Nature, means nothing but the unifoi-mities which exist among
natural phenomena) or, in other words, the results of induction), when re-
duced to their simplest expression. It is, however, something to have ad-
vanced so far, as to see that the study of nature is the study of laws, not a,
law ; of uniformities, in the plural number : that the different natural phe-
nomena have their separate rules or modes of taking place, which, though
much intermixed and entangled with one another, may, to a certain extent,,
be studied apart: that (to resume our former metaphor) the regulai'ity
which exists in nature is a web composed of distinct threads, and only to
be understood by tracing each of the threads separately ; for which pur-
pose it is often necessary to unravel some portion of the web, and exhibit
the fibres apart. The rules of experimental inquiry are the contrivances
for unraveling the web.
§ 2. In thus attempting to ascertain the general order of nature by as-
certaining the particular order of the occurrence of each one of the phe-
nomena of nature, the most scientific proceeding can be no more than an im.
proved form of that which was primitively pursued by the human under-
standing, while undirected by science. When mankind first formed the
idea of studying phenomena according to a stricter and surer method than,
that which they had in the first instance spontaneously adopted, they did
not, conformably to the well-meant but impracticable precept of Descartes,,
set out from the supposition that nothing had been already ascertained.
Many of the uniformities existing among phenomena are so constant, and
so open to observation, as to force themselves upon involuntary recognition.
Some facts are so perpetually and familiarly accompanied by certain oth-
ers, that mankind learned, as children learn, to expect the one where they
found the other, long before they knew how to put their expectation into
words by asserting, in a proposition, the existence of a connection between
those phenomena. No science was needed to teach that food nourishes,,
that water drowns, or quenches thirst, that the sun gives light and heat,,
that bodies fall to the ground. The first scientifixLinnui.r<?.rs..assumfid. these >i
Mdjhejikelas-kiiowii Jruths^ and^aet-Ont ..frQm tbem-tfl-discover others
which were unknown,: nor were they wrong in so _daiog,.S.ubject, however,
as thev afterwardJiegan to see,.lo an ^ulterior revisioaijf.Jij^eJimntaneous
generalizations themselves, when the progress pf^owledge pointed out
limits to TRemToF'showed" their truth, to be contingent on some circum-
stance tfor ongmallylattended to. It will appear, I think, from the subse-
qtleBrparFofour inquiry, that there is no logical fallacy in this mode of
proceeding ; but we may see already that any other mode is rigorously im-
practicable: since it is impossible to^frame any scientific method of induc-
tion, or test of the correctness of inductions, unless on the hypothesis that,
some inductions deserving of reliance have been already made.
Let us revert, for instance, to one of our former illusti-ations, and con-
sider why it is that, with exactly the same amount of evidence, both ne^a-
232 INDUCTION.
tive and positive, we did not reject the assertion tliat there are black
swans, while we should refuse credence to any testimony which asserted
that there were men wearing their heads underneath their shoulders. The
iirst assertion was more credible than the latter. But why more credible ?
So long as neither phenomenon had been actually witnessed, what reason
was there for finding the one harder to be believed than the other ? Ap-
parently because there is less constancy in the colors of animals, than in
the general structure of their anatomy. But how do we know this?
Doubtless, from experience, jj; appears, then, that we need experience to K
informjisjn j^hatjdegr£e,_anJjS^5S5JZrai^^
IS to be relied_on.. Experience must be consulted in ordeFto learn irom it
under what circumstances arguments from it will be valid. We have no
ulterior test to which we subject experience in general; but we make ex-
perience its own test. Experience testj^eSjJhj;t^ amongtheuniformities
which it exhibits or seems to exhibit, some are more tobe relied on than
others ; and uniformity, therefore, may be,pi:fi§iiffl£dfcirom_any^Ji2Btt3ft»m-
ber of instances, with a greater degree of assuraii£g,jn_proportion as the
«ase belongs to a class in which the uniformities h^e^hithertolbeenTound
more uniform. "^ " ~ X
Thisjnode_oXcqn:ecting_XU]£_gmi&raJiza^^ a nar-
\^ in practice,jsjhe_real typeofjscifiDdtificInjductiQn. , All that art can do is
y ^ but to give accuracy and precision to this process, and adapt it to all var
y^op^'ieties of cases, without any essential alteration in its principle. )^
X y There are of course no means of applying such a test as that above de-
(A ^ ascribed, unless we already possess a general knowledge of the prevalent
S / -'character of the uniformities existing throughout nature. The indispen-|C
^ sable foundation, therefore, of a scientific formula of induction, must be a
^ survey of the inductions to which mankind have been conducted in unsci-
entific practice ; with the special purpose of asceitaining what kinds of
"V^ uniformities have been found perfectly invariable, pervading all nature,
y ^ -and what are those which have been found to vary with difference of time,
y / place, or other changeable circumstances. f.
V'\. X/^ § ^' '^^^ necessity of such a survey is confirmed by the consideration, ^
(4.^ Y^'?^* *^^ stronger inductions are the touch-stone to which we always en-
' ^\/. #eavor to bring the weaker. If we find any means of deducing one of
jT ^fe(/the less strong inductions from stronger ones, it acquires, at once, all the,'']
^ //f strength of those from which it is deduced ; .and^even adds^to that strgngth; (y
vj ^^ince the independent experience on which the weaker indHCtionpreviously
"y j^ rested, becomes additional evidence of the truth of the better established
W^ \law in which it is now found to be included. We may have inferred, from
/
historical evidence, that the uncontrolled power of a monarch, of an aris-
tocracy^^or of the majority, will often be abused : but we are entitled to
rely on this generalization with much greater assurance when it is shown
to be a corollary from still better established facts ; the very low degree
-of elevation of character ever yet attained by the average of mankind, and
the little efiicacy, for the most part, of the modes of education hitherto
practiced, in maintaining the predominance of reason and conscience over
the selfish propensities. It is at the same time obvious that even these
more general facts derive an accession of evidence from the testimony
which history bears to. the effects of despotism. The_alronginduction be-
comes stiUstrongei- when a weaker one has been boundiip wit.TPiT: ' —
Y OiTtlTe'olfisr'ITanHTifan induction conflicts with stronger inductions,
LAWS OF NATUIIE. 233
or with conclusions capable of being correctly deduced from them, then,
unless on reconsideration it should appear that some of the strongei' induc-
tions have been expressed with greater universality than their evidence
warrants, the weaker one must give way/ The opinion so long prevalent'*^
that a comet, or any other unusual appearance in the heavenly regions, was
the precursor of calamities to mankind, or to those at least who witnessed
it; the belief in the veracity of the oracles of Delphi or Dodona; the i-eli-
ance on astrology, or on the weather-prophecies in almanacs, were doubt-
less inductions supposed to be grounded on experience :* and faith in such
delusions seems quite capable of holding out against a great multitude of
failures, provided it be nourished by a reasonable number of casual coinci-
dences between the prediction and the event. What has really put an end
to these insufficient inductions, is their inconsistency with the stronger in-
ductions subsequently obtained by scientific inquiry, respecting the causes
on which terrestrial events really depend ; and where those scientific truth&
have not yet penetrated, the same or similar delusions still prevail.
K It^ay be affirmed^ as, a general principle,_that_all inductionH,_wheth<>r^^
stroQg^rJEeak, which can .be.coanfii;lMJbir-raiiQiinatiQn, m^
oToBe anQtiber ; while any which lead ilaductively to consequences that are
iDCompatihle,,become mutually eachjother's test, showing that piae or ather
must.be given up, or at.leastmore guardedly expuesied. In the'case of
inductions which confirm each other, the one which becomes a conclusion
from ratiocination rises to at least the level of certainty of the weakest of
those from which it is deduced ; while in general all are more or less in-
^ creased in certainty.< Thus the Torricellian experiment, though a mere
case of three more general laws, not only strengthened greatly the evidence
on which those laws resNied, but converted one of them (the weight of the
atmosphere) from a still doubtful generalization into a completely estab'
lished doctrine.
^ If. then, a survey of tbo. nnifnrpijtjpa^ wjiinlT_hnyp hoon gfir-ortgino/l to ex-
ist in nature, should point out some which, as far^sanjjiurnan purpose re-
IliyiSL^ciiflj!} ty^JBaX-bs. ,consijdm:ed quite certam^andTquitejiniyei-si^Iihen
by means of these uniformities we may be able toraisejnultitudes^of other
iMuctjgKS'to the~samypointl.il tHe scale. For if we can ^how, with re-
* Dr. Whewell (Phil, of Discern., p. 246) will not allow these and similar erroneous judg-
ments to be called Inductions; inasmuch as such superstitious fancies "were not collected
from the facts by seeking a law of their occun-ence, but were suggested by an imagination of
the anger of superior powers, shown by such deviations from the ordinary course of nature. "
I conceive the question to be, not in what manner these notions were at first suggested, but
by what evidence they have, from time to time, been supposed to be substantiated. If the be-
lievers in these erroneous opinions had been put on their defense, they would have referred
to experience : to the comet which preceded the assassination of Julius Caesar, or to oracles
and other prophecies known to have been fulfilled. It is by such appeals to facts that all
analogous superstitions, even in our day, attempt to justify themselves ; the supposed evi-
dence of experience is necessary to their hold on the mind. I quite admit that the influence
of such coincidences would not be what it is, if strength were not lent to it by an antecedent
presumption ; but this is not peculiar to such cases ; preconceived notions of probability form
part of the explanation of many other cases of belief on insuflfieient evidence. The a priori
prejudice does not prevent the erroneous opinion from being sincerely regarded as a legiti-
mate conclusion from experience ; though it improperly predisposes the mind to that inter-
pretation of experience.
Thus much in defense of the sort of examples objected to. But it would be easy to pro-
duce instances, equally adapted to the purpose, and in which no antecedent prejudice is at all
concerned. "For many ages," says Archbishop Whately, "all farmers and gardeners were
firmly convinced — and convinced of their knowing it by experience — that the crops would
never turn out good unless the seed were sown during the increase of the moon." This was
induction, but bad induction; just as a vicious syllogism is reasoning, but bad reasoning.
234 INDUCTION.
spect to any inductive inference, that either it must be true, or one of these
•certain and universal inductions must admit of an exception ; the former
generalization will attain the same certainty, and indefeasibleness within
the bounds assigned to it, which are the attributes of the latter. It will
be proved to be a law ; and if not a result of other and simpler laws, it will
be a law of nature.
There are such certain and universal inductions ; and it is because there
are such, that a Logic of Induction is possible. ,
I
CHAPTER V.
OP THE LAW OF UNIVERSAL CAUSATION.
The phenomena of nature exist in two distinct relations to one an-
otfi^er; that of simultaneity, and that of succession. Every^ phenomenon is
related, in a uniform manner, to some phenomena that co-exist with it, and
to some that have preceded and will follow it^
Of the uniformities which exist among synchronous phenomena, the most
important, on every account, are the laws of number ; and next to them
those of space, or,- in other words, of extension and figure. The laws of
number are common to synchronous and successive phenomena. That two
and two make four, is equally true whether the second two follow the first
two or accompany them. It is as true of days and years as of feet and
inches. The laws of extension and figure (in other words, the theorems
of geometry, from its lowest to its highest branches) are, on the contrary,
laws of simultaneous phenomena only. The various parts of space, and of
the objects which are said to fill space, co-exist ; and the unvarying laws
which are the subject of the science of geometry, are an expression of the
mode of their co-existence.
This is a class of laws, or in other words, of uniformities, for the com-
prehension and proof of which it is not necessary to suppose any lapse of
time, any variety of facts or events succeeding one another. The proposi-
tions of geometry are independent of the succession of events. All things
which possess extension, oi', in other words, which fill space, are subject to
-geometrical laws. Possessing extension, they possess figure ; possessing
figure, they must possess some figure in particular, and have all the proper-
ties which geometry assigns to that figure. If one body be a sphere and
-another a cylinder, of equal height and diameter, the one will be exactly
two-thirds of the other, let the nature and quality of the material be what
it will. Again, each body, and each point of a body, must occupy some
place or position among other bodies ; and the position of two bodies relar
tively to each other, of whatever nature the bodies be, may be unerringly
inferred from the position of each of them relatively to any third body.
In the laws of number, then, and in those of space, we recognize in the
most unqualified manner, the rigorous universality of which we are in
■quest. Those laws have been in all ages the type of certainty, the standard
•of comparison for all inferior degrees of evidence. Their invariability is so
perfect, that it renders us unable even to conceive any exception to them ;
and philosophers have been led, though (as I have endeavored to show) er-
roneously, to consider their evidence as lying not in experience, but in the
original constitution of the intellect. If, therefore, from the laws of space
and number, we were able to deduce uniformities of any other description,
LAW OF CAUSATION. 235
this would be conclusive evidence to us that those other uniformities pos-
sessed the same rigorous certainty. But this we can not do. From laws
■of space and number alone, nothing can be deduced but law^s of space and
■number.
ycOi all truths relating to phenomena, the most valuable to us are those
which relate to the order of their succession. On a knowledge of these is
founded every reasonable anticipation of future facts, and whatever power
~we possess of influencing those facts to our advantage,^' Even the laws of r
geometry are chiefly of practical importance to us as being a portion of the
premises from which the order of the succession of phenomena may be in-
terred. Inasmuch as the motion of bodies, the action of forces, and the
propagation of influences of all sorts, take place in certain lines and over
•definite spaces, the properties of those lines and spaces are an important
part of the laws to which those phenomena are themselves subject. Again,
. motions, forces, or other influences, and times, are numerable quantities ;
iind the properties of number are applicable to them as to all other things.
But though the laws of number and space are important elements in the
ascertainment of uniformities of succession, they can do nothing toward it
when taken by themselves. They can only be made instrumental to that
purpose when we combine with them additional premises, expressive of
uniformities of succession already known. By taking, for instance, as
premises these propositions, that bodies acted upon by an instantaneous
force move with uniform velocity in straight lines ; that bodies acted upon
by a continuous force move with accelerated velocity in straight lines ; and
that bodies acted upon by two forces in different directions move in the
diagonal of a parallelogram, whose sides represent the direction and quan-
tity of those forces ; we may by combining these truths with propositions
relating to the properties of straight lines and of parallelograms (as that a
triangle is half a parallelogram of the same base and altitude), deduce an-
other important uniformity of succession, viz., that a body moving round
a centre 'of force describes areas proportional to the times. But unless
there had been laws of succession in our premises, there could have been
no truths of succession in our conclusions. A similar remark might be
extended to every other class of phenomena really peculiar ; and, had it
been attended to, would have prevented many chimerical attempts at dem-
onstrations of the indemonstrable, and explanations which do not explain.
/O It is not, therefore, enough for us that the laws of space, which are only
laws of simultaneous phenomenon, and the laws of number, which though
true of successive phenomena do not relate to their succession, possess the
rigorous certainty and universality of which we are in search. We must
endeavor to find some law of succession which has those same attributes,
and is therefore fit to be made the foundation of processes for discovering, ^
and of a test for verifying, all other uniformities of succession. This fun-
damental law must resemble the truths of geometry in their most remark-
able peculiarity, that of never being, in any instance whatever, defeated or
suspended by any change of circumstances. ^^
Now among all those uniformities in the succession of phenomena, which
■common observation is sufiicient to bring to light, there are very few which \
ihave any, even apparent, pretension to this rigorous indefeasibility : and of ^
.those few, one only has been found capable of completely sustaining it. In ,
1;hat one, however, we recognize a law which is universal also in another
sense ; it is co-extensive with the entire field of successive phenomena, all I
instances whatever of succession being examples of it. This law is the
236 INDUCTION.
I Law of Causation. The ti-uth that every fact which has a beginning has a
• cause, is co-extensive with human experience.*;'
I This generalization may appear to some minds not to amount to much^
I since after all it asserts only this: "it is a law, that every event depends-
on some law :" " it is a law, that there is a law for every thing." We must
not, however, conclude that the generality of the principle is merely verbal ;,
I it will be found on inspection to be no vague or unmeaning assertion, but
a most important and really fundamental truth.
§ 2. The notion of Cause being the root of the whole theory of Induc-
tion, it is indispensable that this idea should, at the very outset of our in-
quiry, be, with the utmost practicable degree of precision, fixed and deter-
mined. If, indeed, it were necessary for the purpose of inductive logie
that the strife should be quelled, which has so long raged among the differ-
ent schools of metaphysicians, respecting the origin and analysis of our idea •
of causation ; the promulgation, or at least the general reception, of a true
theory of induction, might be considered desperate for a long time to come.
But the science of the Investigation of Truth by means of Evidence, is i
happily independent of many of the controversies which perplex the sci-
ence of the ultimate constitution of the human mind, and is under no ne-
cessity of pushing the analysis of mental phenomenon to that extreme
limit which alone ought to satisfy a metaphysician.
,J I premise, then, that when in the course of this inquiry I speak of the
cause of any phenomenon; I do not mean a cause which' is not itself a phe-
nomenon; I make no research into the ultimate or ontological cause of
any thing. To adopt a distinction familiar in the writings of the Scotch
! metaphysicians, and especially of Reid, the causes with which I concern
■^' myself are not efficient, hut physical causes. They are causes in that sense
' alone, in which one physical fact is said to be the cause of another. Of
the efficient causes of phenomena, or whether any such causes exist at all>
I am not called upon to give an opinion. The notion of cansation'is deem-
ed, by the schools of metaphysics most in vogue at the present moment, to
imply a mysterious and most powerful tie, such as can not, or at least does
not, exist between any physical fact and that other physical fact on which
it is invariably consequent, and which is popularly termed its cause : and
thence is deduced the supposed necessity of ascending higher, into the es-
sences and inherent constitution of things, to find the true cause, the cause
which is not only followed by, but actually produces, the effect. No such
necessity exists for the purposes of the present inquiry, nor will any such
i doctrine be found in the following pages. ''The only notion of a cause,/
which the theory of induction requires, is such a notion as can be gained ■
I j from experience'. The Law of Causation, the recognition of which is the
main pillar of inductive science, is but the familiar truth, that invariability
of succession is found by observation to obtain between every fact in na-
■j, ture and some other fact which has preceded it ; independently of all, con-
;! siderations respecting the ultimate mode of production of phenomena, and
i of every other question regarding the nature of "Things in themselves." v/
Between the phenomena, then, which exist at any instant, and the phe-
nomena which exist at the succeeding instant, there is an invariable order
of succession ; and, as we said in speaking of the general uniformity of tha
course of nature, this web is composed of separate fibres ; this collective
order is made up of particular sequences, obtaining invariably among the-
separate parts. To certain facts, certain facts always do, and, as we be-
LAW OF CAUSATION. 237
lieve, will continue to, succeed. The invariable antecedent is termed the ;
«ause ; the invariable consequent, the effect. And the universality of the "^
law of causation consists in this, that every consequent is connected in this ;
manner with some particular antecedent, or set of antecedents. Let the '^
fact be what it may, if it has begun to exist, it was preceded by some fact /
or facts, with which it is invariably connected. For every event there ex-
ists some combination of objects or events, some given concurrence of cir-
cumstances, positive and negative, the occurrence of which is always fol-
lowed by that phenomenon. We may not have found out what this con-
currence of circumstances may be ; but we never doubt that there is such
a one, and that it never occurs without having the phenomenon in question
as its effect or consequence. On the universality of this truth depends the
possibility of reducing the inductive process to rules. The undoubted as-
surance we have that there is a law to be found if we only knew how to
find it, will be seen presently to be the source from which the canons of
the Inductive Logic derive their validity.
§ 3. It is seldom, if ever, between a consequent and a single antecedent,
that this invariable sequence subsists. It is usually between a consequent
and the sum of several antecedents ; the concurrence of all of them being
requisite to produce, that is, to be certain of being followed by, the conse- -
~:^uent.'( In such cases it is very common to single out one only of the an- '
tecedents under the denomination of Cause, calling the others merely Con- ,
ditions. Thus, if a person eats of a particular dish, and dies in consequence,
that is, would not have died if he had not eaten of it, people would be apt
to say that eating of that dish was the cause of his death. There needs
not, however, be any invariable connection between eating of the dish and
death ; but there certainly is, among the circumstances which took place,
some combination or other on which death is invariably consequent : as,
for instance, the act of eating of the dish, combined, with a particular bod-
ily constitution, a particular state of present health, and perhaps even a
certain state of the atmosphere; the whole of which circumstances per-
haps constituted in this particular case the conditions of the phenomenon,
or, in other words, the set of antecedents which determined it, and but for ,
■which it would not have happened. ' The real Cause, is the whole of these '
antecedents ; and we have, philosophically speaking, no right to give the \
name of cause to one of them, exclusively of the others. What, in the •
Kjase we have supposed, disguises the incorrectness of the expression, is
this : that the various conditions, except the single one of eating the food,
were not events (that is, instantaneous changes, or successions of instan- '\
taneous changes) but states, possessing more or less of permanency ; and iS
might therefore have preceded the effect by an indefinite length of dura- :
tion, for want of the event which was requisite to complete the required
concurrence of conditions : while as soon as that event, eating the food, ;
occurs, no other cause is waited for, but the effect begins immediately to
' take place : and hence the appearance is presented of a more immediate
and close connection between the effect and that one antecedent, than be-
tween the effect and the remaining conditions. But though we may think V
proper to give the name of cause to that one condition, the fulfillment of
which completes the tale, and brings about the effect without further de-
lay; this condition has really no closer relation to the effect than any .of
the other conditions has. All the conditions were equally indispensable to
the production of the consequent; and the statement of the cause is incom-
^38 INDUCTION.
plete, unless in some shape or other we introduce them all. A man takes
mercury, goes out-of-doors, and catches cold. We say, perhaps, that the
cause of his taking cold was exposure to the air. It is clear, however,
that his having taken mercury may have been a necessary condition of
his catching cold ; and though it might consist with usage to say that the
cause of his attack was exposure to the air, to be accurate we ought to
say that the cause was exposure to the air while under the effect of mer-
cury.
If we do not, when aiming at accuracy, enumerate all the conditions, it
is only because some of them will in most cases be understood without
being expressed, or because for the purpose in view they may without
detriment be overlooked. For example, when we say, the cause of a man's
death was that his foot slipped in climbing a ladder, we omit as a thing
unnecessary to be stated the circumstance of his weight, though quite as
! indispensable a condition of the effect which took place. When we say
\ that the assent of the crown to a bill makes it law, we mean that the as-
; sent, being never given until all the other conditions are fulfilled, makes up
ithe sum of the conditions, though no one now regards it as the principal
i'one. When the decision of a legislative assembly has been determined
■ by the casting vote of the chairman, we sometimes say that this one person
was the cause of all the effects which resulted from the enactment. Yet
•we do not really suppose that his single vote contributed more to the re-
sult than that of any other person who voted in the aflSrinative ; but, for
the purpose we have in view, which is to insist on his individual responsi-
bility, the part which any other person had in the transaction is not ma-
terial.
'^ ,^ In all these instances the fact which was dignified with the name of
■'^ cause, was the one condition which came last into existence. But it must
\ not be supposed that in the employment of the term this or any other rule
is always adhered to. Nothing can better show the absence of any scien-
tific ground for the distinction between the canse of a phenomenon and its
conditions, than the capricious manner in which we select from among the
conditions that which we choose to denominate the cause. However nu-
merous the conditions may be, there is hardly any of them which may not,
: according to the purpose of our immediate discourse, obtain that nominal
I pre-eminence. This will be seen by analyzing the conditions of some one
familiar phenomenon. For example, a stone thrown into water falls to the
bottom. What are the conditions of this event? In the first place there
must be a stone, and water, and the stone must be thrown into the water j
but these suppositions forming part of the enunciation of the phenomenon
itself, to include them also among the conditions would be a vicious tautol-
ogy ; and this class of conditions, therefore, have never received the name
of cause from any but the Aristotelians, by whom they were called the mor
terial cause, causa materialis. The next condition is, there must be an
earth : and accordingly it is often said, that the fall of a stone is caused by
the earth ; or by a power or property of the earth, or a force exerted by the
earth, all of which are merely roundabout ways of saying that it is caused
by the earth ; or, lastly, the earth's attraction ; which also is only a technical
mode of saying that the earth causes the motion, with the additional par-
ticularity that the motion is toward the earth, which is not a character of
the cause, but of the effect. Let us now pass to another condition. It is
not enough that the earth should exist; the body nlust be within that dis-
tance from it, in which the earth's attraction preponderates over that of any
LAW OF CAUSATION. 23»
other body. Accordingly we may say, and the expression would be con-
fessedly correct, that the cause of the stone's falling is its being within the
* y>here of the earth's attraction. "We proceed to a further condition. The
stone is immersed in water : it is therefore a condition of its reaching the
ground, that its specific gravity exceed that of the surrounding fluid, or in
other words that it surpass in weight an equal volume of water. Accord-
ingly any one would be acknowledged to speak correctly who said, that the
cause of the stone's going to the bottom is its exceeding in specific gravity
the fluid in which it is immersed.
v^Thus we see that each and every condition of the phenomenon may be
taken in its turn, and, with equal propriety in common parlance, but with
equal impropriety in scientific discourse, may be spoken of as if it were the
jjentire cause. And in practice, that particular condition is usually styled
the cause, whose share in the matter is superficially the most conspicuous,
or whose requisiteness to the production of the effect we happen to be in-
sisting on at the moment. So great is the force of this last consideration,
that it sometimes induces us to give the name of cause even to one of the
negative conditions. We say, for example. The army was surprised be- ;
cause the sentinel was off his post. But since the sentinel's absence was r
not what created the enemy, or put the soldiers asleep, how did it cause
them to be surprised ? All that is really meant is, that the event would '
not have happened if he had been at his duty. His being off his post was ■
no producing cause, but the mere absence of a preventing cause : it was
simply equivalent to his non-existence. From nothing, from a mere nega- \
tion, no consequences can proceed, 'jf All effects are connected, by the law ?
of causation, with some set oi positive conditions; negative ones, it is true, |
being almost always required in addition. In other words, every fact or ''
phenomenon which has a beginning, invariably arises when some certain 1
combination of positive facts exists, provided certain other positive facts :
do not exist. |v
■i There is, no doubt, a tendency (which our first example, that of death
from taking a particular food, sufficiently illustrates) to associate the idea
of causation with the proximate antecedent eve9it, rather than with any of
the antecedent states, or permanent facts, which may happen also to be
conditions of the phenomenon ; the reason being that the event not only
exists, but begins to exist immediately previous ; while the other condi-
-^ tions may have pre-existed for an indefinite time. And this tendency
shows itself very visibly in the different logical fictions which are resorted
to, even by men of science, to avoid the necessity of giving the name of
cause to any thing which had existed for an indeterminate length of time
before the effect. Thus, rather than say that the earth causes the fall of
bodies, they ascribe it to a force exerted by the earth, or an attraction by
the earth, abstractions which they can represent to themselves as exhausted
by each effort, and therefore constituting at each successive instant a fresh
fact, simultaneous with, or only immediately preceding, the effect. Inas-i
much as the coming of the circumstance which completes the asserablagel
of conditions, is a change or event, it thence happens that an event is al-
ways the antecedent in closest apparent proximity to the consequent : and |
this may account for the illusion which disposes us to look upon the*prox-'
imate event as standing more peculiarly in the position of a cause than any '
of the antecedent states. But even this peculiarity, of being in closer prox-
imity to the effect than any other of its conditions, is, as we have already
Been, far from being necessary to the common notion of a cause; with
A ' ' i
:'fi
1 '■-•
1 Cc- .-'J..
■■- -r ' ' '
240 INDUCTION.
which notion, on the contrary, any one of the conditions, either positive or
negative, is found, on occasion, completely to accord.*
* The assertion, that any and every one of the conditions of a phenomenon may be and is, on
some occasions and for some purposes, spoken of as the cause, has been disputed by an intel-
ligent reviewer of this work in the Prospective Review (the predecessor of the justly esteemed
National Review'), who maintains that "we always apply the word cause rather to that ele-
ment in the antecedents which exercises force, and which would tend at all times to produce
the same or a similar effect to that which, under certain conditions, it would actually pro-
duce." And he says, that "every one would feel" the expression, that the cause of a surprise
was the sentinel's being off his post, to be incorrect ; but that the " allurement or force which
drew him off his post, might be so called, because in doing so it removed a resisting power
which would have prevented the surprise." I can not think that it would be wrong to say,
that the event took place because the sentinel was absent, and yet right to say that it took
place because he was bribed to be absent. Since the only direct effect of the bribe was his
absence, the bribe could be called the remote cause of the surprise, only on the supposition
that the absence was the proximate cause ; nor does it seem to me that any one (who had
not a theory to support) would use the one expression and reject the other.
The reviewer observes, that when a person dies of poison, his possession of bodily organs is
a necessary condition, but that no one would ever speak of it as the cause. I admit the fact;
^ but I believe the reason to be, that the occasion could never arise for so speaking of it ; for
, when in the inaccuracy of common discourse we are led to speak of some one condition of a
phenomenon as its cause, the condition so spoken of is always one which it is at least possi-
ble that the hearer may require to be informed of The possession of bodily organs is a
known condition, and to give that as the answer, when asked the cause of a person's death,
would not supply the information sought. Once conceive that a doubt could exist as to his
having bodily organs, or that he were to be compared with some being who had them not,
and cases may be imagined in which it might be said that his possession of them was the
cause of his death. If Faust and Mephistopheles together took poison, it might be said that
j Faust died because he was a human being, and had a body, while Mephistopheles survived
because he was a spirit.
It is for the same reason that no one (as the reviewer remarks) " calls the cause of a leap,
the muscles or sinews of the body, though they are necessary conditions ; nor the cause of a
self-sacrifice, the knowledge which was necessary for it ; nor the cause of writing a book, that
a man has time for it, which is a necessary condition." These conditions (besides that they
are antecedent states, and not proximate antecedent events, and are therefore never the con-
' ditions in closest apparent proximity to the effect) are all of them so obviously implied, that it
is hardly possible there should exist that necessity for insisting on them, which alone gives
occasion for speaking of a single condition as if it were the cause. Wherever this necessity
exists in regard to some one condition, and does not exist in regard to any other, I 'conceive
that it is consistent with usage, when scientific accuracy is not aimed at, to apply the name
cause to that one condition. If the only condition which can be supposed to be unknown is
a negative condition, the negative condition may be spoken of as the cause. It might be said
that a person died for want of medical advice : though this would not be likely to he said, un-
less the person was already understood to be ill, and in order to indicate that this negative cir-
cumstance was what made the illness fatal, and not the weakness of his constitution, or the
original virulence of the disease. It might be said that a person was drowned because he
could not swim ; the positive condition, namely, that he fell into the water, being already im-
plied in the word drowned. And here let me remark, that his falling into the water is. in
this case the only positive condition : all the conditions not expressly or virtually included in
this (as that he could not swim, that nobody helped him, and so forth) are negative. Yet, if
it were simply said that the cause of a man's death was falling into the water, there would be
quite as great a sense of impropriety in the expression, as there would be if it were said that
the cause was his inability to swim ; because, though the one condition is positive and the oth-
er negative, it would be felt that neither of them was sufficient, without the other, to produce
death.
With regard to the assertion that nothing is termed the cause, except the element which
exerts active force ; I waive the question as to the meaning of active force, and accepting the
phrase.in its popular sense, I revert to a former example, and I ask, would it be more agree-
able to custom to say that a man fell because his foot slipped in climbing a ladder, or that he
' fell because of his weight ? for his weight, and not the motion of his foot, was the active force
which determined his fall. If a person walking out in a frosty day, stumbled and fell, it
might be said that he stumbled because the ground was slippery, or because he was not suf-
ficiently careful : but few people, I suppose, would say, that he stumbled because he walked.
i Yet the only active force concerned was that which he exerted in walking : the others were
LAW OF CAUSATION. 241
_ The cause, then, philosophically speaking, is the sum total of the condi- f
tions, positive and negative taken together ; the whole of the contingencies /
of every description, which being realized, the consequent invariably fol- I
lows./ The negative conditions, however, of any phenomenon, a special ,f
enumeration of which would generally be very prolix, may be all summed
up under one head, namely, the absence of preventing or counteracting
causesK The convenience of this mode of expression is mainly grounded
on the fact, that the effects of any cause in counteracting another cause
may in most cases be, with strict scientific exactness, regarded as a mere
extension of its own proper and separate effects. If gravity retards the
upward motion of a projectile, and deflects it into a parabolic trajectory,
it produces, in so doing, the very same kind of effect, and even (as mathe-
maticians know) the same quantity of effect, as it does in its ordinary op-
eration of causing the fall of bodies when simply deprived of their support.
If an alkaline solution mixed with an acid destroys its sourness, and pre-
vents it from reddening vegetable blues, it is because the specific effect of
the alkali is to combine with the acid, and form a compound with totally
y different qualities. This property, which causes of all descriptions possess,
of pi-eventing the effects of other causes by virtue (for the most pai-t) of
the same laws according to which they produce their own,* enables us, by
establishing the general axiom that all causes are liable to be counteracted
in their effects by one another, to dispense with the consideration of nega-,
tive conditions entirely, and limit the notion of cause to the assemblage of
the positive conditions of the phenomenon : one negative condition invaria- ;
bly understood, and the same in all instances (namely, the absence of coun- '
teracting causes) being sufficient, along with the sum of the positi\'e condi- |
tions, to make up the whole set of circumstances on which the phenomenon f
is dependent. /
§ 4. Among the positive conditions, as we have seen that there are some
mere negative conditions ; but they happened to he the only ones which there could be any
necessity to state ; for he walked, most likely, in exactly his usual manner, and the nega-
tive conditions made all the difference. Again, if a person were asked why the army of
Xerxes defeated that of Leonidas, he would probably say, because they were a thousand times
the number ; but I do not think he would say, it was because they fought, though that was
the element of active force. To borrow another example, ifSed by Mr. Grove and by Mr.
Baden Powell, the opening of flood-gates is said to be the cause of the flow of water ; yet the
active force is exerted by the water itself, and opening the flood-gates merely supplies a nega-
tive condition. The reviewer adds, "There are some conditions absolutely passive, and yet
absolutely necessary to physical phenomena, viz. , the relations of space and time ; and to
these no one ever applies the word cause without being immediately anested by those who
hear him." Even from this statement I am compelled to dissent. Few persons would feel it
incongruous to say (for example) that a secret became known because it was spoken of when
A. B. was within hearing ; which is a condition of space ; or that the cause why one of two
particular trees is taller than the other, is that it has been longer planted ; which is a condi-
tion of time.
* There are a few exceptions ; for there are some properties of objects which seem to be
purely preventive ; as the property of opaque bodies, by which they intercept the passage of
light. This, as far as we are able to understand it, appears an instance not of one cause
counteracting another by the same law whereby it produces its own effects, but of an agency
which manifests itself in no other way than in defeating the effects of another agency. If
we knew on what other relations to light, or on what peculiarities of structure, opacity de-
pends, we might find that this is only an apparent, not a real, exception to the general propo-
sition in the text. In any case it needs not affect the practical application. The formula
which includes all the negative conditions of an effect in the single one of the absence of
counteracting causes, is not violated by such cases as this ; though, if all counteracting agen-
cies were of this description, there would be no purpose sei-ved by employing the formula.
16
242 INDUCTION.
to which, in common parlance, the term cause is more readily and frequent-
ly awarded, so there are others to which it is, in ordinary circumstances,,
refused. In most cases of causation a distinction is commonly drawn be-
tween something which acts, and some other thing which is acted upon;
between an agent and a, patient. Both of these, it would be universally al-
lowed, are conditions of the phenomenon ; but it would be thought absurd
to call the latter the cause, that title being reserved for the former. The
distinction, however, vanishes on examination, or rather is found to be only
verbal ; arising from an incident of mere expression, namely, that the ob-
ject said to be acted upon, and which is considered as the scene in which
the effect takes place, is commonly included in the phrase by which the ef-
fect is spoken of, so that if it were also reckoned as part of the cause, the-
seeming incongruity would arise of- its being supposed to cause itself. In
the instance which we have already had, of falling bodies, the question was
thus put : What is the cause which makes a stone fall ? and if the answer
had been " the stone itself," the expression would have been in apparent
contradiction to the meaning of the word cause. The stone, therefore, is.
conceived as the patient, and the earth (or, according to the common and
most unphilosophical practice, an occult quality of the earth) is represented
as the agent or cause. But that there is nothing fundamental in the dis-
tinction may be seen from this, that it is quite possible to conceive the
stone as causing its own fall, provided the language employed be such as-
to save the mere verbal incongruity. We might say that the stone moves
toward the earth by the properties of the matter composing it ; and ac-
cording to this mode of presenting the phenomenon, the stone itself might
without impropriety be called the agent ; though, to save the established
doctrine of the inactivity of matter, men usually prefer here also to ascribe
the effect to an occult quality, and say that the cause is not the stone itself,
but the weight or gravitation of the stone.
\ Those who have contended for a radical distinction between agent and
patient, have generally conceived the agent as that which causes some state
of, or some change in the state of, another object which is called the pa-
tient. But a little reflection will show that the license we assume of speak-
ing of phenomena as states of the various objects which take part in them
(an artifice of which so much use has been made by some philosophers,
Brown in particular, for -the apparent explanation of phenomena), is sim-
ply a sort of logical fiction, useful sometimes as one among several modes
of expression, but which should ne> er be supposed to be the enunciation
n of a scientific truth. Even those attributes of an object which might
seem with greatest propriety to be called states of the object itself, its sen-
sible qualities, its color, hardness, shape, and the like, are in reality (as no
one has pointed out more clearly than Brown himself) phenomena of cau-
sation, in which the substance is distinctly the agent, or producing cause,
^ the patient being our own organs, and those of other sentient beings.
\ What we call states of objects, are always sequences into which the objects
enter, generally as antecedents or causes ; and things are never more active
than in the production of those phenomena in which they are said to be
., acted upon.\ Thus, in the example of a stone falling to the earth, according
to the theoi-y of gravitation the stone is as much an agent as the earth,
which not only attracts, but is itself attracted by, the stone. In the case of
a sensation produced in our organs, the laws of our organization, and even
those of our minds, are as directly operative in determining the effect pro-
duced, as the laws of the outward object. Though we call prussic acid
LAW OF CAUSATION. 243
the agent of a person's death, the whole of the vital and organic properties
of the patient are as actively .instrumental as the poison, in the chain of ef-
fects which so rapidly terminates his sentient existence. In the process of
education, we may call the teacher the agent, and the scholar only the ma-
terial acted upon ; yet in truth all the facts which pre-existed in the schol-
ar's mind exert either co-operating or counteracting agencies in relation to
the teacher's efforts. It is not light alone which is the agent in vision, but
light coupled with the active properties of the eye and brain, and with
j<j those of the visible object. /"The distinction between agent and patient \4
merely verbal : patients are always agents ; in a great proportion, indeed[
of all natural phenomena, they are so to such a degree as to react forcibly
on the causes which acted upon them : and even when this is not the case,
they contribute, in the same manner as any of the other conditions, to the
production of tlie effect of which they are vulgarly treated as the mere the-
/atre.i All the positive conditions of a phenomenon are alike agents, alike
' active ; and in any expression of the cause yhich professes to be complete,
none of them can with reason be excluded, except such as have already
been implied in the words used for describing the effect ; nor by including
even these would there be incurred any but a merely verbal impropriety.
§ 5. There is a case of causation which calls for separate notice, as it
possesses a peculiar feature, and presents a greater degree of complexity
than the common case. ^It often happens that the effect, or one of the efX
fects, of a cause, is, not to produce of itself a certain phenomenon, but to
fit something else for producing it. In other words, there is a case of cau-
sation in which the effect is to invest an object with a certain property.-''
When sulphur, charcoal, and nitre are put together in certain proportions
and in a certain manner, the effect is, not an explosion, but that the mixture
acquires a property by which, in given circumstances, it will explode. The
various causes, natural and artificial, ■vVhich educate the human body or the
human mind, have for their principal effect, not to make the body or mind
immediately do any thing, but to endow it with certain properties — in oth-
er words, to give assurance that in given circumstances certain results will
take place in it, or as consequences of it. Physiological agencies often
have for the chief part of their operation to predispose the constitution to
some mode of action. To take a simpler instance than all these: putting
a coat of white paint upon a wall does not merely produce in those who
see it done, the sensation of white ; it confers on the wall the permanent
property of giving that kind of sensation. Regarded in reference to the
sensation, the putting on of the paint is a condition of a condition ; it is a
condition of the wall's causing that particular fact. The wall may have
been painted years ago, but it has acquired a property which has lasted till
now, and will last longer ; the antecedent condition necessary to enable the
wall to become in its turn a condition, has been fulfilled once for all. In a
case like this, where the immediate consequent in the sequence is a proper-
ty produced in an object, no one now supposes the property to be a sub-
stantive entity " inherent " in the objecli What has been produced,is what, y
in other language, may be called a state of preparation in an object for pro-
ducing an effect. ^ The ingredients of the gunpowder have been brought into
a state of preparation for exploding as soon as the other conditions of an
explosion shall have occurred. In the case of the gunpowdei", this state of
preparation consists in a certain collocation of its particles relatively to one
another. In the example of the wall, it consists in a new collocation of two
244 INDUCTION.
things relatively to each other — the wall and the paint. In the example of
the molding influences on the human mind, its being a collocation at all is
only conjectural; for, even on the materialistic hypothesis, it would remain
to be proved that the increased facility with which the brain sums up a
column of figures when it has been long trained to calculation, is the result .
of a permanent new arrangement of some of its material particles. I We^
must, therefore, content ourselves with what we know, and must include
; among the efEects of causes, the capacities given to objects of being causes
i of other effects. This capacity is not a real thing existing in the objects ;
it is but a name for our conviction that they will act in a particular man-
ner when certain new circumstances arise./- We may invest this assurance
of future events with a fictitious objective existence, by calling it a state of
I the object. I But unless the state consists, as in the case of the gunpowder
it does, in a collocation of particles, it expresses no present fact ; it is but
the contingent future fact brought back under another name.
It may be thought that this form of causation requires us to admit an
exception to the doctrine that the conditions of a phenomenon — the ante-
cedents required for calling it into existence — must all be found among the
facts immediately, not remotely, preceding its commencement. But what
we have arrived at is not a correction, it is only an explanation, of that doc-
trine. In the enumeration of the conditions required for the occurrence of
any phenomenon, it always has to be included that objects must be present,
possessed of given properties. It is a condition of the phenomenon explo-
sion that an object should be present, of one or other of certain kinds,
which for that reason are called explosive. The presence of one of these
objects is a condition immediately precedent to the explosion. The condi-
tion which is not immediately precedent is the cause which produced, not
the explosion, but the explosive property. The conditions of the explosion
itself were all present immediately before it took place, and the general law,
therefore, remains intact.
§ 6. It now remains to advert to a distinction which is of first-rate im-
portance both for clearing up the notion of cause, and for obviating a very
specious objection often made against the view which we have taken of the
subject.
1 i^When we define the cause of any thing (in the only sense in which the
present inquiry has any concern with causes) to be "the antecedent which
it invariably follows," we do not use this phrase as exactly synonymous
with " the antecedent which it invariably has followed in our past expe-
rience." Such a mode of conceiving causation would be liable to the ob-
jection very plausibly urged by Dr. Reid, namely, that according to this
doctrine night must be the cause of day, and day the cause of night; since
these phenomena have invariably succeeded one another from the begin-
, ning of the world. But it is necessary to our using the word cause, that
\ we should believe not only that the antecedent always has been followed by
the consequent, but that, as long as the present constitution of things* en-
dures, it always will be so. '^ And this would not be true of day and night.
"We do not believe that night will be followed by/3ay under all imaginable
circumstances, but only that it will be so provided the sun rises above the
* I mean by this expression, the ultimate laws of nature (whatever they may be) as distin-
guished from the derivative laws and from the collocations. The diurnal revolution of the
j earth (for example) is not a part of the constitution of things, because nothing can be so called
/ which might possibly be terminated or altered by natural causes.
LAW OF CAUSATION. 245
horizon. If the sun ceased to rise, which, for aught we know, may be per- I
fectly compatible with the general laws of matter, night would be, or might /
be, eternal. On the other hand, if the sun is above the horizon, his light '
not extinct, and no opaque body between us and him, we believe firmly that
unless a change takes place in the properties of matter, this combination of
antecedents will be followed by the consequent, day ; that if the combina-
tion of antecedents could be indefinitely prolonged, it would be always day ;
and that if the same combination had always existed, it would always have
been day, quite independently of night as a previous condition. Therefore
'is it that we do not call night the cause, nor even a condition, of day. The
existence of the sun (or some such luminous body), and there being no
opaque medium in a straight line* between that body and the part of the
earth where we are situated, are the sole conditions ; and the union of j
these, without the addition of any superfluous circumstance, constitutes the |
cause. This is what writers mean when they say that the notion of cause i
involves the idea of necessity. If there be any meaning which confessedly j
belongs to the term necessity,.it is unconditionalness. That which is nee- I
essary, that which must be, means that which will be, whatever supposition
we may make in regard to all other things. The succession of day and
night evidently is not necessary in this sense. It is conditional on the oc-
currence of other antecedents. That which will be followed by a given
consequent when, and only when, some third circumstance also exists, is not
the cause, even though no case should ever have occurred in which the phe-
nomenon took place without it.
Invariable sequence, therefore, is not synonymous with causation, unless )
the sequence, besides being invariable, is unconditional. Tliere are se- j
quences, as uniform in past experience as any others whatever, which yet
we do not regard as cases of causation, but as conjunctions in some sort
accidental. Such, to an accurate thinker, is that of day and night. The one
might have existed for any length of time, and the other not have followed
the sooner for its existence ; it follows only if certain other antecedents
exist ; and where those antecedents existed, it would follow in any case.
No one, probably, ever called night the cause of day ; mankind must so .
soon have arrived at the very obvious generalization, that the state of gen-
eral illumination which we call day would follow from the presence of a
sufiiciently luminous body, whether darkness had pi^iceded or not.
'^We may define, therefore, the cause of a phenomenon, to be the ante- |
cedent, or the concurrence of antecedents, on which it is invariably and I
unconditionally consequent. *'^0r if we adopt the convenient modification f;
of the meaning of the word cause, which confines it to the assemblage of |
positive conditions without the negative, then instead of " unconditional- Ji
ly," we must say, " subject to no other than negative conditions."
To some it may appear, that the sequence between night and day being
invariable in our experience, we have as much ground in this case as ex-
perience can give in any case, for recognizing the two phenomena as cause
and effect ; and that to say that more is necessary^ — to require a belief that
the succession is unconditional, or, in other words, that it would be invari-
able under all changes of circumstances, is to acknowledge in causation an
* I use the words " straight line "• for brevity and simplicity. In reality the line in question
is not exactly straight, for, from the effect of refraction, we actually see the sun for a short
interval during which the opaque mass of the earth is interposed in a direct line between the
sun and our eyes ; thus realizing, though but to a limited extent, the coveted desideratum of
seeing round a corner.
246 INDUCTION.
element of belief not derived from experience. The answer to this is, that
/ it is experience itself which teaches us that one uniformity of sequence is
( conditional and another unconditional. When we judge that the succes-
sion of night and day is a derivative sequence, depending on something
else, we proceed on grounds of experience. It is the evidence of experi-
ence which convinces us that day could equally exist without being fol-
lowed by night, and that night could equally exist without being followed
by day. To say that these beliefs are " not generated by our mere ob-
servation of sequence,"* is to forget that twice in every twenty-four hours,
when the sky is clear, we have an experimentum criicis that the cause of
day is the sun. We have an experimental knowledge of the sun which
justifies us on experimental grounds in concluding, that if the sun were
always above the horizon there would be day, though there had been no
night, and that if the sun were always below the horizon there would be
night, though there had been no day. We thus know from experience
that the succession of night and day is not unconditional. Let me add,
that the antecedent which is only conditionally invariable, is not the in-
variable antecedent. Though a fact may, in experience, have always been
; followed by another fact, yet if the remainder of our experience teaches
us that it might not always be so followed, or if the experience itself is
i such as leaves room for a possibility that the known cases may not cor-
rectly represent all possible cases, the hitherto invariable antecedent is not
accounted the cause; but why? Because we are not sure that, it is the in-
variable antecedent.
Such cases of sequence as that of day and night not only do not contra-
dict the doctrine which resolves causation into invariable sequence, but are
necessarily implied in that doctrine. It is evident, that from a limited
number of unconditional sequences, there will result a much greater num-
ber of conditional ones. Certain causes being given, that is, certain ante-
cedents which are unconditionally followed by certain consequents; the
mere co-existence of these causes will give rise to an unlimited number
of additional uniformities. If two causes exist together, the effects of both
will exist together ; and if many causes co-exist, these causes (by what we
shall terra hereafter the intermixture of their laws) will give rise to new ef-
fects, accompanying or succeeding one another in some particular order,
which order will be invariable while the causes continue to co-exist, but no
longer. The motion of the earth in a given orbit round the sun, is a series
of changes which follow one another as antecedents and consequents, and
will continue to do so while the sun's attraction, and the force with which
the earth tends to advance in a direct" line through space, continue to co-
exist in the same quantities as at present. But vary either of these causes,
and this particular succession of motions would cease to take place. The
series of the earth's motions, therefore, though a case of sequence invari-
able within the limits of human experience, is not a case of causation. It
is not unconditional.
This distinction between the relations of succession which, so far as we
know, are unconditional, and those relations, whether of succession or of
co-existence, which, like the earth's motions, or the succession of day and
night, depend on the existence or on the co-existence of other antecedent
facts — corresponds to the great division which Dr. Whewell and other
writers have made of the field of science, into the investigation of what
* Second Burnett Prize Essay, by Principal Tulloch, p. 25.
LAW OF CAUSATION. 247
they tevra the Laws of Phenomena, and the investigation of causes ; a
phraseology, as I conceive, not philosophically sustainable, inasmuch as the
ascertainment of causes, such causes as the human faculties can ascertain,
namely, causes which are themselves phenomena, is, therefore, merely the
ascertainment of other and more universal Laws of Phenomena. And let
me here observe, that Dr. Whewell, and in some degree even Sir John
Herschel, seem to have misunderstood the meaning of those writers who,
like M. Comte, limit the sphere of scientific investigation to Laws of Phe-
nomena, and speak of the inquiry into causes as vain and futile. The
causes which M. Comte designates as inaccessible, are efficient causes. The
investigation of physical, as opposed to efficient, causes (including the study
■of all the active forces in Nature, considered as facts of observation) is as
important a part of M. Comt6's conception of science as of Dr. Whewell's.
His objection to the wore? cause is a mere matter of nomenclature, in which,
as a matter of nomenclature, I consider him to be entirely wrong. " Those,"
it is justly remarked by Mr. Bailey,* " who, like M. Comt6, object to desig-
nate events as causes, are objecting without any real ground to a mere but
-extremely convenient generalization, to a very useful common name, the
employment of which involves, or needs involve, no particular theory." To
which it may be added, that by rejecting this form of expression, M. Comte
leaves himself without any term for marking a distinction which, however
incorrectly expressed, is not only real, but is one of the fundamental dis-
tinctions in science; indeed it is on this alone, as we shall hereafter find,
that the possibility rests of framing a rigorous Canon of Induction. And
as things left without a name are apt to be forgotten, a Canon of that de-
scription is not one of the many benefits which the philosophy of Induction
has received from M. Comte's great powers.
§ V Does a cause always stand with its effect in the relation of anteced-
ent and consequent ? Do we not often say of two simultaneous facts that
they are cause and effect — as when we say that fire is the cause of warmth,
the sun and moisture the cause of vegetation, and the like? Since a cause
does not necessarily perish because its effect has been produced, the two
things do very generally co-exist; and there are some appearances, and
some common expressions, seeming to imply not only that causes may, but
that they must, be contemporaneous with their eSeots-Jf^essante causd
cessat et effectus, has been a dogma of the schools : the necessity for the
continued existence of the cause in order to the continuance of the effect,
seems to have been once a generally received doctrine. Kepler's numerous
-attempts to account for the motions of the heavenly bodies on mechanical
^principles, were rendered abortive by his always supposing that the agency
which set those bodies in motion must continue to operate in order to keep
up the motion which it at first produced. Yet there were at all times
many familiar instances of the continuance of effects, long after their causes
had ceased. A coup de soleil gives a person brain-fever : will the fever go
off as soon as he is moved out of the sunshine ? A sword is run through
his body : must the sword remain in his body in order that he may con-
tinue dead ? A plowshare once made, remains a plowshare, without any
continuance of heating and hammering, and even after the man who heat-
ed and hammered it has been gathered to his fathers. On the other hand,
the pressure which forces up the mercury in an exhausted tube must be
* Letters on the Philosophy of the Human Mind, First Series, p. 219.
248 INDUCTION.
continued in order to sustain it in the tube. This (it may be replied) ii
because another force is acting without intermission, the force of gravity,
which would restore it to its level, unless counterpoised by a force equally
constant. But again: a tight bandage causes pain, which pain will some-
times go off as soon as the bandage is removed. The illumination which
the sun diffuses over the earth ceases when the sun goes down.
-/There is, therefore, a distinction to be drawn. The conditions which are
necessary for the first production of a phenomenon, are occasionally also
necessary for its continuance; though more commonly its continuance re-
quires no condition except negative ones. Most things, once produced, con-
tinue as they are, until something changes or destroys them ; but some re-
quire the permanent presence of the agencies which produced them at first.
These may, if we please, be considered as instantaneous phenomena, re-
quiring to be renewed at each instant by the cause by which they were at
first generated.^ Accordingly, the illumination of any given point of space
has always been looked upon as an instantaneous fact, which perishes and
is perpetually renewed as long as the necessary conditions subsist. If we
adopt this language we avoid the necessity of admitting that the continu-
ance of the cause is ever required to maintain the effect. We may say, it
is not I'equired to maintain, but to reproduce, the effect, or else to coun-
teract some force tending to destroy it. And this may be a convenient
phraseology. But it is only a phraseology. The fact remains, that in
some cases (though those are a minority) the continuance of the conditions
which produced an effect is necessary to the continuance of the effect.
As to the ulterior question, whether it is strictly necessary that the
cause, or assemblage of conditions, should precede, by ever so short an in-
stant, the production of the effect (a question raised and argued with much
ingenuity by Sir John Herschel in an Essay already quoted),* the inquiry
is of no consequence for our present purpose. There certainly are cases
in which the effect follows without any interval perceptible by our faculties ;
and when there is an interval, we can not tell by how many intermediate
links imperceptible to us that inverval may really be filled up. But even
granting that an effect may commence simultaneously with its cause, the
view I have taken of causation is in no way practically affected. Wheth-
I er the cause and its effect be necessarily successive or not, the begin-
ning of a phenomenon is what implies a cause, and causation is the law of
the succession of phenomena. If these axioms be granted, we can afford,
though I see no necessity for doing so, to drop the words antecedent and
consequent as applied to cause and effect. I have no objection to define a
cause, the assemblage of phenomena, which occurring, some other phenom-
enon invariably commences,- or has its origin. Whether the effect coin-
cides in point of time with, oi- immediately follows, the hindmost of its
conditions, is immaterial. At all events, it does not precede it ; and when
we are in doubt, between two co-existent phenomena, which is cause and
which effect, we rightly deem the question solved if we can ascertain which
of them preceded the other. . .
§ 8. It continually happens that several different phenomena, which are
not in the slightest degree dependent or conditional on one another, are
found all to depend, as the phrase is, on one and the same agent ; in other
words, one and the same phenomenon is seen to be followed by several
* Essays, pp. 206-208.
LAW OF CAUSATION. 249
sorts of effects quite heterogeneous, but which go on simultaneously one
with another ; provided, of course, that all other conditions requisite for
each of them also exist. Thus, the sun produces the celestial motions ; it
pi-oduces daylight, and it produces heat. The earth causes the fall of heavy
bodies, and it also, in its capacity of a great magnet, causes the phenomena
of the magnetic needle. A crystal of galena causes the sensations of hard-
ness, of weight, of cubical form, of gray color, and many others between
which we can trace no interdependence. The purpose to which the phrase-
ology of Properties and Powers is specially adapted, is. the expression of ,
this sort of cases. When the same phenomenon is followed (either sub,)!
ject or not to the presence of other conditions) by effects of different and
dissimilar orders, it is usual to say that each different sort of effect is pro-
s/ duced by a different property of the cause.'^ Thus we distinguish the at-'
tractive or gravitative property of the earth, and its magnetic property:'
the gravitative, luminiferous, and calorific properties of the sun : the color,
shape, weight, and hardness of a crystal. These are mere phrases, which
explain nothing, and add nothing to our knowledge of the subject ; but,
considered as abstract names denoting the connection between the differ-
ent effects produced and the object which produces them, they are a very
powerful instrument of abridgment, and of that acceleration of the proc-
ess of thought which abridgment accomplishes.
i/^ This class of considerations leads to a conception which we shall find to
be of great importance, that of a Permanent Cause, or original natural \
agent. There exist in nature a number of permanent causes, which have
subsisted ever since the human race has been in existence, and for an in- i,
definite and probably an enormous length of time previous. The sun, the
earth, and planets, with their various constituents, air, water, and other dis-
tinguishable substances, whether simple or compound, of which nature is
made up, are such Permanent Causes. These have existed, and the effects
or consequences which they were fitted to produce have taken place (as
often as the other conditions of the production met), from the very begin-
ning of our experience. But we can give no account of the origin of the
Permanent Causes themselves. Why these particular natural agents ex-
isted originally and no others, or why they are commingled in such and
such proportions, and distributed in such and such a manner throughout
space, is a question we can not answer. More than this : we can discover
nothing regular in the distribution itself ; we can reduce it to no uniformi-
ty, to no law. There are no means by which, from the distribution of these
causes or agents in one part of space, we could conjecture whether a simi-
^lar distribution prevails in another. The co-existence, therefore, of Prime-*^ —
val Causes ranks, to us, among merely casual concurrences : and all those
sequences or co-existences among the effects of several such causes, which,
though invariable while those causes co-exist, would, if the co-existence ter-
minated, terminate along with it, we do not class as cases of causation, or
laws of nature : we can only calculate on finding these sequences or co-ex-
istences where we know by direct evidence, that the natural agents on the
properties of which they ultimately depend, are distributed in the requisite
manner. These Permanent Causes are not always objects; they are some-
times events, that is to say, periodical cycles of events, that being the only i
mode in which events can possess the property of permanence.^ Not only, \
for instance, is the earth itself a permanent cause, or primitive natural
agent, but the earth's rotation is so too : it is a cause which has produced,
from the earliest period (by the aid of other necessary conditions), the sue-
250 INDUCTION.
cession of day and night, the ebb and flow of the sea, and many other ef-
fects, while, as we can assign no cause (except conjecturally) for the rota-
tion itself, it is entitled to be ranked as a primeval cause. It is, however^
only the origin of the rotation which is mysterious to us : once begun, its
continuance is accounted for by the first law of motion (that of the perma-
nence of rectilinear motion once impressed) combined with the gravitation,
of the parts of the earth toward one another.
All phenomena without exception which begin to exist, that is, all except
the primeval causes, are effects either immediate or remote of those primi-
; tive facts, or of some combination of them. There is no Thing produced,.
\ no event happening, in the known universe, which is not connected by a
I uniformity, or invariable sequence, with some one or more of the phenom-
; ena which preceded it; insomuch that it will happen again as often as-
I those phenomena occur again, and as no other phenomenon having the
■ character of a counteracting cause shall co-exist.f/ These antecedent phe-
nomena, again, were connected in a similar manner with some that pre-
ceded them ; and so on, until we reach, as the ultimate step attainable by
us, either the properties of some one primeval cause, or the conjunction of
V several. ^ The whole of the phenomena of nature were therefore the neces-
sary, or, in other words, the unconditional, consequences of some former col-
location of the Permanent Causes. \
'i The state of the whole universe at any instant, we believe to be the con-
/ sequence of its state at the previous instant; insomuch that one who knew
j all the agents which exist at the present moment, their collocation in space,
;■ and all their properties; in other words, the laws of their agency, could pre-
dict the whole subsequent history of the universe, at least unless some new
volition of a power capable of controlling the universe should supervene.*-
And if any particular state of the entire universe could ever recur a second
time, all subsequent states would return too, and history would, like a cir-
culating decimal of many figures, periodically repeat itself : '
Jam redit et virgo, redeunt Saturnia regna
Alter eiit turn Tiphys, et altera qua! vehat Argo
DelectOs heroas ; erunt quoque altera bella,
Atque iterum ad Trojam magnus mittetur Achilles.
And though things do not really revolve in this eternal round, the whole-
series of events in the history of the universe, past and future, is not the-
less capable, in its own nature, of being constructed a priori by any one
* To the universality which mankind are agreed in ascribing to the Law of Causation, there
is one claim of exception, one disputed case, that of the Human Will ; the determinations of
which, a lai-ge class of metaphysicians are not willing to regard as following the causes called
motives, according to as strict laws as those which they suppose to exist in the world of mere
matter. This controverted point will undergo a special examination when we come to treat
particularly of the Logic of the Moral Sciences (Book vi. , chap. 2). In the mean time, I may
remark that these metaphysicians, who, it must be observed, ground the main part of their ob-
I jection on the supposed repugnance of the doctrine in question to our consciousness, seem to-
' me to mistake the fact which consciousness testifies against. What is really in contradiction
I to consciousness, they would, I think, on strict self-examination, find to be, the application to-
'. human actions and volitions of the ideas involved in the common use of the term Necessity;
! I which I agree with them in objecting to. But if they would consider that by saying that a-
I person's actions necessarily follow from his character, all that is really meant (for no more is^
1 meant in any case whatever of causation) is that he invariably does act in conformity to his
' character, and that any one who thoroughly knew his character could certainly predict how he
j vvould act in any supposable case ; they probably would not find this doctrine either contrary
to their experience or revolting to their feelings. And no more than this is contended for by
any one but an Asiatic fatalist.
LAW OF CAUSATION. 251
■whom we can suppose acquainted with the original distribution of all nat.
ural agents, and with the whole of their properties, that is, the laws of suc-
cession existing between them and their effects : saving the far more than
human powers of combination and calculation which would be required,
even in one possessing the data, for the actual performance of the task.
§ 9. Since every thing which occurs is determined by laws of causation
and collocations of the original causes, it follows that the co-existences
which are observable among effects can not be themselves the subject of
any similar set of laws, distinct from laws of causation. Uniformities^^
there are, as well of co-existence as of succession, among effects ; but these
must in all cases be a mere result either of the identity or of the co-exist-
ence of their causes : if the causes did not co-exist, neither could the ef-
■^ fects^ And these causes being also effects of prior causes, and these of
I others, until we reach the primeval causes, it follows that (except in the
case of effects which can be traced ' immediately or remotely to on§ and
the same cause) the co-existences of phenomena can in no case be univers-
al, unless the co-existences of the primeval causes to which the effects are
ultimately traceable can be reduced to a universal law : but we have seen
that they can not. There are, accordingly, no original and independent, in i
other words no unconditional, uniformities of co-existence, between effects j
of different causes; if they co-exist, it is only because the causes have cas-i
" ually co-existed.'l^The only independent and unconditional co - existences 1 v
which are sufficiently invariable to have any claim to the' character of
laws, are between different and mutually independent effects of the same
cause; in other words, between different properties of the same natural
y agent. ' This portion of the Laws of Nature will be treated of in the lat-
ter part of the present Book, under the name of the Specific Properties of
Kinds. >
§ 10. Since the first publication of the present treatise, the sciences of
physical nature have made a great advance in generalization, through the
doctrine known as the Conservation or Persistence of Force. This impo-
sing edifice of theory, the building and laying out of which has for some
time been the principal occupation of the most systematic minds among
physical inquirers, consists of two stages : one, of ascertained fact, the oth-
er containing a large element of hypothesis.
To begin with the first. It is proved by numerous facts, both natural
and of artificial production, that agencies which had been regarded as dis-
tinct and independent sources of force — heat, electricity, chemical action,
nervous and muscular action, mpmentum of moving bodies — are inter-
changeable, in definite and fixed quantities, with one another. It had long
been known that these dissimilar phenomena had the power, under certain
conditions, of producing one another : what is new in the theory is a more
accurate estimation of what this production consists in. What happens is,
that the whole or part of the one kind of phenomena disappears, and is re-
placed by phenomena of one of the other descriptions, and that there is an
equivalence in quantity between the phenomena that have disappeared and
those which have been produced, insomuch that if the process be reversed,
the very same quantity which had disappeared will re-appear, without in-
crease or diminution. Thus the amount of heat which will raise the tem-
perature of a pound of water one degree of the thermometer, will, if ex-
pended, say in the expansion of steam, lift a weight of 112 pounds one
252 INDUCTION.
foot, or a weight of one pound 772 feet: and the same exact quantity of
heat can, by certain means, be recovered, through the expenditure of exact-
ly that amount of mechanical motion.
The establishment of this comprehensive law has led to a change in the
language in which the scientific world had been accustomed to speak of
what are called the Forces of nature. Before this correlation between phe-
nomena most unlike one another had been ascertained, their unlikeness had
caused them to be referred to so many distinct forces. Now that they are
known to be convertible into one another without loss, they are spoken of
as all of them results of one and the same force, manifesting itself in dif-
ferent modes. This force (it is said) can only produce a limited and defi-
nite quantity of effect, but always does produce that definite quantity; and
produces it, according to circumstances, in one or another of the forms, or
divides it among several, but so as (accoi'ding to a scale of numerical
equivalents established by experiment) always to make up the same sum ;
and no one of the manifestations can be produced, save by the disappear-
ance of the equivalent quantity of another, which in its turn, in appropriate
circumstances, will re-appear undiminished. This mutual interchangeabil-
ity of the forces of nature, according to fixed numerical equivalents, is the
part of the new doctrine which rests on irrefragable fact.
To make the statement true, however, it is necessary to add, that an in-
definite and perhaps immense interval of time may elapse between the dis-
appearance of the force in one form and its re-appearance in another. A
stone thrown up into the air with a given force, and falling back immedi-
ately, will, by the time it reaches the earth, recover the exact amount of me-
chanical momentum which was expended in throwing it up, deduction be-
ing made of a small portion of motion which has been communicated to
the air. But if the stone has lodged on a height, it may not fall back for
years, or perhaps ages, and until it does, the force expended in raising it is
temporarily lost, being represented only by what, in the language of the
new theory, is called potential energy. The coal imbedded in the earth is
considered by the theory as a vast reservoir of force, which has remained
dormant for many geological periods, and will so remain until, by being
burned, it gives out the stored-up force in the form of heat. Yet it is
not supposed that this force is a material thing which can be confined by
bounds, as used to be thought of latent heat when that important phenom-
enon was first discovered. What is meant is that when the coal does at
last, by combustion, generate a quantity of heat (transformable like all oth-
er heat into mechanical momentum, and the other forms of force), this ex-
trication of heat is the re-appearance of a force derived from the sun's rays,
expended myriads of ages ago in the vegetation of the organic substances
which were the material of the coal.
Let us now pass to the higher stage of the theory of Conservation of
Force ; the part which is no longer a generalization of proved fact, but a
combination of fact and hypothesis. Stated in few words, it is as follows:
That the Conservation of Force is really the Conservation of Motion ; that
in the various interchanges between the forms of force, it is always motion
that is transformed into motion. To establish this, it is necessary to as-
sume motions which are hypothetical. The supposition is, that there are
motions which manifest themselves to our senses only as heat, electricity,
etc., being molecular motions ; oscillations, invisible to us, among the mi-
nute particles of bodies ; and that these molecular motions are transmutable
into molar motions (motions of masses), and molar motions into molecular.
LAW OF CAUSATION. 253
Now there is a real basis of fact for this supposition : we have positive evi-
dence of the existence of molecular motion in these manifestations of force.
In the case of chemical action, for instance, the particles separate and form
new combinations, often with a great visible disturbance of the mass. In
the case of heat, the evidence is equally conclusive, since heat expands bod-
ies (that is, causes their particles to move from one another) ; and if of
sufficient amount, changes their mode of aggregation from solid to liquid,
or from liquid to gaseous. Again, the mechanical actions which produce
heat — friction, and the collision of bodies — must from the nature of the
case produce a shock, that is, an internal motion of particles, which indeed,
we find, is often so violent as to break them permanently asunder. ' Such
I facts are thought to warrant the inference, that it is not, as was supposed,
heat that causes the motion of particles, but the motion of particles that
causes heat ; the original cause of both being the previous motion (whether
molar or molecular — collision of bodies or combustion of fuel) which form-
ed the heating agency. This inference already contains hypothesis ; but at
least the supposed cause, the intestine motion of molecules, is a vera causa.
But in order to reduce the Conservation of Force to Conservation of Mo-
tion, it was necessary to attribute to motion the heat propagated, through
apparently empty space, from the sun. This required the supposition
(already made for the explanation of the laws of light) of a subtle ether
pervading space, which, though impalpable to us, must have the property
which constitutes matter, that of resistance, since waves are propagated
through it by an impulse from a given point. The ether must be sujiposed
(a supposition not required by the theory of light) to penetrate into the
minute interstices of all bodies. The vibratory motion supposed to be tak-
ing place in the heated mass of the sun, is considered as imparted from
that mass to the particles of the surrounding ether, and through them to
the particles of the same ether in the interstices of terrestrial bodies ; and
this, too, with a sufficient mechanical force to throw the particles of those
bodies into a state of similar vibration, producing the expansion of their
mass, and the sensation of heat in sentient creatures. All this is hypothe-
sis, though, of its legitimacy as hypothesis, I do not mean to express any
doubt. It would seem to follow as a consequence from this theory, that
Force may and should be defined, matter in motion. This definition, how-
ever, will not stand, for, as has already been seen, the matter needs not be
in actual motion. It is not necessary to suppose that the motion after-
ward manifested, is actually taking place among the molecules of the coal
during its sojourn in the earth ;* certainly not in the stone which is at rest
on the eminence to which it has been raised. The true definition of Force
must be, not motion, but Potentiality of Motion ; and what the doctrine,
if established, amounts to, is, not that there is at all times the same quan-
tity of actual motion in the universe ; but that the possibilities of motion
are limited to a definite quantity, which can not be added to, but which
can not be exhausted ; and that all actual motion which takes place in Na-
ture is a draft upon this limited stock. It needs not all of it have ever ex-
isted as actual motion. There is a vast amount of potential motion in the
universe in the form of gravitation, which it would be a great abuse of
* I believe, however, the accredited authorities do suppose that molecalar motion, equiva-
lent in amount to that which will be manifested in the combustion of the coal, is actually tak-
ing place during the whole of the long interval, if not in the coal, yet in the oxygen whieh
will then combine with it. But how purely hypothetical this supposition is, need hardly be
remarked ; I venture to say, unnecessarily and extravagantly hypothetical.
254 INDUCTION.
hypothesis to suppose to have been stored up by the expenditure of an
equal amount of actual motion in some former state of the universe. Nor
does the motion produced by gravity take place, so far as we know, at the
expense of any other motion, either molar or molecular.
It isproper to consider whether the adoption of this theory as a scien-
tific truth, involving as it does a change in the conception hitherto enter-
tained of the most general physical agencies, requires any modification in
the view I have taken of Causation as a law of nature. As it appears to
me, none whatever. The manifestations which the theory regards as
modes of motion, are as much distinct and separate phenomena when re-
ferred to a single force, as when attributed to several. Whether the phe-
nomenon is called a transformation of force or the generation of one, it has
its own set or sets of antecedents, with which it is connected by invariable
and unconditional sequence ; and that set, or those sets, of antecedents are
its cause. The relation of the Conservation theory to the principle of
Causation is discussed in much detail, and very instructively, by Professor
Bain, in the second volume of his Logic. The chief practical conclusion
I drawn by him, bearing on Causation, is, that we must distinguish in the
assemblage of conditions which constitutes the Cause of a phenomenon,
two elements : one, the presence of a force ; the other, the collocation or
position of objects which is required in order that the force may undergo
the particular transmutation which constitutes the phenomenon. Now, it
might always have been said with acknowledged correctness, that a force
and a j3ollocation were both of them necessary to produce any phenomenon.
The law of causation is, that change can only be produced by change.
'Along with~aiiy number of stationary antecedents, wKioh are coltoijations,
1 there must be at least one changing antecedent, which is a force. To pro-
/ duce a bonfire, there must not only be fuel, and air, and a spark, which are
I collocations, but chemical action between the air and the materials, which
is a force. To grind corn, there must be a certain collocation of the parts
composing a mill, relatively to one another and to the corn ; but there must
also be the gravitation of water, or the motion of wind, to supply a force.
But as the force in these cases was regarded as a property of the objects
in which it is embodied, it seemed tautology to say that there must be the
collocation and the force. As the collocation must be a collocation of ob-
jects possessing the force-giving property, the collocation, so understood,
included the force.
How, then, shall we have to express these facts, if the theory be finally
substantiated that all Force is reducible to a previous Motion ? We shall
have to say, that one of the conditions of every phenomenon is an ante-
cedent Motion. But it will have to be explained that this needs not be
actual motion. The coal which supplies the foi'ce exerted in combustion
is not shown to have been exerting that force in the form of molecular
motion in the pit; it was not even exerting pressure. The stone on the
eminence is exerting a pressure, but only equivalent to its weight, not to
the additional momentum it would acquire by falling. The antecedent,
therefore, is not a force in action ; and we can still only call it a property
of the objects, by which they would exert a force on the occurrence of a
fresh collocation. The collocation, therefore, still includes the force. The
force said to be stored up, is simply a particular property which the object
has acquired. The cause we are in search of, is a collocation of objects
possessing that particular property. When, indeed, we inquire further into
the cause from which they derive that property, the new conception intro-
LAW OF CAUSATION. 255
<3uced by the Conservation theory comes in : the property is itself an ef-
fect, and its cause, according to the theory, is a former motion of exactly
equivalent amount, which has been impressed on the particles of the body,
perhaps at some very distant period. But the case is simply one of those
we have already considered, in which the efficacy of a cause consists in its
investing an object with a property. The force said to be laid up, and
merely potential, is no more a really existing thing than any other proper-
ties of objects are really existing things. The expression is a mere arti-
fice of language, convenient for describing the phenomena : it is unneces-
sary to suppose that any thing has been in continuous existence except an
abstract potentiality. A force suspended in its operation, neither mani-
festing itself by motion nor by pressure, is not an existing fact, but a name
for our conviction that in appropriate circumstances a fact would take
place. We know that a pound weight, were it to fall from the earth into
the sun, would acquire in falling a momentum equal to millions of pounds ;
but we do not credit the pound weight with more of actually existing force
than is equal to the pressure it is now exerting on the earth, and that is
■exactly a pound. We might as well say that a force of millions of pounds
exists in a pound, as that the force which will manifest itself when the
coal is burned is a real thing existing in the coal. What is fixed in the coal
• is only a certain property : it has become fit to be the antecedent of an ef-
fect called combustion, which partly consists in giving out, under certain
conditions, a given definite quantity of heat.
We thus see that no new general conception of Causation is introduced
by the Conservation theory. The indestructibility of Force no more in-
terferes with the theory of Causation than the indestructibility of Matter,
meaning by matter the element of resistance in the sensible world. It
only enables us to understand better than before the nature and laws of
some of the sequences.
This better understanding, however, enables us, with Mr. Bain, to admit,*
as one of the tests for distinguishing causation from mere concomitance,!
the expenditure or transfer of energy. If the effect, or any part of thej
effect, to be accounted for, consists in putting matter in motion, then any]
of the objects present which has lost motion has contributed to the effects
and this is the true meaning of the proposition that the cause is that one
of the antecedents which exerts active force.
§ 11. It is proper in this place to advert to a rather ancient doctrine re-
specting causation, which has been revived during the last few years in
many quarters, and at present gives more signs of life than any other the-
ory of causation at variance with that set forth in the preceding pages.
According to the theory in question, Mind, or to speak more precisely.
Will, is the only cause of phenomena. The type of Causation, as well as
the exclusive source from which we derive the idea, is our own voluntary
■agency. Here, and here only (it is said), we have direct evidence of causa-
tion. We know that we can move our bodies. Respecting the phenom-
ena of inanimate nature, we have no other direct knowledge than that of
antecedence and sequence. But in the case of our voluntary actions, it is
affirmed that we are conscious of power before we have experience of re-
sults. An act of volition, whether followed by an effect or not, is ac-
companied by a consciousness of effort, " of force exerted, of power in ac- ,
tion, which is necessarily causal, or causative." This feeling of energy or''
force, inherent in an act of will, is knowledge a priori; assurance, prior to
256 INDUCTION.
I experience, that we have the power of causing effects. Volitioi%, therefore,
it is asserted, is something more than an unconditional antecedent ; it is a
cause, in a different sense from that in which physical phenomena are said
M to cause one another: it is an EiBcient Cause. From this the transition is
'' easy to the further doctrine, that Volition is the sole Efficient Cause of all
phenomena. " It is inconceivable that dead force could continue unsup-
ported for a moment beyond its creation. We can not even conceive of
change or phenomena without the energy of a mind." " The word action "
itself, says another writer of the same school, " has no real significance ex-
cept when applied to the doings of an intelligent agent. Let any one con-
ceive, if he can, of any power, energy, or force inherent in a lump of mat-
ter." Phenomena may have the semblance of being produced by phys-
ical causes, but they are in reality produced, say these writers, by the im-
mediate agency of mind. All things which do not proceed from a human
(or, I suppose, an animal) will proceed, they say, directly from divine will.
The earth is not moved by the combination of a centripetal and a pro-
jectile force ; this is but a mode of speaking, which serves to facilitate our
conceptions. It is moved by the direct volition of an omnipotent Being, in
a path coinciding with that which we deduce from the hypothesis of these
two forces.
As I have so often observed, the general question of the existence of Ef-.
ficient Causes does not fall within the limits of our subject; but a theory
which represents them as capable of being subjects of human knowledge,
and which passes off as efficient causes what are only physical or phenom-
enal causes, belongs as much to Logic as to metaphysics, and is a fit sub-
ject for discussion here.
To my apprehension, a volition is not an efficient, but simply a physical
cause. Our will causes our bodily actions in the same sense, and in no
other, in which cold causes ice, or a spark causes an explosion of gunpow-
der. The volition, a state of our mind, is the antecedent; the motion of
our limbs in conformity to the volition, is the consequent. This sequence
I conceive to be not a subject of direct consciousness, in the sense intend-
ed by the theory. The antecedent, indeed, and the consequent, are sub-
jects of consciousness. Bat the connection between them is a subject of
experience. I can not admit that our consciousness of the volition con-
tains in itself any a priori knowledge that the muscular motion will fol-
low. If our nerves of motion were paralyzed, or our muscles stiff and in-
flexible, and had been so all our lives, I do not see the slightest ground for
supposing that we should ever (unless by information from other people)
have known any thing of volition as a physical power, or been conscious or
any tendency in feelings of our mind to produce motions of our body, or of
other bodies. I will not undertake to say whether we should in that case
have had the physical feeling which I suppose is meant when these writers
speak of "consciousness of effort:" I see no reason why we should not;,
since that physical feeling is probably a state of nervous sensation begin-
ning and ending in the brain, without involving the motory apparatus:
but we certainly should not have designated- it by any term equivalent to
effort, since effort implies consciously aiming at an end, which we should
not only in that case have had no reason to do, but could not even have
had the idea of doing. If conscious at all of this peculiar sensation, we
should have been conscious of it, I conceive, only as a kind of uneasiness,
accompanying our feelings of desire.
It is well arguedby Sir William Hamilton against the theory in question^
LAW OF CAUSATION. 257
that it " is refuted by the consideration that between the overt fact of cor-
poreal movement of which we are cognizant, and the internal act of mental
determination of which we are also cognizant, there intervenes a numerous
series of intermediate agencies of which we have no knowledge ; and, con-
sequently, that we can have no consciousness of any causal connection be-
tween the extreme links of this chain, the volition to move and the limb
moving, as this hypothesis asserts. N"o one is immediately conscious, for
example, of moving his arm through his volition. Previously to this ulti-
mate movement, muscles, nerves, a multitude of solid and fluid parts, must
be set in motion by the will, but of this motion we know, from conscious-
ness, absolutely nothing. A person struck with paralysis is conscious of
no inability in his limb to fulfill the determinations of" his will ; and it is
only after having willed, and finding that his limbs do not obey his volition,,
that he learns by this experience, that the external movement does not fol-
low the internal act. But as the paralytic learns after the volition that his
limbs do not obey his mind ; so it is only after volition that the man in
health learns, that his limbs do obey the mandates of his will."*
Those against whom I am contending have never produced, and do not
pretend to produce, any positive evidencef that the power of our will to
move our bodies would be known to us independently of experience. What ^
they have to say on the subject is, that the production of physical events-
by a will seems to carry its own explanation with it, while the action of
matter upon matter seems to require something else to explain it ; and is
even, according to them, " inconceivable " on a-jy other supposition than
that some will intervenes between the apparent cause and its apparent
effect. They thus rest their case on an appeal to the inherent laws of our con-
ceptive faculty; mistaking, as I apprehend, for the laws of that faculty its
acquired habits, grounded on the spontaneous tendencies of its uncultured
state. The succession between the will to move a limb and the actual mo-
tion is one of the most direct and instantaneous of all sequences which
come under our observation, and is familiar to every moment's experience
from our earliest infancy ; more familiar than any succession of events ex-
* Lectures on Metaphysics, vol. ii., Lect. xxxix., pp. 391-2.
■ I regret that I can not invoke the authority of Sir William Hamilton in favor of my own
opinions on Causation, as I can against the particular theory which I am now combating.
But that acute thinker has a theory of Causation peculiar to himself, which has never yet, as
far as I know, been analytically examined, but which, I venture to think, admits of as com-
plete refutation as any one of the false or insuflScient psychological theories which strew the
ground in such numbers under his potent metaphysical scythe. (Since examined and contro-
verted in the sixteenth chapter oi An Examination of Sir William Hamilton's Philosophy.)
t Unless we are to consider as such the following statement, by one of the writers quoted
in the text : "In the case of mental exertion, the result to be accomplished is preconsidered
or meditated, and is therefore known a priori, or before experience." — (Bowen's Lowell Lec-
tures on the Application of Metaphysical and Ethical Science to the Evidence of Religion.
Boston, 1849.) This is merely saying that when we will a thing we have an idea of it. But
to have an idea of what we wish to happen, does not imply a prophetic knowledge that it will
happen. Perhaps it will be said that the first time we exerted our will, when we had of
course no experience of any of the powers residing in us, we nevertheless must already have
known that we possessed them, since we can not will that which we do not believe to be in
our power. But the impossibility is perhaps in the words only, and not in the facts ; for we
may desire what we do not know to be in our power ; and finding by experience that our
bodies move according to our desire, we may then, and only then, pass into the more compli-
cated mental state which is teimed will.
.After all, even if we had an instinctive knowledge that our actions would follow our will,
this, as Brown remarks, would prove nothing as to the nature of Causation. Our knowing,
previous to experience, that an antecedent will be followed by a certain consequent, would
not prove the relation between them to be any thing more than antecedence and consequence.
17
■258 INDUCTION.
terior to our bodies, and especially more so than any other case of the ap-
parent origination (as distinguished from the mere communication) of mo-
tion. Now, it is the natural tendency of the mind to be always attempting
to facilitate its conception of unfamiliar facts by assimilating them to oth-
ers which are familiar. Accordingly, our voluntary acts, being the most
familiar to us of all cases of causation, are, in the infancy and early youth
•of the human race, spontaneously taken as the type of causation in general,
and all phenomena are supposed to be directly produced by the will of
flome sentient being. This original Fetichism I shall not characterize in
the words of Hume, or of any follower of Hume, but in those of a religious
metaphysician, Dr. Reid, in order more effectually to show the unanimity
which exists on the subject among all competent thinkers.
" When we turn our attention to external objects, and begin to exercise '
our rational faculties about them, we find that there are some motions and
•changes in them which we have power to produce, and that there are many
which must have some other cause. Either the objects must have life and
active power, as we have, or they must be moved or changed by something
that has life and active power, as external objects are moved by us.
" Our first thoughts seem to be, that the objects in which we perceive
such motion have understanding and active power as we have. ' Savages,'
says the Abbe Raynal, ' wherever they see motion which they can not ac-
count for, there they suppose a soul.' All men may be considered as sav-
ages in this respect, until they are capable of instruction, and of using their
faculties in a more perfect manner than savages do.
"The Abb6 Raynal's observation is sufficiently confirmed, both from
fact, and from the structure of all languages.
" Rude nations do really believe sun, irioon, and stars, earth, sea, and air,
fountains, and lakes, to have understanding and active power. To pay
homage to them, and implore their favor, is a kind of idolatry natural to
savages.
"All languages carry in their structure the marks of their being formed
when this belief prevailed. The distinction of verbs and participles into
active and passive, which is found in all languages, must have been origi-
nally intended to distinguish what is really active from what is merely pas-
sive ; and in all languages, we find active verbs applied to those objects, in
which, according to the Abb6 Raynal's observation, savages suppose a soul.
" Thus we say the sun rises and sets, and comes to the meridian, the
moon changes, the sea ebbs and flows, the winds blow. Languages were
formed by men who believed these objects to have life and active power
in themselves. It was therefore proper and natural to express their mo-
tions and changes by active verbs.
" There is no surer way of tracing the sentiments of nations before they
have records, than by the structure of their language, which, notwithstanding
the changes produced in it by time, will always retain some signatures of
the thoughts of those by whom it was invented. When we find the same
sentiments indicated in the structure of all languages, those sentiments must
have been common to the human species when languages were invented.
" When a few, of superior intellectual abilities, find leisure for specula-
tion, they begin to philosophize, and soon discover, that many of those ob-
jects which at first they believed to be intelligent and active are really
lifeless and passive. This is a very important discovery. It elevates the
tnind, emancipates from many vulgar superstitions, and invite? to further
discoveries of the same kind.
LAW OF CAUSATION. 259
"As philosophy advances, life and activity in natural objects retires, and
leaves them dead and inactive. Instead of moving voluntarily, we find
them to be moved necessarily ; instead of acting, we find them to be acted
upon ; and Nature appears as one great machine, where one wheel is turn-
ed by another, that by a third ; and how far this necessary succession may
reach, the philosopher does not know."*
There is, then, a spontaneous tendency of the intellect to account to it
■self for all cases of causation by assimilating them to the intentional acts
of voluntary agents like itself. This is the instinctive philosophy of the
human mind in its earliest stage, befoi'e it has become familiar with any
•other invariable sequences than those between its own volitions or those
■of other human beings and their voluntary acts. As the notion of fixed
laws of succession among external phenomena gradually establishes itself,
the propensity to refer all phenomena to voluntary agency slowly gives
■way before it. The suggestions, however, of daily life continuing to be
more powerful than those of scientific thought, the original instinctive phi-
losophy maintains its ground in the mind, underneath the growths obtain-
«d by cultivation, and keeps up a constant resistance to their throwing
their roots deep into the soil. The theory against which I am contend-
ing derives its nourishment from that substratum. Its strength does not
lie in argument, but in its aflSnity to an obstinate tendency of the infancy
of the human mind.
That this tendency, however, is not the result of an inherent mental law,
is proved by superabundant evidence. The history of science, from its
earliest dawn, shows that mankind have not been unanimous in thinking
either tliat the action of matter upon matter was not conceivable, or that
the action of mind upon matter was. To some thinkers, and some schools
of thinkers, both in ancient and in modern times, this last has appeared
much more inconceivable than the former. Sequences entirely physical
and material, as soon as they had become suificiently familiar to the human
mind, came to be thought perfectly natural, and were regarded not only as
needing no explanation themselves, but as being capable of affording it to
others, and even of serving as the ultimate explanation of things in gen-
eral.
One of the ablest recent supporters of the Volitional theory has furnish-
ed an explanation, at once historically true and philosophically acute, of
the failure of the Greek philosophers in physical inquiry, in which, as I
<!onceive, he unconsciously depicts his own state of mind. " Their stum-
bling - block was one as to the nature of the evidence they had to expect
for their conviction. .... They had not seized the idea that they must not
expect to understand the processes of outward causes, but only their re-
sults ; and consequently, the whole physical philosophy of the Greeks was
an attempt to identify mentally the effect with its cause, to feel after some
not only necessary but natural connection, where they meant by natural
that which would per se carry some presumption to their own mind.
They wanted to see some reason why the physical antecedent should
produce this particular consequent, and their only attempts were in direc-
tions where they could find such reasons. "f In other words, they were
not content merely to know that one phenomenon was always followed by
another ; they thought that they had not attained the true aim of science,
Unless they could perceive something in the nature of the one phenomenon
* Eeid's Essays on the Active Powers, Essay iv., chap. 3.
t Prospective Review for February, 1850.
260 INDUCTION.
from which it might have been known or presumed previous to trial that
it would be followed by the other : just what the writer, who has so clear-
ly pointed out their error, thinks that he perceives in the nature of the
phenomenon Volition. And to complete the statement of the case, he
^ should have added that these early speculators not only made this their
aim, but were quite satisfied with their success in it ; not only sought for
causes which should carry in their mere statement evidence of their eiB-
/ cienoy, but fully believed that they had found such causes. The reviewer
( can see plainly that this was an error, because he does not believe that
there exist any relations between material phenomena which can account
for their producing one another ; but the very fact of the persistency of
the Greeks in this error, shows that their minds were in a very different
state : they were able to derive from the assimilation of physical facts to
other physical facts, the kind of mental satisfaction which we connect with
the word explanation, and which the reviewer would have us think can
only be found in referring phenomena to a will. When Thales and Hippo
held that moisture was the universal cause, and external element, of which
all other things were but the infinitely various sensible manifestations j
when Anaximenes predicated the same thing of air, Pythagoras of numbers,
and the like, they all thought that they had found a real explanation ; and
were content to rest in this explanation as ultimate. The ordinary se-
quences of the external universe appeared to them, no less than to their
critic, to be inconceivable without the supposition of some universal agen-
cy to connect the antecedents with the consequents; but they did not
think that Volition, exerted by minds, was the only agency which fulfilled
this requirement. Moisture, or air, or numbers, carried to their minds a
precisely similar impression of rqaking intelligible what was otherwise in-
conceivable, and gave the same full satisfaction to the demands of their
conceptive faculty.
It was not the Greeks alone, who " wanted to see some reason why the
physical antecedent should produce this particular consequent," some con-
nection " which would per se carry some presumption to their own mind."
Among modern philosophers, Leibnitz laid it down as a self-evident prin-
ciple that all physical causes without exception must contain in their own
nature something which makes it intelligible that they should be able to
produce the effects which they do produce. Far from admitting Volition
as the only kind of cause which carried internal evidence of its own pow-
er, and as the real bond of connection between physical antecedents and
their consequents, he demanded some naturally and per se efficient physic-
al antecedent as the bond of connection between Volition itself and its ef-
fects. He distinctly refused to admit the will of God as a suflicient ex-
planation of any thing except miracles ; and insisted upon finding some-
thing that would account better for the phenomena of nature than a mere
reference to divine volition.*
Again, and conversely, the action of mind upon matter (which, we are
now told, not only needs no explanation itself, but is the explanation of all
other effects), has appeared to some thinkers to be itself the grand incon-
ceivability. It was to get over this very difficulty that the Cartesians in.
vented the system of Occasional Causes. They could not conceive that.
thoughts in a mind could produce movements in a body, or that bodily
movements could produce thoughts. They could see no necessary conneo-
♦ Vide supra, p. 178, note.
LAW OF CAUSATION. 261
tion, no relation a priori, between a motion and a thought. And as the
Cartesians, more than any other school of philosophical speculation before
or since, made their own minds the measure of all things, and refused, on
principle, to believe that Nature had done what they were unable to see
any reason why she must do, they affirmed it to be impossible that a ma-
terial and a mental fact could be causes one of another. They regarded
them as mere Occasions on which the real agent, God, thought fit to exert
his power as a Cause. When a man wills to move his foot, it is not his
will that moves it, but God (they said) moves it on the occasion of his
■will. God, according to this system, is the only efficient cause, not qud
mind, or qud endowed with volition, but qud omnipotent. This hypoth-
esis was, as I said, originally suggested by the supposed inconceivability
of any real mutual action between Mind and Matter ; but it was afterward
extended to the action of Matter upon Matter, for on a nicer examination
they found this inconceivable too, and therefore, according to their logic,
impossible. The deus ex machind was ultimately called in to produce a
spark on the occasion of a flint and steel coming together, or to break an
egg on the occasion of its falling on the ground.
All this, undoubtedly, shows that it is the disposition of mankind in gen-
eral, not to be satisfied with knowing that one fact is invariably anteced-
ent and another consequent, but to look out for something which may seem
to explain their being so. But we also see that this demand may be com-
pletely satisfied by an agency purely physical, provided it be much more
familiar than that which it is invoked to explain. To Thales and Anaxim-
enes, it appeared inconceivable that the antecedents which we see in nature
should produce the consequents; but perfectly natural that watei-, or air,
should produce them. The writers whom I oppose declare this inconceiv-
able, but can conceive that mind, or volition, is per se an efficient cause :
while the Cartesians could not conceive even that, but peremptorily de-
clared that no mode of production of any fact whatever was conceivable,
except the direct agency of an omnipotent being; thus giving additional
proof of what finds new confirmation in every stage of the history of sci-
ence : that both what persons can, and what they can not, conceive, is very
much an affair of accident, and depends altogether on their experience, and
their habits of thought; that by cultivating the requisite associations of
ideas, people may make themselves unable to conceive any given thing ;
and may make themselves able to conceive most things, however inconceiv-
able these may at first appear ; and the same facts in each person's mental
history which determine what is or is not conceivable to him, determine
also which among the various sequences in nature will appear to him so
natural and plausible, as to need no other proof of their existence ; to be
evident by their own light, independent equally of experience and of ex-
planation.
By what rule is any one to decide between one theory of this descrip-
tion and another ? The theorists do not direct us to any external evidence ;
they appeal each to his own subjective feelings. One says, the succession
C B appears to me more natural, conceivable, and credible per se, than the
succession A B ; you are therefgre mistaken in thinking that B depends
upon A; I am certain, though I can give no other evidence of it, that C
comes in between A and B, and is the i-eal and only cause of B. The oth-
er answers, the successions C B and A B appear to me equally natural and
conceivable, or the latter more so than the former : A is quite capable of
producing B without any other intervention. A third agrees with the first
262 INDUCTION.
in being unable to conceive that A can produce B, but finds the sequence
D B still more natural than C B, or of nearer kin to the subject-matter, and
prefers his D theory to the C theory. It is plain that there is no universal
law operating here, except the law that each person's conceptions are gov-
erned and limited by his individual experiences and habits of thought..
We are warranted in saying of all three, what each of them already be-
\Jlieves of the other two,namely, that they exalt into an original law of the-
human intellect and of outward nature one particular sequence of phe-
nomena, which appears to them more natural and more conceivable than
other sequences, only because it is more familiar. And from this judg-
ment I am unable to except the theory, that Volition is an Efficient Cause.
I am unwilling to leave the subject without adverting to the additional
fallacy contained in the corollary from this theory; in the inference that
because Volition is an efficient cause, therefore it is the only cause, and the
j direct agent in producing even what is apparently produced by something
else. Volitions are not known to produce any thing directly except nerv-
ous action, for the will influences even the muscles only through the nerves..
, Though it were granted, then, that every phenomenon has an efficient, and
J not merely a phenomenal cause, and that volition, in the case of the pe-
culiar phenomena which are known to be produced by it, is that efficient
cause ; are we therefore to say, with these writers, that since we know of
no other efficient cause, and ought not to assume one without evidence,
there is no other, and volition is the direct cause of all phenomena ? A
more outrageous stretch of inference could hardly be made. Because
among the infinite vai-iety of the phenomena of nature there is one, namely,
a particular mode of action of certain nerves, which has for its cause, and
as we are now supposing for its efficient cause, a state of our mind ; and
because this is the only efficient cause of which we are conscious, being the
only one of which in the nature of the case we can be conscious, since it is
the only one which exists within ourselves ; does this justify us in conclud-
ing that all other phenomena must have the same kind of efficient cause
■with that one eminently special, narrow, and peculiarly human or animal,
phenomenon ? The nearest parallel to this specimen of generalization is
suggested by the recently revived controversy on the old subject of Plural-
ity of Worlds, in which the contending parties have been so conspicuously
successful in overthrowing one another. Here also we have experience
only of a single case, that of the world in which we live, but that this is in-
habited we know absolutely, and without possibility of doubt. Now if on
this evidence any one were to infer that every heavenly body without ex-
ception, sun, planet, satellite, comet, fixed star or nebula, is inhabited, and
must be so from the inherent constitution of things, his inference would
exactly resemble that of the writers who conclude that because volition is
the efficient cause of our own bodily motions, it must be the efficient cause
of every thing else in the universe. It is true there are cases in which,
with acknowledged propriety, we generalize from a single instance to 3
multitude of instances. But they must be instances which resemble the
one known instance, and not such as have no circumstance in common with
it except that of being instances. I have, for example, no direct evidence
that any creature is alive except myself, yet I attribute, with full assur-
ance, life and sensation to other human beings and animals. But I do not
conclude that all other things are alive merely because I am. I ascribe tO'
certain other ci'eatures a life like my own, because they manifest it by the
same sort of indications by which mine is manifested. I find that their
LAW OF CAUSATION. 26S
phenomena and mine conform to the same laws, and it is for this reason
that I believe both to arise from a similar cause. Accordingly I do not
extend the conclusion beyond the grounds for it. Earth, fire, mountains,,
trees, are remarkable agencies, but their phenomena do not conform to the.
same laws as my actions do, and I therefore do not believe earth or fii-e,
nriountains or trees, to possess animal life. But the supporters of the Voli-
tion Theory ask us to infer that volition causes every thing, for no reason-
except that it causes one particular thing ; although that one phenomenon,,
far from being a type of all natural phenomena, is eminently peculiar ; its.
laws bearing scarcely any resemblance to those of any other phenomenon^
whether of inorganic or of organic nature.
NOTE SUPPLEMENTAKY TO THE PRECEDING CHAPTER.
The author of the Second Burnett Prize Essay (Dr. TuUoch), who has employed a consid-
erable number of pages in controverting the doctrines of the preceding chapter, has somewhat
BUi-prised me by denying a fact, which I imagined too well known to require proof^that there
have been philosophers who found in physical explanations of phenomena the same complete
mental satisfaction which we are told is only given by volitional explanation, and others who-
denied the Volitional Theory on the same ground of inconceivability on which it is defended.
The assertion of the Essayist is countersigned still more positively by an able reviewer of the.
Essay:* "Two illustrations," says the reviewer, "are advanced by Mr. Mill: the case of
Thales and Anaximenes, stated by him to have maintained, the one Moisture and the other
Air to be the origin of all things; and that of Descartes and Leibnitz, whom he asserts to-
have found the action of Mind upon Matter the grand inconceivability. In counter-statement
as to the first of these cases the author shows — what we believe now hardly admits of doubt
— that the Greek philosophers distinctly recognized as beyond and above their primal materiat
source, the vov^, or Divine Intelligence, as the efficient and originating Source of all ; and as
to the second, by proof that it was the mode, not the fact, of that action on matter, which was-
represented as inconceivable."
A greater quantity of historical error has seldom been comprised in a single sentence.
With regard to Thales, the assertion that he considered water as a mere material in the hands
of voi( rests on a passage of Cicero de Naturd Deorum ; and whoever will refer to any of
the accurate historians of philosophy, will find that they treat this as a mere fancy of Cicero,
resting on no authority, opposed to all the evidence ; and make surmises as to the manner inf
which Cicero may have been led into the error. (See Hitter, vol. i., p. 211, 2d ed. ; Brandis,
vol. i., pp. 118-9, 1st ed. ; Preller, Historia Philosophim Grceco- Romance, p. 10. "Schiefe-
Ansicht, durchaus zu verwerfen;" " augenscheinlich folgernd statt zu berichten;'' "quibus-
vera sententia Thaletis plane detorquetur," are the expressions of these writei-s.) As for An-
aximenes, he even according to Cicero, maintained, not that air was the material out of which.
God made the world, but that the air was a god : "Anaximenes aera deum statuit ;" or, ac-
cording to St. Augustine, that it was the material out of which the gods were made ; " non
tamen ab ipsis [Diis] aerem factum, sed ipsos ex aere ortos credidit. " Those who are not fa-
miliar with the metaphysical terminology of antiquity, must not be misled by finding it stated
that Anaximenes attributed inix^ (translated soul, or life) to his universal element, the air.
The Greek philosophers acknowledged several kinds of ijmx^, the nutritive, the sensitive, and
the intellective. t Even the moderns, with admitted correctness, attribute life to plants. As-
far as we can make out the meaning of Anaximenes, he made choice of Air as the universal
agent, on the ground that it is perpetually in motion, without any apparent cause external to-
itself : so that he conceived it as exercising spontaneous force, and as the principle of life and
activity in all things, men and gods inclusive. If this be not representing it as the Efficient
Cause the dispute altogether has no meaning.
If either Anaximenes, or Thales, or any of their contemporaries, had held the doctrine that
vmic was the Efficient Cause, that doctrine could not have been reputed, as it was throughout
antiquity, to have originated with Anaxagoras. The testimony -of Aristotle, in the first book
of his Metaphysics, is perfectly decisive with respect to these early speculations. After enu-
merating four kinds of causes, or rather four different meanings of the word Cause, viz., th&
Essence of a thing, the Matter of it, the Origin of Motion (Efficient Cause), and the End or
* Westminster Beview for October, 1855.
t See the whole doctrine in Aristotle de Amma, where the Speimiiij fux^ is treated a»
exactly equivalent to Bpenrimj dvvafug.
264 INDUCTION.
Pinal Cause, he proceeds to say, that most of the early philosophers reeognizeiS only the sec-
ond kind of Cause, the Matter of a thing, tH; tv i)%rit elSei jiovaQ ^Btjaav apxii( elvat iravrav.
As his first example he specifies Thales, whom he describes as taking the lead in this view of
the subject, 6 rfjc roiavrtic dpxvy^C ^i/loffo^jof, and goes on to Hippon, Anaximenes, l)ioge-
nes (of ApoUonia), Hippasus of Metapontum, Heraclitus, and Empedocles. Anaxagoras,
however (he proceeds to say), taught a different doctrine, as we know, and it is alleged that
Hermotimus of Clazomencs taught it before him. Anaxagoras represented, that even if these
■various theories of the universal material were true, there would be need of some other cause
to account for the transformations of the materials, since the material can not originate its
own changes: ou yap dy to ys vTronetfievov aitrb iroiel fiEra^aXketv havTO' Tisyu ff olov ovte
rb ^vXcyv ovts 6 ;i;aA/c6f alnoQ tov nerajidWeiv iicuTepov avTuv, ovSk noiel rS fiiv ^vTiOv kMviiv
o 6i x(iy^fib(: avdpidvra, dXX' brtpov n ttjq fierafioX^g alriov, viz, , the other kind of cause, 56ev
7/ dpxT) T^f Kivqaeuf — an Efficient Cause. Aristotle expresses great approbation of this doc-
trine (which he says made its author appear the only sober man among persons raving, olov
vij<po>v i(puvri trap' eUij Xeyovrai roOf npoTepov) ; but while describing the influence which it ex-
ercised over subsequent speculation, he remarks that the philosophers against whom this, as he
thinks, insuperable difficulty was urged, had not felt it to be any difficulty : ovSh t&uax^pdvav
iv iavTolg. It is surely unnecessary to say more in proof of the matter of fact which Dr. Tul-
loch and his reviewer disbelieve.
Having pointed out what he thinks the error of these early speculators in not recognizing
the need of an efficient cause, Aristotle goes on to mention two other efficient causes to which
they might have had recourse, instead of intelligence : rixVy chance, and rb aiiTOfidrov, spon-
taneity. He indeed puts these aside as not sufficiently worthy causes for the order in the uni-
verse, oi& av Tfyt avTOfjuTu Kai r^ Tvx''^ togovtov ^irirpeipai Trpuyfia KaXug elxev ; but he does
not reject them as incapable of prod ucing any effect, but only as incapable of producing that
«tfect. He himself recognizes tvxi and rb avTO/idrov as co-ordinate agents with Mind in pro-
ducing the phenomena of the universe ; the department allotted to them being composed of
-all the classes of phenomena which are not supposed to follow any uniform law. By thus in.
eluding Chance among efficient causes, Aristotle fell into an error which philosophy has now
outgrown, but which is by no means so alien to the spirit even of modern speculation as it
may at first sight appear. Up to quite a recent period philosophers went on ascribing, and
many of them have not yet ceased to ascribe, a real existence to the results of abstraction.
Chance could make out as good a title to that dignity as many other of the mind's abstract
creations : it had had a name given to it, and why should it not be a reality ? As for rb ai-
To/idrov, it is recognized even yet as one of the modes of origination of phenomena by all
those thinkers who maintain what is called the Freedom of the Will. The same self-deter-
mining power which that doctrine attributes to volitions, was supposed by the ancients to be
possessed also by some other natural phenomena : a circumstance which throws considerable
light on more than one of the supposed invincible necessities of belief I have introduced it
here, because this belief of Aristotle, or rather of the Greek philosophers generally, is as fatal
as the doctrines of Thales and the Ionic school to the theory that the human mind is com-
pelled by its constitution to conceive volition as the origin of all force, and the efficient cause
of all phenomena. *
* It deserves notice that the parts of nature which Aristotle regards as representing evi-
dence of design, are the Uniformities : the phenomena in so far as reducible to law. Tvxri
and rb avTOfmrov satisfy him as explanations of the variable element in phenomena, but their
occurring according to a fixed rule can only, to his conceptions, be accounted for by an In-
telligent Will. The common, or what may be called the instinctive, religious interpretation
of nature, is the reverse of this. The events in which men spontaneously see the hand of a
supernatural being, are those which can not, as they think, be reduced to a physical law.
What they can distinctly connect with physical causes, and especially what they can predict,
though of course ascribed to an Author of Nature, if they already recognize such an author,
might be conceived, they think, to arise from a blind fatality, and in any case do not appear
to them to bear so obviously the mark of a divine will. And this distinction has been counte-
nanced by eminent writers on Natural Theology, in particular by Dr. Chalmers, who thinks
that though design is present everywhere, the irresistible evidence of it is to he found not in
the laws of nature but in the- collocations, i. e. , in the part of nature in which it is impossible
to trace any law. A few properties of dead matter might, he thinks, conceivably account for
the regular and invariable succession of effects and causes ; but that the different kinds of
matter have been so placed as to promote beneficent ends, is what he regards at the proof of
a Divine Providence. Mr. Baden Powell, in his Essay entitled "Philosophy of Creation,"
has returned to the point of view of Aristotle and the ancients, and vigorously re-asserts the
<ioctrine that the indication of design in the universe is not special adaptations, but Uniformi-
ty and Law, these being the evidences of mind, and not what appears to us to be a provisioa
LAW OF CAUSATION. 265
With regard to the modern philosophers (Leibnite and the CartesianB) whom I had cited as
having maintained that the action of mind upon matter, so far from being the only conceiva-
ble origin of material phenomena, is itself inconceivable ; the attempt to rebut this argument
by asserting that the mode, not the fact, of the action of mind on matter was represented as
inconceivable, is an abuse of the privilege of writing confidently about authors without read-
ing them ; tor any knowledge whatever of Leibnitz would have taught those who thus speak
of him, that the inconceivability of the mode, and the impossibility of the thing, were in his
mind convertible expressions. What was his famous Principle of the Sufficient Reason, the
very corner-stone of his Philosophy, from which the Pre-established Harmony, the doctrine
of Monads, and all the opinions most characteristic of Leibnitz, were corollaries ? It was,
that nothing exists, the existence of which is not capable of being proved and explained a
priori; 4he proof and explanation in the case of contingent facts being derived from the na-
ture of their causes ; which could not be the causes unless there was something in their nature
showing them to be capable of producing those particular effects. And this "something"
which accounts for the production of physical effects, he was able to find in many physical
causes, but could not find it in any finite minds, which therefore he unhesitatingly asserted to
be incapable of producing any physical effects whatever. " On ne saurait concevoir," he says,
" une action reciproque de la matiere et de I'intelligence I'nne sur I'autre," and there is there-
fore (he contends) no choice but between the Occasional Causes of the Cartesians and his
own Pre-established Harmony, according to which there is no more connection between our
volitions and our muscular actions than there is between two clocks which are wound up
to strike at the same instant. But he felt no similar difficulty as to physical causes ; and .
throughout his speculations, as in the passage I have already cited respecting gravitation, he
distinctly refuses to consider as part of the order of nature any fact which is not explicable
from the nature of its physical cause.
With regard to the Cartesians (not Descartes ; I did not make that mistake, though the re-
viewer of Dr. Tulloch's Essay attributes it to me) I take a passage almost at random from
Malebranche, who is the best known of the Cartesians, and, though not the inventor of the sys-
tem of Occasional Causes, is its principal expositor. In Part II., chap. iii. , of his Sixth Book,
having first said that matter can not have the power of moviijg itself, he proceeds to argue
that neither can mind have the power of moving it. " Quand on examine I'id^e que Ion a da
tons les esprits f.i'is, on ne voit point de liaison necessaire entre lenr volonte et'le mouvement
de quelque coi-ps que ce soit, on voit au contraire qu'il n'y en a point, et qu'il n'y en peut avoir "
(there is nothing in the idea of finite mind which can account for its causing the motion of a
body) ; "on doit aussi conclure, si on vent raisonner selon ses lumieres, qu'il n'y a aucun esprit
cre^ qui puisse remuer quelque corps que ce soit comme cause veritable ou principale, da
meme que Ton a dit qu'aucnn corps ne se pouvait remuer soi-meme :" thus the idea of Mind
is according to him as incompatible as the idea of Matter with the exercise of active force.
But when, he continues, we consider not a, created but a Divine Mind, the case is altered ;
for the idea of a Divine Mind includes omnipotence ; and the idea of omnipotence does con-
tain the idea of being able to move bodies. Thus it is the nature of omnipotence which ren-
ders the motion of bodies even by the Divine Mind credible or conceivable, while, so far a»
depended on the mere nature of mind, it would have been inconceivable and incredible. If
Malebranche had not believed in an omnipotent Being, he would have held all action of mind
on body to be a demonstrated impossibility.*
A doctrine more precisely the reverse of the Volitional theory of causation can not well be
imagined. The Volitional theory is, that we know by intuition or by direct experience the
action of our own mental volitions on matter ; that we may hence infer all other action upon
matter to be that of volition, and might thus know, without any other evidence, that matter
is under the government of a Divine Mind. Leibnitz and the Cartesians, on the contrary,
maintain that our volitions do not and can not act upon matter, and that it is only the ex-
istence of an all-governing Being, and that Being omnjpotent, which can account for the se-
quence between our volitions and our bodily actions. When we consider that each of these two
theories, which, as theories of causation, stand at the opposite extremes of possible divergence
for our uses. While I decline to express any opinion here on this vexata qutestio, I ought
not to mention Mr. Powell's volume without the acknowledgment due to the philosophic
spirit which peiTades generally the three Essays composing it, forming in the case of one of
them (the " Unity of Worlds ") an honorable contrast with the other dissertations, so far as
they have come under my notice, which have appeared on either side of that controversy.
* In the words of Fontenelle, another celebrated Cartesian, "les philosophes aussi bien qua
le peuple avaient cru que I'slme et le corps agissaient reellement et physiquemeht I'un sur
I'autre. Descartes vint, qui prouva que leur nature ne permettait point cette sorte de coni-
munication veritable, et qu'ils n'en pouvaient avoir qu'une apparente, dont Dieu etait le Medi-
ateur." — CCEuvres de Fontenelle, ed. 1767, torn, v., p. 534.)
■266 INDUCTION.
from one another, invokes not only as its evidence, but as its sole evidence, the absolute in-
conceivability of any theory bat itself, we are enabled to measure the worth of this kind of
•evidence : and when we find the Volitional theory entirely built upon the assertion that by
our mental constitution we are compelled to recognize our volitions as efficient causes, and
then find other thinkers maintaining that we know that they are not and can not be such
causes, and can not conceive them to be so, I think we have a right to say that this supposed
law of our mental constitution does not exist.
Dr. TuUoch (pp. 45-47) thinks it a sufficient answer to this, that Leibnitz and the Cartesians
-were Theists, and believed the will of God to be an efficient cause. Doubtless they did, and
the Cartesians even believed (though Leibnitz did not) that it is the only such cause. Dr.
TuUoch mistakes the nature of the question. I was not writing on Theism, as Dr. Tulloch
is, but against a particular theory of causation, which, if it be unfounded, can give no effect-
ive support to Theism or to any thing else. I found it asserted that volition is the only ef-
ficient cause, on the ground that no other efficient cause is conceivable. To this assertion I
oppose the instances of Leibnitz and of the Cartesians, who affirmed with equal positiveness
that volition as an efficient cause is itself not conceivable, and that omnipotence, which ren-
<Jers all things conceivable, can alone take away the impossibility. This I thought, and think,
a conclusive answer to the argument on which this theory of causation avowedly depends.
But I certainly did not imagine that Theism was bound up with that theory ; nor expected
to be charged with denying Leibnitz and the Cartesians to be Theists because I denied that
they held the theory.
CHAPTER VI.
OK THE COMPOSITION OF CAUSES.
§ 1. To complete the general notion of causation on which the rules of
•experimental inquiry into the laws of nature must be founded, one dis-
tinction still remains to be pointed out: a distinction so radical, and of so
much importance, as to require a chapter to itself.
The preceding discussions have rendered us familiar with the case in
which several agents, or causes, concur as conditions to the production of
an effect ; a case, in truth, almost universal, there being very few effects to
the production of which no more than one agent contributes. Suppose,,
then, that two different agents, operating jointly, are followed, under a
■certain set of collateral conditions, by a given effect. If either of these
■agents, instead of being joined with the other, had operated alone, under
the same set of conditions in all other respects, some effect would probably
have followed, which would have been different from the joint effect of
the two, and more or less dissimilar to it. Now, if we happen to know
what would be the effect of each cause when acting separately from the
other, we are often able to arrive deductively, or a priori, at a correct pre-
diction of what will arise from their conjunct agency. To render this pos-
sible, it is only necessary that, the same law which expresses the effect of
each cause acting by itself, shall also correctly express the part due to that
•cause of the effect which follows from the two together. This condition is
realized in the extensive and important class of phenomena commonly call-
•ed mechanical, namely the phenomena of the communication of motion (or
of pressure, which is tendency to motion) from one body to another. In
this important class of cases of causation, one cause never, properly speak-
ing, defeats or frustrates another ; both have their full effect. If z, body is
propelled in two dii-ections by two forces, one tending to drive it to the
north and the other to the east, it is caused to move in a given time exact-
ly as far in both directions as the two forces would separately have carried
it ; and is left precisely where it would have arrived if it had been acted
COMPOSITION OF CAUSES. 267
upon first by one of the two forces, and afterward by the other. This law
■of nature is called, in dynamics, the principle of the Composition of Forces ;
and in imitation of that well-chosen expression, I shall give the name of the
■Composition of Causes to the principle which is exemplified in all cases in
■which the joint effect of several causes is identical with the sum of their
separate effects.
This principle, however, by no means prevails in all departments of the
field of nature. The chemical combination of two substances produces, as
is well known, a third substance, with properties different from those of
■either of the two substances separately, or of both of them taken together.
Not a trace of the properties of hydrogen or of oxygen is observable in
those of their compound, water. The taste of sugar of lead is not the
sum of the tastes of its component elements, acetic acid and lead or its
oxide; nor is the color of blue vitriol a mixture of the colors of sulphuric
acid and copper. This explains why mechanics is a deductive or demon-
strative science, and chemistry not. In the one, we can compute the ef-
fects of combinations of causes, whether real or hypothetical, from the
laws which we know to govern those causes when acting separately, be-
cause they continue to observe the same laws when in combination which
they observe when separate: whatever would have happened in conse-
quence of each cause taken by itself, happens when they are together,
and we have only to cast up the results. Not so in the phenomena which
are the peculiar subject of the science of chemistry. There most of the
uniformities to which the causes conform when separate, cease altogether
when they are conjoined ; and we are not, at least in the present state of
our knowledge, able to foresee what result will follow from any new com-
bination until we have tried the specific experiment.
If this be true of chemical combinations, it is still more true of those far
more complex combinations of elements which constitute organized bodies ;
and in which those extraordinary new uniformities arise which are called
the laws of life. All organized bodies are composed of parts similar to
those composing inorganic nature, and which have even themselves existed
in an inoi'ganic state ; but the phenomena of life, which result from the
juxtaposition of those parts in a certain manner, bear no analogy to any
of the effects which would be produced by the action of the component
substances considered as mere physical agents. To whatever degree we
might imagine our knowledge of the properties of the several ingredients
of a living body to be extended and perfected, it is certain that no mere
summing up of the separate actions of those elements will ever amount to
the action of the living body itself. The tongue, for instance, is, like all
other parts of the animal frame, composed of gelatine, fibrine, and other
products of the chemistry of digestion ; but from no knowledge of the
properties of those substances could we ever predict that it could taste, un-
less gelatine or fibrine could themselves taste ; for no elementary fact can t
be in the conclusion which was not in the premises.
"There are thus two different modes of the conjunct action of causes ;
irom which arise two modes of conflict, or mutual interference, between
laws of nature. Suppose, at a given point of time and space, two or more
•causes, which, if they acted separately, would produce effects contrary, or
at least conflicting with each other; one of them tending to undo, wholly
or partially, what the other tends to do. Thus the expansive force of the
gases generated by the ignition of gunpowder tends to project a bullet
toward the sky, while its gravity tends to make it fall to the ground. A
268 INDUCTION.
Stream running into a reservoir at one end tends to fill it higher and high-
er, while a drain at the other extremity tends to empty it. Now, in such
cases as these, even if the two causes which are in joint action exactly an-
nul one another, still the laws of both are fulfilled ; the effect is the same
as if the drain had been open for half an hour first,* and the stream had
flowed in for as long afterward. Each agent produces the same amount of
effect as if it had acted separately, though the contrary effect which was
taking place during the same time obliterated it as fast as it was produced.
Here, then, are two causps, producing by their joint operations an effect
which at first seems quite dissimilar to those which they produce separate-
ly, but which on examination proves to be really the sum of those separate
effects. It will be noticed that we here enlarge the idea of the sum of two
effects, so as to include what is commonly called their difference, but which
is in reality the result of the addition of opposites ; a conception to which
mankind are indebted for that admirable extension of the algebraical cal-
culus, which has so vastly increased its powers as an instrument of discov-
ery, by introducing into its reasonings (with the sign of subtraction pre-
fixed, and under the name of Negative Quantities) every description what-
ever of positive phenomena, provided they are of such a quality in reference
to those previously introduced, that to add the one is equivalent to suIk
tracting an equal quantity of the other.
There is, then, one mode of the mutual interference of laws of nature, in
which, even when the concurrent causes annihilate each other's effects, each
exerts its full efficacy according to its own law — its law as a separate agent.
But in the other description of cases, the agencies which are brought to-
gether cease entirely, and a totally different set of phenomena arise : as in
the experiment of two liquids which, when mixed in cei-tain proportions,,
instantly become, not a larger amount of liquid, but a solid mass.
§ 2. This difference between the case in which the joint effect of causes
is the sum of their separate effects, and the case in which it is heteroge-
neous to them — between laws which work together without alteration, and
laws which, when called upon to work together, cease and give place to oth-
ers— is one of the fundamental distinctions in nature. The former case,
that of the Composition of Causes, is the general one; the other is always
special and exceptional. There are no objects which do not, as to some of
their phenomena, obey the principle of the Composition of .Causes; none
that have not some laws which are rigidly fulfilled in every combination
into which the objects enter. The weight of a body, for instance, is a
property which it retains in all the combinations in which it is placed.
The weight of a chemical compound, or of an oi'ganized body, is equal to
the sum of the weights of the elements which compose it. The weight
either of the elements or of the compound will vary, if they be carried far-
ther from their centre of attraction, or brought nearer to it ; but whatever
effects the one effects the other. They always remain precisely equal. So,
again, the component parts of a vegetable or animal substance do not lose
their mechanical and chemical properties as separate agents, when, by a
peculiar mode of juxtaposition, they, as an aggregate whole, acquire physi-
ological or vital properties in addition. Those bodies continue, as before,
* I omit, for simplicity, to take into account the eflFeet, in tliis latter case, of the diminution
of pressure, in diminishing the flow of water through the drain ; which evidently in no way
affects the truth or applicability of the principle, since when the two causes act simultaneously
the conditions of that diminution of pressure do not arise.
COMPOSITION OF CAUSES. 269
to obey mechanical and chemical laws, in so fav as the operation of those
laws is not counteracted by the new laws which govern them as organized
beings ; when, in short, a concurrence of causes takes place which calls into
action new laws bearing no analogy to any that we can trace in the sepa-
rate operation of the causes, the new laws, while they supersede one portion
■of the previous laws, may co-exist with another portion, and may even com-
pound the effect of those previous laws with their own.
Again, laws which were themselves generated in the second mode, may
generate others in the first. Though there are laws which, like those of
chemistry and physiology, owe their existence to a breach of the principle
■of Composition of Causes, it does not follow that these peculiar, or, as they
might be termed, heteropathic laws, are not capable of composition with
one another. The causes which by one combination have had their laws
altered, may carry their new laws with them unaltered into their ulterior
■combinations. And hence there is no reason to despair of ultimately raising
•chemistry and physiology to the condition of deductive sciences ; for though
it is impossible to deduce all chemical and physiological truths from the
laws or properties of simple substances or elementary agents, they may
possibly be deducible from laws which commence when these elementary
agents are brought together into some moderate number of not very com-
plex combinations. The Laws of Life will never be deducible from the
mere laws of the ingredients, but the prodigiously complex Facts of Life
may all be deducible from comparatively simple laws of life ; which laws
(depending indeed on combinations, but on comparatively simple combi-
nations, of antecedents) may, in more complex circumstances, be strictly
compounded with one another, and with the physical and chemical laws of
the ingredients. The details of the vital phenomena, even now, afford innu-
merable exemplifications of the Composition of Causes ; and in proportion
as these phenomena are more accurately studied, there appears more reason
to believe that the same laws which operate in the simpler combinations
of circumstances do, in fact, continue to be observed in the more complex.
This will be found equally true in the phenomena of mind ; and even in
social and political phenomena, the results of the laws of mind. It is in
the case of chemical phenomena that the least progress has yet been made
in bringing the special laws under general ones from which they may be
deduced ; but there are even in chemistry many circumstances to encourage
the hope that such general laws will hereafter be discovered. The differ-
ent actions of a chemical compound will never, undoubtedly, be found to
be the sums of the actions of its separate elements ; but there may exist,
between the propeilies of the compound and those • of its elements, some
constant relation, which, if discoverable by a sufficient induction, would en-
able us to foresee the sort of compound which will result from a new com-
bination before we have actually tried it, and to judge of what sort of el-
ements some new substance is compounded before we have analyzed it.
The law of definite pi-oportions, first discovered in its full generality by
Dalton, is a complete solution of this problem in one, though but a second-
ary aspect, that of quantity ; and in respect to quality, we have already
some partial generalizations, sufficient to indicate the possibility of ulti-
mately proceeding farther. We can predicate some common properties
of the kind of compounds which result from the combination, in each of the
small number of possible proportions, of any acid whatever with any base.
We have also the curious law, discovered by Berthollet, that two soluble
salts mutually decompose one another whenever the new combinations
270 INDUCTION.
which result produce an insoluble compound, or one less soluble than the
two former. Another uniformity is that called the law of isomorphism;
the identity of the crystalline forms of substances which possess in common
certain peculiarities of cljemical composition.* Thus it appears that even
heteropathio laws, such laws of combined agency as are not compounded
of the laws of the separate agencies, are yet, at least in some cases, derived
from them according to a fixed principle. There may, therefore, be laws
of the generation of laws from others dissimilar to them ; and in chemis-
try, these undiscovered laws of the dependence of the properties of the
compound on the properties of its elements, may, together with the laws of
the elements themselves, furnish the premises by which the science is per-
haps destined one day to be rendered deductive.
It would seem, therefore, that there is no class of phenomena in which
the Composition of Causes does not obtain : that as a general rule, causes
in combination produce exactly the same effects as when acting singly : but
that this rule, though general, is not universal : that in some instances, at
some particular points in the transition from separate to united action, the
laws change, and an entirely new set of effects are either added to, or take
the place of, those which arise from the separate agency of the same causes :
the laws of these new effects being again susceptible of composition, to an
indefinite extent, like the laws which they superseded.
§ 3, That effects are proportional to their causes is laid down by some
writers as an axiom in the theory of causation ; and great use is sometimes
made of this principle in reasonings respecting the laws of nature, though it
is encumbered with many diflBculties and apparent exceptions, which much
ingenuity has been expended in showing not to be real ones. This propo-
sition, in so far as it is true, enters as a particular case into the general
principle of the Composition of Causes; the causes compounded being, in
this instance, homogeneous ; in which case, if in any, their joint effect might
be expected to be identical with the sum of their separate effects. If a
force equal to one hundred weight will raise a certain body along an in-
clined plane, a force equal to two hundred weight will raise two bodies ex-
actly similar, and thus the effect is proportional to the cause. But does
not a force equal to tvvo hundred weight actually contain in itself two forces
each equal to one hundred weight, which, if employed apart, would sepa-
rately raise the two bodies in question? The fact, therefore, that when ex-
erted jointly they raise both bodies at once, results from the Composition
of Causes, and is a mere instance of the general fact that mechanical forces
are subject to the lavv of Composition. And so in every other ease which
can be supposed. For the doctrine of the proportionality of effects to their
causes can not of course be applicable to cases in which the augmentation,
of the cause alters the Jcind of effect ; that is, in which the surplus quanti-
ty superadded to the Cause does not become compounded with it, but the
two together generate an altogether new phenomenon. Suppose that the
application of a certain quantity of heat to a body merely increases its
bulk, that a double quantity melts it, and a triple quantity decomposes it:
these three effects being heterogeneous, no ratio, whether corresponding
* Professor Bain adds several other well-established chemical generalizations: "The laws
that simple substances exhibit the strongest affinities ; that compounds are more fusible than,
their elements ; that combination tends to a lower state of matter from gas down to soUd;"
and some general propositions concerning the circumstances which facilitate or resist chem-
ical combination. (Logic, ii., 254.)
COMPOSITION OF CAUSES. 271
or not to that of the quantities of heat applied, can be established between
them. Thus the supposed axiona of the proportionality of effects to their
causes fails at the precise point where the principle of the Composition of
Causes also fails ; viz., where the concurrence of causes is such as to deter-
mine a change in the properties of the body generally, and render it sub-
ject to new laws, more or less dissimilar to those to which it conformed in
Its previous state. The recognition, therefore, of any such law of propor-
tionality is superseded by the more comprehensive principle, in which as.
much of it as is true is implicitly asserted.*
The general remarks on causation, which seemed necessary as an intro-
duction to the theory of the inductive process, may here terminate. That
process is essentially an inquiry into cases of causation. All the uniformi-
ties which exist in the succession of phenomena, and most of the uniformi-
ties in their co-existence, are either, as we have seen, themselves laws of
causation, or consequences resulting from, and corollaries capable of being
deduced from, such laws. If we could determine what causes are correct-
ly assigned to what effects, and what effects to what causes, we should bo
virtually acquainted with the whole course of nature. All those uniformi-
ties which are mere results of causation might then be explained and ac-
counted for ; and every individual fact or event might be predicted, pro-
vided we had the requisite data, that is, the requisite knowledge of the cir-
cumstances which, in the particular instance, preceded it.
To ascertain, therefore, what are the laws of causation which exist in na-
ture; to determine the effect of every cause, and the causes of all effects,!
is the main business of Induction ; and to point out how this is done is the'
chief object of Inductive Logic.
* Professor Bain (Logic, ii. , 39) points out a class of cases, other than that spoken of in
the text, which he thinks must be regarded as an exception to the Composition of Causes.
" Causes that merely make good the collocation for bringing a prime mover into action, or
that release a potential force, do not follow any such rule. One man may direct a gun upon
a fort as well as three : two sparks are not more effectual than one in exploding a barrel of
gunpowder. In medicine there is a certain dose that answers the end ; and adding to it does,
no more good."
I am not sure that these cases are really exceptions. The law of Composition of Causes, I
think, is really fulfilled, and the appearance to the contrary is produced by attending to the
remote instead of the immediate effect of the causes. In the cases mentioned, the immedi-
ate effect of the causes in action is a collocation, and the duplication of the cause does double
the quantity of collocation. Two men could raise the gun to the required angle twice as
quickly as one, though one is enough. Two sparks put two sets of particles of the gunpow-
der into the state of intestine motion which makes them explode, though one is sufficient. It
is the collocation itself that does not, by being doubled, always double the effect ; because in
many cases a certain collocation, once obtained, is all that is required for the production of
the whole amount of effect which can be produced at all at the given time and place. Dou-
I>ling the collocation with difference of time and place, as by pointing two guns, or exploding
a second barrel after the first, does double the effect. This remark applies still more to Mr.
Bain's third example, that of a double dose of medicine ; for a double dose of an aperient
does purge more violently, and a double dose of laudanum does produce longer and sounder
sleep. But a double purging, or a double amount of narcotism, may have remote effects dif-
ferent in kind from the effect of the smaller amount, reducing the case to that of heteropathic
laws, discussed in the text.
272 INDUCTION.
CHAPTER VII.
OF OBSEEVATION AND EXPERIMENT.
§ 1. It results from the preceding exposition, that the process of ascer-
taining what consequents, in nature, are invariably connected with what
antecedents, or in other words what phenomena are related to each other
as causes and effects, is in some sort a process of analysis. That every
fact which begins to exist has a cause, and that this cause must be found
in some fact or concourse of facts which immediately preceded the occur-
rence, may be taken for certain. The whole of the present facts are the
infallible result of all past facts, and more immediately of all the facts
which existed at the moment previous. Here, then, is a great sequence,
which we know to be uniform. If the whole prior state of the entire uni-
verse could again recur, it would again be followed by the present state.
The question is, how to resolve this complex uniformity into the simpler
uniformities which compose it, and assign to each portion of the vast an-
tecedent the portion of the consequent which is attendant on it.
This operation, which we have called analytical, inasmuch as it is the
resolution of a complex whole info the component elements, is more than
a merely mental analysis. No mere contemplation of the phenomena, and
partition of them by the intellect alone, will of itself accomplish the end we
have now in view. Nevertheless, such a mental partition is an indispensa-
ble first step. The order of nature, as perceived at a first glance, presents
at every instant a chaos followed by another chaos. We must decompose
each choas into single facts. We must learn to see in the chaotic ante-
cedent a multitude of distinct antecedents, in the chaotic consequent a mul-
titude of distinct consequents. This, supposing it done, will not of itself
tell us on which of the antecedents each consequent is invariably attendant.
To determine that point, we must endeavor to effect a separation of the
facts from one another, not in our minds only, but in nature. The mental
analysis, however, must take place first. And every one knows that in the
mode of performing it, one intellect differs immensely from another. It is
the essence of the act of observing ; for the observer is not he who merely
sees the thing which is before his eyes, but .he who sees what parts that
thing is composed of. To do this well is a rare talent. One person, from
inattention, or attending only in the wrong place, overlooks half of what he
sees ; another sets down much more than he sees, confounding it with what
he imagines, or with what he infers ; aribther takes note of the kind of all
the circumstances, but being inexpert in estimating their degree, leaves the
quantity of each vague and uncertain ; another sees indeed the whole, but
makes such an awkward division of it into parts, throwing things into one
mass which require to be separated, and separating others which might
more conveniently be considered as one, that the result is much the same,
sometimes even worse, than if no analysis had been attempted at all. It
would be possible to point out what qualities of mind, and modes of men-
tal culture, fit a person for being a good observer: that, however, is a
question not of Logic, but of the Theory of Education, in the most en-
larged sense of the term. There is not properly an Art of Observing.
OBSERVATION AND EXPERIMENT. 2'? 3
There may be rules for observing. But these, like rules for inventing, are
properly instructions for the preparation of one's own mind ; for putting
it into the state in which it will be most fitted to observe, or most likely
to invent. They are, therefore, essentially rules of self-education, which is
a different thing from Logic. They do not teach how to do the thing, but
how to make ourselves capable of doing it. They are an art of strength-
ening the limbs, not an art of using them.
The extent and minuteness of observation which may be requisite, and
the degree of decomposition to which it may be necessary to carry the
mental analysis, depend on the particular purpose in view. To ascertain
the state of the whole universe at any particular moment is impossible, but
would also be useless. In making chemical experiments, we do not think
it necessary to note the position of the planets; because experience has
shown, as a very supei-ficial experience is sufficient to show, that in such
cases that circumstance is not material to the result : and accordingly, in
the ages when men believed in the occult influences of the heavenly bodies,
it might have been unphilosophical to omit ascertaining the precise condi-
tion of those bodies at the moment of the experiment. As to the degree
of minuteness of the mental subdivision, if we were obliged to break down
what we observe into its very simplest elements, that is, literally into sin-
gle facts, it would be difficult to say where we should find them ; we can
hardly ever affirm that our divisions of any kind have reached the ultimate
unit. But this, too, is fortunately unnecessary. The only object of the
mental separation is to suggest the requisite physical separation, so that
we may either accomplish it ourselves, or seek for it in nature ; and we
have done enough when we have carried the subdivision as far as the point
at which we are able to see what observations or experiments we require.
It is only essential, at whatever point our mental decomposition of facts
may for the present have stopped, that we should hold ourselves ready and
able to carry it further as occasion requires, and should not allow the free-
dom of our discriminating faculty to be imprisoned by the swathes and
bands of ordinary classification ; as was the case with all early speculative
inquirers, not excepting the Greeks, to whom it seldom occurred that what
was called by one abstract name might, in reality, be several phenomena,
or that there was a possibility of decomposing the facts of the universe into
any elements but those which ordinary language already recognized.
§ 2. The different antecedents and consequents being, then, supposed to
be, so far as the case requires, ascertained and discriminated from one an-
other, we are to inquire which is connected with which. In every instance
which comes under our observation, there are many antecedents and many
•consequents. If those antecedents could not be severed from one another
except in thought, or if those consequents never were found apart, it would
be impossible for us to distinguish (a posteriori at least) the real laws, or
to assign to any cause its effect, or to any effect its cause. To do so, we
must be able to meet with some of the antecedents apart from the rest, and
observe what follows from them ; or some of the consequents, and observe
by what they are preceded. We must, in short, follow the Baconian rule
of varying the circumstances. This is, indeed, only the first rule of phys-
ical inquiry, and not, as some have thought, the sole rule ; but it is the
foundation of all the rest.
For the purpose of varying the circumstances, we may have recourse
(according to a distinction commonly made) either to observation or to ex-
18
2 '74 INDUCTION.
periment; we may either Jind an instance in nature suited to our purposes,.
or, by an artificial arrangement of circumstances, make one. The value of
the instance depends on what it is in itself, not on the mode in which it is-
obtained: its employment for the purposes of induction depends on the-
same principles in the one case and in the other ; as the uses of money are
the same whether it is inherited or acquired. There is, in short, no differ-
ence in kind, no real logical distinction, between the two processes of in-
vestigation. There are, however, practical distinctions to which it is of
considerable importance to advert.
§ 3. The first and most obvious distinction between Observation and
Experiment is, that the latter is an immense extension of the former. It
not only enables us to produce a much greater number of variations in the-
circumstances than nature spontaneously ofEers, but also, in thousands of
cases, to produce the precise sort of variation which we are in want of for
discovering the law of the phenomenon ; a service which nature, being cour
structed on a quite different scheme from that of facilitating our studies,,
is seldom so friendly as to bestow upon us. For example, in order to as-
certain what principle in the atmosphere enables it to sustain life, the
variation we require is that a living animal should be immersed in each
component element of the atmosphere separately. But nature does not
supply either oxygen or azote in a separate state. We are indebted to ar-
tificial experiment for our knowledge that it is the former, and not the lat-
ter, which supports respiration ; and for our knowledge of the very exist-
ence of the two ingredients.
Thus far the advantage of experimentation over simple observation is-
universally recognized : all are aware that it enables us to obtain innumer-
able combinations of circumstances which are not to be found in nature,,
and so add to nature's experiments a multitude of experiments of our own.
But there is another superiority (or, as Bacon would have expressed it, an-
other prerogative) of instances artificially obtained over spontaneous in-
stances— of our own experiments over even the same experiments when
made by nature — which is not of less importance, and which is far from
being felt and acknowledged in the same degree.
When we can produce a phenomenon artificially, we can take it, as it
were, home with us, and observe it in the midst of circumstances with
which in all other respects we are accurately acquainted. If we desire to-
know what are the effects of the cause A, and are able to produce A by
means at our disposal, we can generally determine at our own discretion, so-
far as is compatible with the nature of the phenomenon A, the whole of
the circumstances which shall be present along with it : and thus, knowing
exactly the simultaneous state of every thing else which is within the reach
of A's influence, we have only to observe what alteration is made in that
state by the presence of A.
For example, by the electric machine we can produce, in the midst of
known circumstances, the phenomena which nature exhibits on a grander
scale in the form of lightning and thunder. Now let any one consider
•what amount of knowledge of the effects and laws of electric agency man-
kind could have obtained from the mere observation of thunder-storms, and
compare it with that which they have gained, and may expect to gain, from
electrical and galvanic experiments. This example is the more striking,,
now that we have reason to believe that electric action is of all natural
phenomena (except heat) the most pervading and universal, which, therer
OBSERVATION AND EXPERIMENT. 275
fore, it might antecedently have been supposed could stand least in need of
artificial means of production to enable it to be studied ; while the fact is
so much the contrary, that without the electric machine, the Leyden jar,
and the voltaic battery, we probably should never have suspected the ex-
istence of electricity as one of the great agents in nature ; the few electric
phenomena we should have known of would have continued to be regard-
ed either as supernatural, or as a sort of anomalies and eccentricities in the
order of the universe.
When we have succeeded in insulating the phenomenon which is the
subject of inquiry, by placing it among known circumstances, we may pro^
duce further variations of circumstances to any extent, and of such kinds
as we think best calculated to bring the laws of the phenomenon into a
clear light. By introducing one well-defined circumstance after anothei'
into the experiment, we obtain assurance of the manner in which the phe-
nomenon behaves under an indefinite variety of possible circumstances.
Thus, chemists, after having obtained some newly-discovered substance in
a pure state (that is, having made sure that there is nothing present which
can interfere with and modify its agency), introduce various other sub-
stances, one by one, to ascertain whether it will combine with them, or de-
compose them, and with what result ; and also apply heat, or electricity, or
pressure, to discover what will happen to the substance under each of these
circumstances. 1
But if, on the other hand, it is out of our power to produce the phenom-
enon, and we have to seek for instances in which nature produces it, the
task before us is very different.
Instead of being able to choose what the concomitant circumstances
shall be, we now have to discover what they are; which, when we go be-
yond the simplest and most accessible cases, it is next to impossible to do
with any precision and completeness. Let us take, as an exemplification of
a phenomenon which we have no means of fabricating artificially, a human
mind. Nature produces many; but the consequence of our not being able
to produce them by art is, that in every instance in which we see a human
mind developing itself, or acting upon other things, we see it surrounded
and obscured by an indefinite multitude of unascertainable circumstances,
rendering the use of the common experimental methods almost delusive.
We may conceive to what extent this is true, if we considei', among
other things, that whenever Nature produces a human mind, she produces,
in close connection with it, a body ; that is, a vast complication of physical
facts, in no two cases perhaps exactly similar, and most of which (except
the mere structure, which we can examine in a sort of coarse way after it
has ceased to act), are radically out of the reach of our means of explora-
tion. If, instead of a human mind, we suppose the subject of investiga-
tion to be a human society or State, all the same difiiculties recur in a great-
ly augmented degree.
We have thus already come within sight of a conclusion, which the prog-
ress of the inquiry will, I think, bring before us with the clearest evi-
dence : namely, that in the sciences which deal with phenomena in which
artificial experiments are impossible (as in the case of astronomy), or in
which they have a very limited range (as in mental philosophy, social
science, and even physiology), induction from direct experience is practiced
at a disadvantage in most cases equivalent to impracticability ; from which
it follows that the methods of those sciences, in order to accomplish any
thing worthy of attainment, must be to a great extent, if not principally,
276 INDUCTION.
deductive. This is already known to be the case with the first of the soi.
ences we have mentioned, astronomy; that it is not generally recognized
as true of the others, is probably one of the reasons why they are not in a
more advanced state.
§ 4. If what is called pure observation is at so great a disadvantage,
compared with artificial experimentation, in one department of the direct
exploration of phenomena, there is another branch in which the advantage
is all on the side of the former.
j Inductive inquiry having for its object to ascertain what causes are con-
nected with what effects, we may begin this search at either end of the road
which leads from the one point to the other : we may either inquire into
the effects of a given cause or into the causes of a given effect. The fact
that light blackens chloride of silver might have been discovered either by
experiments on light, trying what effect it would produce on various sub-
stances, or by observing that portions of the chloride had repeatedly be-
come black, and inquiring into the circumstances. The effect of the urali
poison might have become known either by administering it to animals,
or by examining how it happened that the wounds which the Indians of
Guiana inflict with their arrows prove so uniformly mortal. Now it is
manifest from the mere statement of the examples, without any theoretical
discussion, that artificial experimentation is applicable only to the former of
these modes of investigation. We can take a cause, and try what it will
Erodnce ; but we can not take an effect, and try what it will be produced
y. We can only watch till we see it produced, or are enabled to produce
it by accident.
This would be of little importance, if it always depended on our choice
from which of the two ends of the sequence we would undertake our in-
quiries. But we have seldom any option. As we can only travel from
the known to the unknown, we are obliged to commence at whichever end
we are best acquainted with. If the agent is more familiar to us than its
effects, we watch for, or contrive, instances of the agent, under such vari-
eties of circumstances as are open to us, and observe the result. If, on the
contrary, the conditions on which a phenomenon depends are obscure, but
the phenomenon itself familiar, we must commence our inquiry from the
effect. If we are struck with the fact that chloride of silver has been
blackened, and have no suspicion of the cause, we have no resource but to
compare instances in which the fact has chanced to occur, until by that
comparison we discover that in all those instances the substances had been
exposed to light. If we knew nothing of the Indian arrows but their fa-
tal effect, accident alone could turn our attention to experiments on the
urali ; in the regular course of investigation, we could only inquire, or try
to observe, what had been done to the arrows in particular instances.
Wherever, having nothing to guide us to the cause, we are obliged to
set out from the effect, and to apply the rule of varying the circumstances
to the consequents, not the antecedents, we are necessarily destitute of the
resource of artificial experimentation. We can not, at our choice, obtain
consequents, as we can antecedents, under any set of circumstances com-
patible with their nature. There are no means of producing effects but
through their causes, and by the supposition the causes of the effect in ques-
tion are not known to us. We have, therefore, no expedient but to study it
where it offers itself spontaneously. If nature happens to present us with
instances sufficiently varied in their circumstances, and if we are able to dis-
OBSERVATION AND EXPERIMENT. 277
cover, either among the proximate antecedents or among some other order
of antecedents, something which is always found when the effect is found,
however various the circumstances, and never found when it is not, we
may discover, by mere observation without experiment, a real uniformity
in nature.
But though this is certainly the most favorable case for sciences of pure
observation, as contrasted with those in which artificial experiments are
possible, there is in reality no case which more strikingly illustrates the
inherent imperfection of direct induction when not founded on experimen-
tation. Suppose that, by a comparison of cases of the effect, we have found
an antecedent which appears to be, and perhaps is, invariably connected
with it : we have not yet proved that antecedent to be the cause until we
have reversed the process, and produced the effect by means of that ante-
cedent. If we can produce the antecedent artificially, and if, when we do
so, the- effect follows, the induction is complete ; that antecedent is the
cause of that consequent.* But we have then added the evidence of ex-
periment to that of simple observation. Until we had done so, we had
only proved invariable antecedence within the limits of experience, but
not unconditional antecedence, or causation. Until it had been shown by
the actual production of the antecedent under known circumstances, and
the occurrence thereupon of the consequent, that the antecedent was really
the condition on which it depended; the uniformity of succession which
was proved to exist between them might, for aught we knew, be (like the
succession of day and night) not a case of causation at all; both antecedent
and consequent might be successive stages of the effect of an ulterior cause.
Observation, in short, without experiment (supposing no aid from deduction)
can ascertain sequences and co-existences, but can not prove causation.
In order to see these remarks verified by the actual state of the sciences,
we have only to think of the condition of natural history. In zoology, for
example, there is an immense number of uniformities ascertained, some of
co-existence, others of succession, to many of which, notwithstanding con-
siderable variations of the attendant circumstances, we know not any ex-
ception : but the antecedents, for the most part, are such as we can not
artificially produce ; or if we can, it is only by setting in motion the ex-
act process by which nature produces them ; and this being to us a myste-
rious process, of which the main circumstances are not only unknown but
unobservable, we do not succeed in obtaining the antecedents under known
circumstances. What is the result ? That on this vast subject, which af-
fords so much and such varied scope for observation, we have made most
scanty progress in ascertaining any laws of causation. We know not with
certainty, in the case of most of the phenomena that we find conjoined,
which is the condition of the other ; which is cause, and which effect, or
whether either of them is so, or they are not rather conjunct effects of
causes yet to be discovered, complex results of laws hitherto unknown.
Although some of the foregoing observations may be, in technical strict-
ness of arrangement, premature in this place, it seemed that a few general
remarks on the difference between sciences of mere observation and sciences
of experimentation, and the extreme disadvantage under which directly in-
ductive inquiry is necessarily carried on in the former, were the best prep-
* Unless, indeed, the consequent was generated, not by the antecedent, but by the means
employed to produce the antecedent. As, however, these means are under our power, there
is so far a probability that they are also sufficiently within our knowledge to enable us to
judge whether that could be the case or not.
278 INDUCTION.
aration for discussing the methods of direct induction ; a preparation ren-
dering supei-fluous much that must otherwise have been introduced, with
some inconvenience, into the heart of that discussion. To the consideration
of these methods we now proceed.
CHAPTER VIII.
OF THE POFE METHODS OE EXPERIMENTAL UNQUIET.
§ 1. The simplest and most obvious modes of singling out from among
the circumstances which precede or follow a phenomenon, those with which
it is really connected by an invariable law, are two in number. One is, by
comparing together difEerent instances in which the phenomenon occurs.
The other is, by comparing instances in which the phenomenon does occur,
with instances in other respects similar in which it does not. These two
methods may be respectively denominated, the Method of Agreement, and
the Method of Difference.
In illustrating these methods, it will be necessary to bear in mind the
twofold character of inquiries into the laws of phenomena; which may
be either inquiries into the cause of a given effect, or into the effects or
properties of a given cause. We shall consider the methods in their ap-
plication to either order of investigation, and shall draw our examples
equally from both.
We shall denote antecedents by the large letters of the alphabet, and
the consequents corresponding to them by the small. Let A, then, be an
agent or cause, and let the object of our inquiry be to ascertain what are
the effects of this cause. If we can either find, or produce, the agent A in
such varieties of circumstances that the different cases have no circumstance
in common except A ; then whatever effect we find to be produced in all
our trials, is indicated as the effect of A. Suppose, for example, that A is
tried along with B and C, and that the effect is a ft c; and suppose that
A is next tried with D and E, but without B and C, and that the effect is
ade. Then we may reason thus : ft and c are not effects of A, for they were
not produced by it in the second experiment; nor are <?ande, for they
were not produced in the first. Whatever is really the effect of A must
have been produced in both instances ; now this condition is fulfilled by
no circumstance except a. The phenomenon a can not have been the ef-
fect of B or C, since it was produced where they were not ; nor of D or E,
since it was produced where they were not. Therefore it is the effect
of A.
■-^ For example, let the antecedent A be the contact of an alkaline sub-
stance and an oil. This combination being tried under several varieties
of circumstances, resembling each other in nothing else, the results agree in
the production of a greasy and detersive or saponaceous substance: it is
therefore concluded that the combination of an oil and an alkali causes the
production of a soap. It is thus we inquire, by the Method of Agreement,
into the effect of a given cause. /
"'' In a similar manner we may inquire into the cause of a given effect.
Let a be the effect. Here, as shown in the last chapter, we have only the
resource of observation without experiment: we can not take a phenome-
non of which we know not the origin, and try to find its mode of produc>
THE FOUR EXPERIMENTAL METHODS. 279
tion by producing it : if we succeeded in such a random trial it could only
be by accident. But if we can observe a in two different combinations,
-ahc and ade ; and if we know, or can discover, that the antecedent cir-
-cumstances iu these cases respectively were ABC and ADE, we may
-conclude by a reasoning similar to that in the preceding example, that A is
the antecedent connected with the consequent a by a law of causation.
B and C, we may say, can not be causes of a, since on its second occur-
rence they were not present ; nor are D and E, for they were not present on
its first occurrence. A, alone of the five circumstances, was found among
the antecedents of a in both instances^^
For example, let the effect a be crystallization. "We compare instances
rin which bodies are known to assume crystalline structure, but which have
.no other point of agreement; and we find them to have one, and as far as
we can observe, only one, antecedent in common : the deposition of a solid
matter from a liquid state, either a state of fusion or of solution. We
■ conclude, therefore, that the solidification of a substance from a liquid state
is an invariable antecedent of its crystallization.
/In this example we may go further, and say, it is not only the invariable
antecedent but the cause ; or at least the proximate event which completes
the cause. For in this case we are able, after detecting the antecedent A,
-to produce it artificially, and by finding that a follows it, verify the result
of our induction.^ The importance of thus reversing the proof was strik-
ingly manifested when, by keeping a phial of water charged with siliceous
particles undisturbed for years, a chemist (I believe Dr. WoUaston) suc-
ceeded in obtaining crystals of quartz; and in the equally interesting ex-
periment in which Sir James Hall produced artificial marble by the cool-
ing of its materials from fusion under immense pressure : two admirable
«xaraples of the light which may be thrown upon the most secret processes
-of Nature by well-contrived interrogation of her.
«* But if we can not artificially produce the phenomenon A, the conclusion
that it is the cause of a remains subject to very considerable doubt.
Though an invariable, it may not be the unconditional antecedent of a, but
may precede it as day precedes night or night day. This uncertainty arises
from the impossibility of assuring ourselves that A is the only immediate
antecedent common to both the instances. If we could be certain of hav-
ing ascertained all the invariable antecedents, we might be sure that the
unconditional invariable antecedent, or cause, must be found somewhere
among them. Unfortunately it is hardly ever possible to ascertain all the
antecedents, unless the phenomenon is one which we can produce artificial-
ly^ Even then, the difficulty is merely lightened, not removed : men knew
^^w to raise water in pumps long before they adverted to what was really
the operating circumstance in the means they employed, namely, the press-
ure of the atmosphere on the open surface of the water. It is, however,
much easier to analyze qompletely a set of arrangements made by our-
:selves, than the whole complex mass of the agencies which nature happens
to be exerting at the moment of the production of a given phenomenon.
We may overlook some of the material circumstances in an experiment
with an electrical machine; but we shall, at the worst, be better acquainted
with them than with those of a thunder-storm.
/The mode of discovering and proving laws of nature, which we have
-now examined, proceeds on the following axiom : Whatever circumstances
■can be excluded, without prejudice to the phenomenon, or can be absent
•notwithstanding its presence, is not connected with it in the way of causa-
280 INDUCTION.
tion. The casual circumstances being thus eliminated, if only one remains,
that one is the cause which we are in search of: if more than one,.^y ei-
ther are, or contain among them, the cause; and so, mutatis mutandis, oi
the effect. As this method proceeds by comparing different instances to
ascertain in what they agree, I have termed it the Method of Agreement;
and we may adopt as its regulating principal the following canon :
FiEST Canon.
Jf two or more instances of the phenomenon under investigation have
only one circumstance in common, the circumstance in which alone all
the instances agree, is the cause {or effect) of the given phenomenon.^
Quitting for the present the Method of Agreement, to which we shall
almost immediately return, we proceed to a still more potent instrument
of the investigation of nature, the Method of Difference.
§ 2. In the Method of Agreement, we endeavored to obtain instances
which agreed in the given circumstance but differed in every other : in the
present method we require, on the contrary, two instances resembling one
another in every other respect, but differing in the presence or absence of
the phenomenon we wish to study. If our object be to discover the effects
of an agent A, we must procure A in some set of ascertained circum-
stances, as A B C, and having noted the effects produced, compare them
with the effect of the remaining circumstances B C, when A is absent. If
the effect of A B C is a 6 c, and the effect of B C 6 c, it is evident that the
effect of A is a. So again, if we begin at the other end, and desire to in-
vestigate the cause of an effect a, we must select an instance, as ah c, in
which the effect occurs, and in which the antecedents were ABC, and we
must look out for another instance in which the remaining circumstances,
b c, occur without a. If the antecedents, in that instance, are B C, we
know that the cause of a must be A: either A alone, or A in conjunction
with some of the other circumstances present.
It is scarcely necessary to give examples of a logical process to which
we owe almost all the inductive conclusions we draw in daily life. When
a man is shot through the heart, it is by this method we know that it was
the gunshot which killed him : for he was in the fullness of life immedi-
ately before, all circumstances being the same, except the wound.
,-~ The axioms implied in this method are evidently the following. Whatr
ever antecedent can not be excluded without preventing the phenome-
non, is the cause, or a condition, of that phenomenon : whatever consequent
can be excluded, with no other difference in the antecedents than the ab-
sence of a particular one, is the effect of that one. Instead of comparing
different instances of a phenomenon, to discover in what they agree, this
method compares an instance of its occurrence with an instance of its non-
occurrence, to discover in what they differ. The canon which is the regu-
lating principle of the Method of Difference may be expressed as follows :
Second Canon.
If an instance in which the phenomenon under investigation occurs,
and an instance in which it does not occur, have every circumstance in
common save one, that one occurring only in the former; the cireum<
stance in which alone the two instances differ, is the effect, or the cause, of
an indispensable part of the cause, of the phenomenon.
THE FOUR EXPERIMENTAI, METHODS. 281
§ 3. The two methods which we have now stated have many features
of resemblance, but there are also many distinctions between them. Both
are methods of elimination. This term (employed in the theory of equa-
tions to denote the process by which one after another of the elements of
a question is excluded, and the solution made to depend on the relation
between the remaining elements only) is well suited to express the opera-
tion, analogous to this, which has been understood since the time of Bacon
to be the foundation of experimental inquiry : namely, the successive ex-
clusion of the various circumstances which are found to accompany a phe-
nomenon in a given instance, in order to ascertain what are those among
them which can be absent consistently with the existence of the phenome-
non. The Method of Agreement stands on the ground that whatever can '
be eliminated, is not connected with the phenomenon by any law. The
Method of Difference has for its foundation, that whatever can not be
eliminated, is connected with the phenomenon by a law. ''
y^Oi these methods, that of Difference is more particularly a method of
artificial experiment ; while that of Agreement is more especially the re-
source employed where experimentation is impossible. ( A few reflections
will prove the fact, and point out the reason of it.
It is inherent in the peculiar character of the Method of Difference, that
the nature of the combinations which it requires is much more strictly de-
fined than in the Method of Agreement. The two instances which are to
be compared with one another must be exactly similar, in all circumstances
except the one which we are attempting to investigate : they must be in
the relation of A B C and B C, or oi ab c and b c. It is true that this
similarity of circumstances needs not extend to such as are already known
to be immaterial to the result. And in the case of most phenomena we
learn at once, from the commonest experience, that most of the co-existent
phenomena of the universe may be either present or absent without affect-
ing the given phenomenon ; or, if present, are present indifferently when
the phenomenon does not happen and when it does. Still, even limiting
the identity which is required between the two instances, A B C and B C,
to such circumstances as are not already known to be indifferent, it is
very seldom that nature affords two instances, of which we can be assured
that they stand in this precise i-elation to one another. In the spontane-
ous operations of nature there is generally such complication and such ob-
scurity, they are mostly either on so ovei'whelmingly large or on so inac-
cessibly minute a scale, we are so ignorant of a great part of the facts
which really take place, and even those of which we are not ignorant are
so multitudinous, and therefore so seldom exactly alike in any two cases,
that a spontaneous experiment, of the kind required by the Method of Dif-
ference, is commonly not to be found. When, on the contrary, we obtain
a phenomenon by an artificial experiment, a pair of instances such as the
method requires is obtained almost as a matter of course, provided the
process does not last a long time. A certain state of suri-ounding circum-
stances existed before we commenced the experiment ; this is B C. We
then introduce A ; say, for instance, by merely bringing an object from
another part of the room, befoi-e there has been time for any change in the
other elements. It is, in short (as M. Comte observes), the very nature of
an experiment, to introduce into the pre-existing state of circumstances a
change perfectly definite. We choose a previous state of things with
which we are well acquainted, so that no unforeseen alteration in that state
is likely to pass unobserved ; and into tMs we introduce, as rapidly as pos-
282 INDUCTION.
sible, the phenomenon which we wish to study ; so that in general we are
entitled to feel complete assurance that the pre-existing state, and the stat&
which we have produced, differ in nothing except the presence or absenee-
of that phenomenon. If a bird is taken from a cage, and instantly plunged
into carbonic acid gas, the experimentalist may be fully assured (at all
events after one or two repetitions) that no circumstance capable of caus-
ing suffocation had supervened in the interim, except the change from im-
mersion in the atmosphere to immersion in carbonic acid gas. There is
one doubt, indeed, which may remain in some cases of this description;,
the effect may have been produced not by the change, but by the means
employed to produce the change. The possibility, however, of this last
supposition generally admits of being conclusively tested by other experi-
ments. It thus appears that in the study of the various kinds of phenome-
na which we can, by our voluntary agency, modify or control, we can in
general satisfy the requisitions of the Method of Difference ; but that by
the spontaneous operations of nature those requisitions are seldom fulfilled.
The reverse of this is the case with the Method of Agreement. We d»
not here require instances of so special and determinate a kind. Any in-
stances whatever, in which nature presents us with a phenomenon, may be-
examined for the purposes of this method ; and if all such instances agree
in any thing, a conclusion of considerable value is already attained. We-
can seldom, indeed, be sure that the one point of agreement is the only
one ; but this ignorance does not, as in the Method of Difference, vitiate
the conclusion ; the certainty of the result, as far as it goes, is not affected.
We have ascertained one invariable antecedent or consequent, howevei-
many other invariable antecedents or consequents may still remain unas-
certained. If A B C, A D E, A F G, are all equally followed by a, then a\sa.n.
invariable consequent of A. If abc,ade, afg, all number A among their
antecedents, then A is connected as an antecedent, by some invariable law,.
J with a. But to determine whether this invariable antecedent is a causBj.
* or this invariable consequent an effect, we must be able, in addition, ta
' produce the one by means of the other ; or, at least, to obtain that which
alone constitutes our assurance of having produced any thing, namely, aa
instance in which the effect, a, has come into existence, with no other
change in the pre-existing circumstances than the addition of A. And
this, if we can do it, is an application of the Method of Difference, not of
the Method of Agreement.
It thus appears to be by the Method of Difference alone that we can
ever, in the way of direct experience, an-ive with certainty at causes. The
Method of Agreement leads only to laws of phenomena (as some writers
call them, but improperly, since laws of causation are also laws of phenom-
ena) : that is, to uniformities, which either are not laws of causation, or in
which the question of causation must for the present remain undecided..
The Method of Agreement is chiefly to be resorted to, as a means of sug-
igesting applications of the Method of Difference (as in the last example
the comparison of A B C, A D E, A P G, suggested that A was the ante-
cedent on which to try the experiment whether it could produce a); or
as an inferior resource, in case the Method of Difference is impracticable ;
which, as we before showed, generally arises from the impossibility of ar-
tificially producing the phenomena. And hence it is that the Method of
Agreement, though applicable in principle to either case, is more emphat-
ically the method of investigation on those subjects where artificial experi-
mentation is impossible ; because "on those it is, generally, our only resourcfr
THE FOUR EXPEBIMENTAL METHODS. 283
of a directly inductive nature; while, in the phenomena which we can
produce, at pleasure, the Method of Difference generally affords a more
efficacious process, which will ascertain causes as well as mere laws.
§ 4/There are, however, many cases in •^hich, though our power of
producing the phenomenon is complete, the Method of Difference either
can not be made available at all, or not without a previous employment of
the Method of Agreement. This occurs when the agency by which we
can produce the phenomenon is not that of one single antecedent, but a
combination of antecedents, which we have no power of separating from
i each other, and exhibiting apart.#^ For instance, suppose the subject of
inquiry to be the cause of the double refraction of light. We can produce
this phenomenon at pleasure, by employing any one of the many substances
which are known to refract light in that peculiar manner. But if, taking
one of those substances, as Iceland spar, for example, we wish to determine
on which of the properties of Iceland spar this remarkable phenomenon
depends, we can make no use, for that purpose, of the Method of DiffeT-
ence; for we can not find another substance precisely resembling Iceland
spar except in some one property. The only mode, therefore, of prosecu-
ting this inquiry is that afforded by the Method of Agreement ; by which,
in fact, through a comparison of all the known substances which have the
property of doubly refracting light, it was ascertained that they agree in
the circumstance of being crystalline substances ; and though the converse
does not hold, though all crystalline substances have not the property of
double refraction, it was concluded, with reason, that there is a real con-
nection between these two properties ; that either crystalline structure, or
the cause which gives rise to that structure, is one of the conditions of
double ref I'action.
(^Out of this employment of the Method of Agreement arises a peculiar
modification of that method, which is sometimes of great avail in the in-
vestigation of nature.^' In cases similar to the above, in which it is not
possible to obtain the precise pair of instances which our second canon
requires — instances agreeing in every antecedent except A, or in every
consequent except a, we may yet be able, by a double employment of the
Method of Agreement, to discover in what the instances which contain A
on a differ from those which do not.
If we compare various instances in which a occurs, and find that they all
have in common the circumstance A, and (as far as can be observed) no
other circumstance, the Method of Agreement, so far, bears testimony to a
connection between A and a. In order to convert this evidence of connec-
tion into proof of causation by the direct Method of Difference, we ought
to be able, in some one of these instances, as for example, A B C, to leave
out A, and observe'whether by doing so, a is prevented. Now supposing
(what is often the case) that we are not able to try this decisive experi-
ment ; yet, provided we can by anj- means discover what would be its re-
sult if we could try it, the advantage will be the same. Suppose, then,
that as we previously examined a variety of instances in which a occurred,
and found them to agree in containing A, so we now observe a variety of
instances in which a does not occur, and find them agree in not containing
A; which establishes, by the Method of Agreement, the same connection
between the absence of A and the absence of a, which was before estab-
lished between their presence./ As, then, it had been shown that whenever
A is present a is present, so, it being now shown that when A is taken
. 2S4 INDUCTION.
away a. is removed along with it, we have by the one proposition ABC,
a 6 c, by the other B C, be, the positive and negative instances which the
Method of Diffei-ence requires^
This method may be called the Indirect Method of Difference, or the
Joint Method of Agreement and Difference ; and consists in a double em-
ployment of the Method of Agreement, each proof being independent of
the other, and corroborating it. But it is not equivalent to a proof by
the direct Method of Difference. For the requisitions of the Method of
Difference are not satisfied, unless we can be quite sure either that the in-
stances afiirmative of a agree in no antecedent whatever but A, or that the
instances negative of a agree in nothing but the negation of A. Now, if it
were possible, which it never is, to have this assurance, we should not need
the joint method ; for either of the two sets of instances separately would
then be suflBcient to prove causation. This indirect method, therefore, can
only be regarded as a great extension and improvement of the Method of
Agreement, but not as participating in the more cogent nature of the Meth-
od of Difference. The following may be stated as its canon :
Thikd Canon.
If two or more instances in which the phenomenon occurs have only
one circumstance in common, while two or more instances in which it does
not occur have nothing in common save the absence of that, circumstance,
the circumstance in which alone the two sets of instances differ, is the
effect, or the cause,or an indispensable part of the cause, of the phenomenon. .
We sh^ll presently see that the Joint Method of Agreement and Differ-
ence constitutes, in another respect not yet adverted to, an improvement
upon the common Method of Agreement, namely, in being unaffected by
a characteristic imperfection of that method, the nature of which still re-
mains to be pointed out. But as we can not enter into this exposition
without introducing a new element of complexity into this long and intri-
cate discussion, I shall postpone it to a subsequent chapter, and shall at
once proceed to a statement of two other methods, which will complete
the enumeration of the means which mankind possess for exploring the
laws of nature by specific observation and experience.
§ 5. The first of these has been aptly denominated the Method of Resi-
dues. Its principle is very simple. Subducting from any given phenome-
non all the portions which, by virtue of preceding inductions, can be assigned
to known causes, the remainder will be the effect of the antecedents which
had been overlooked, or of which the effect was as yet an unknown quantity.
Suppose, as before, that we have the antecedents ABC, followed by the
consequents abc, and that by pi'evious inductions (founded, we will sup-
pose, on the Method of Difference) we have ascertained the causes of some
of these effects, or the effects of some of these causes ; and are thence ap-
prised that the effect of A is a, and that the effect of B is b. Subtracting
the sum of these effects from.the total phenomenon, there remains c, which
now, without any fresh experiments, we may know to be the effect of 0.
This Method of Residues is in truth a peculiar modification of the Method
of Difference. If the instance ABC, abc, could have been compared
with a single instance AB, a J, we should have proved C to be the cause
of c, by the common process of the Method of Difference. In the present
case, however, instead of a single instance A B, we have had to study sep-
THE FOUR EXPERIMENTAL METHODS. 285
arately the causes A and B, and to infer from the effects which they pro-
duce separately what effect they must produce in the case ABC, where
they act together. Of the two instances, therefore, which the Method of
Difference requires — the one positive, the other negative — the negative
one, or that in which the given phenomenon is absent, is not the direct re-
sult of observation and experiment, but has been arrived at by deduction.
As one of the forms of the Method of Difference, the Method of Residues
partakes of its rigorous certainty, provided the previous inductions, those
which gave the effects of A and B, were obtained by the same infallible
method, and provided we are certain that C is the only antecedent to
which the residual phenomenon c can be referred ; the only agent of which
we had not already calculated and subducted the effect. But as we can
never be quite certain of this, the evidence derived from the Method of
Residues is not complete unless we can obtain C artificially, and try it sep-
arately, or unless its agency, when once suggested, can be accounted for,
and proved deductively from known laws.
Even with these reservations, the Method of Residues is one of the most
important among our instruments of discovery. Of all the methods of in-
vestigating laws of nature, this is the most fertile in unexpected results :
often informing us of sequences in which neither the cause nor the effect
were sufficiently conspicuous to atti-act of themselves the attention of ob-
servers. The agent C may be an obscure circumstance, not likely to have
been perceived unless sought for, nor likely to have been sought for until
attention had been awakened by the insufficiency of the obvious causes to
account for the whole of the effect. And c may be so disguised by its in-
termixture with a and h, that it would scarcely have presented itself spon-
taneously as a subject of separate study. Of these uses of the method, we
shall presently cite some remarkable examples. The canon of the Method
of Residues is as follows :
FouETH Canon.
Subduct from any phenomenon such part as is known by previous in-
ductions to be the effect of certain antecedents, and the residue of the phe-
nomenon is the effect of the remaining antecedents.
§ 6. There remains a class of laws which it is impracticable to ascertain
by any of the three methods which I have attempted to characterize :
namely, the laws of those Permanent Causes, or indestructible natural
agents, which it is impossible either to exclude or to isolate ; which we can
neither hinder from being present, nor contrive that they shall be present
alone. It would appear at first sight that we could by no means separate
the effects of these agents from the effects of those other phenomena with
which they can not be prevented from co-existing. In respect, indeed, to
most of the permanent causes, no such difficulty exists ; since, though we
can not eliminate them as co-existing facts, we can eliminate them as influ-
encing agents, by simply trying our experiment in a local situation beyond
the limits of their influence. The pendulum, for example, has its oscilla-
tions disturbed by the vicinity of a mountain : we remove the pendulum to
a sufficient' distance from the mountain, and the disturbance ceases : from
these data we can determine by the Method of Difference, the amount of ef-
fect due to the mountain ; and beyond a certain distance every thing goes;
on precisely as it would do if the mountain exercised no influence what-
ever, which, accordingly, we, with sufficient reason, conclude to be the fact.
286 INDUCTION.
The difficulty, therefore, in applying the methods ah-eady treated of to
determine the effects of Permanent Causes, is confined to the cases in
■which it is impossible for us to get out of the local limits of their influ-
ence. The pendulum can be removed from the influence of the mountain,
but it can not be removed from the influence of the earth : we can not take
away the earth from the pendulum, nor the pendulum from the earth, to
ascertain whether it would continue to vibrate if the action which the
earth exerts upon it were withdrawn. On what evidence, then, do we
ascribe its vibrations to the earth's influence ? Not on any sanctioned by
the Method of Difference ; for one of the two instances, the negative in-
stance, is wanting. Nor by the Method of Agreement ; for though all
pendulums agree in this, that during their oscillations the earth is always
present, why may we not as well ascribe the phenomenon to the sun, which
is equally a co-existent fact in all the experiments ? It is evident that to
establish even so simple a fact of causation as this, there was required
some method over and above those which we have yet examined.
As another example, let us take the phenomenon Heat. Independently
of all hypothesis as to the real nature of the agency so called, this fact is
certain, that we are unable to exhaust any body of the whole of its heat.
It is equally certain that no one ever perceived heat not emanating from a
body. Being unable, then, to separate Body and Heat, we can not effect
such a variation of circumstances as the foregoing three methods require ;
we can not ascertain, by those methods, what portion of the phenomena
exhibited by any body is due to the heat contained in it. If we could ob-
serve a body with its heat, and the same body entirely divested of heat,
the Method of Difference would show the effect due to the heat, apart
from that due to the body. If we could observe heat under circumstances
agreeing in nothing but heat, and therefore not characterized also by the
presence of a body, we could ascertain the effects of heat, from an instance
of heat with a body and an instance of heat without a body, by the Meth-
od of Agreement; or we could determine by the Method of Difference
what effect was due to the body, when the remainder which was due to the
heat would be given by the Method of Residues. But we can do none of
these things ; and without them the application of any of the three meth-
ods to the solution of this problem would be illusory. It would be idle,
for instance, to attempt to ascertain the effect of heat by subtracting from
the phenomena exhibited by a body all that is due. to its other properties;
for as we have never been able to observe any bodies without a portion of
heat in them, effects due to that heat might rforra a part of the very re-
sults which we were affecting to subtract, in order that the effect of heat
might be shown by the residue.
If, therefore, there were no other methods of experimental investigation
than these three, we should be unable to determine the effects due to heat
as a cause. But we have still a resource. Though we can not exclude an
antecedent altogether, we may be able to produce, or nature may produce
for us some modification in it. By a modification is here meant, a change
in it not amounting to its total removal. If some modification in the an-
tecedent A is always followed by a change in the consequent a, the other
consequents b and c remaining the same ; or vicb versa, if every change in
a is found to have been preceded by some modification in A, none being
observable in any of the other antecedents, we may safely conclude that a
is, wholly or in part, an effect traceable to A, or at least in some way con-
nected with it through causation. For example, in the case of heat, though
THE FOUR EXPERIMENTAL METHODS. 287
-we can not expel it altogether from any body, we can modify it in quantity,
■we can increase or diminish it ; and doing so, we find by the various meth-
ods of experimentation or observation already treated of, that such increase
■or diminution of heat is followed by expansion or contraction of the body.
In this manner we arrive at the conclusion, otherwise unattainable by us,
that one of the effects of heat is to enlarge the dimensions of bodies ; or,
■what is the same thing in other words, to widen the distances between their
particles.
A change in a thing, not amounting to its total removal, that is, a change
-which leaves it still the same thing it was, must be a change either in its
quantity, or in some of its variable relations to other things, of which va-
riable relations the principal is its position in space. In the previous ex-
:ample, the modification which was produced in the antecedent was an al-
teration in its quantity. Let us now suppose the question to be, what in-
fluence the moon exerts on the surface of the earth. We can not try an
«xperiment in the absence of the moon, so as to observe what terrestrial
phenomena her annihilation would put an end to; but when we find that
all the variations in the position of the moon are followed by correspond-
ing variations in the time and place of high water, the place being alvPays
«ither the part of the earth which is nearest to, or that which is most re-
mote from, the moon, we have ample evidence that the moon is, wholly or
partially, the cause which determines the tides. It very commonly hap-
pens, as it does in this instance, that the variations of an effect are corre-
spondent, or analogous, to those of its cause ; as the moon moves farther
toward the east, the high-water point does the samef but this is not an in-
dispensable condition, as may be seen in the same example, for along with
that high-water point there is at the same instant another high-water point
diametrically opposite to it, and which, therefore, of necessity, moves toward
the west, as the moon, followed by the nearer of the tide waves, advances
toward the east: and yet both these motions are equally effects of the
moon's motion.
That the oscillations of the pendulum are caused by the earth, is proved
by similar evidence. Those oscillations take place between equidistant
points on the two sides of a line, which, being perpendicular to the earth,
varies with every variation in the earth's position, either in space or rela-
tively to the object. Speaking accurately, we only know by the method
BOW characterized, that all terrestrial bodies tend to the earth, and not to
some unknown fixed point lying in the same direction. In every twenty-
fo*r hours, by the earth's rotation, the line drawn from the body at right
angles to the earth coincides successively with all the radii of a circle, and
in the course of six months the place of that circle varies by nearly two
hundred millions of miles ; yet in all these changes of the earth's position,
the line in which bodies tend to fall continues to be directed toward it :
"which proves that terrestrial gravity is directed to the earth, and not, as
was once fancied by some, to a fixed point of space.
The method by which these results were obtained may be termed the
Method of Concomitant Variations ; it is regulated by the following canon:
Fifth Canoit.
Whatever phenomenon varies in any manner whenever another phe-
nomenon varies in some particular manner, is either a cause or an effect
•of that phenomenon, or is connected with it through some fact of causa-
tion.
288 INDUCTION.
The last clause is subjoined, because it by no means follows when two
phenomena accompany each other in their variations, that the one is cause
and the other effect. The same thing may, and indeed must happen, sup-
posing them to be two different effects of a common cause : and by this
method alone it would never be possible to ascertain which of the suppo-
sitions is the true one. The only way to solve the doubt would be that
which we have so often adverted to, viz., by endeavoring to ascertain wheth-
er we can produce the one set of variations by means of the other. In the
case of heat, for example, by increasing the temperature of a body we in-
crease its bulk, but by increasing its bulk we do not increase its temper-
ature; on the contrary (as in the rarefaction of air under the receiver
of an air-pump), we generally diminish it: therefore heat is not an effect,
but a cause, of increase of bulk. If we can not ourselves produce the va-
riations, we must endeavor, though it is an attempt which is seldom suc-
cessful, to find them produced by nature in some case in which the pre-
existing circumstances are perfectly known to us.
It is scarcely necessary to say, that in order to ascertain the uniform con-
comitance of variations in the effect with variations in the cause, the same
precautions must be used as in any other case of the determination of an
invariable sequence. "We must endeavor to retain all the other anteced-
ents unchanged, while that particular one is subjected to the requisite se-
ries of variations ; or, in other words, that we may be warranted in infer-
ring causation from concomitance of variations, the concomitance itself
must be proved by the Method of Difference.
It might at first appear that the Method of Concomitant Variations as-
sumes a new axiom, or law of causation in general, namely, that every mod-
ification of the cause is followed by a change in the effect. And it does
usually happen that when a phenomenon A causes a phenomenon a, any
variation in the quantity or in the various relations of A, is uniformly fol-
lowed by a variation in the quantity or relations of a. To take a familiar
instance, that of gravitation. The sun causes a certain tendency to motion
in the earth ; here we have cause and effect ; but that tendency is toward
the sun, and therefore varies in direction as the sun varies in the relation
of position; and, moreover, the tendency varies in intensity, in a certain
numerical correspondence to the sun's distance from the earth, that is, ac-
cording to another relation of the sun. Thus we see that there is not
only an invariable connection between the sun and the earth's gravitation,
but that two of the relations of the sun, its position with respect to the
earth and its distance from the earth, are invariably connected as anteced-
ents with the quantity and direction of the earth's gravitation. The cause
of the earth's gravitating at all, is simply the sun ; but the cause of its
gravitating with a given intensity and in a given direction, is the existence
of the sun in a given direction and at a given distance. It is not strange
that a modified cause, which is in truth a different cause, should produce a
different effect.
Although it is for the most part true that a modification of the cause is
followed by a modification of the effect, the Method of Concomitant Variar
tions does not, however, presuppose this as an axiom. It only requires
the converse pi-oposition : that any thing on whose modifications, modifi-
cations of an effect are invariably consequent, must be the cause (or con-
nected with the cause) of that effect ; a proposition, the truth of which is
evident ; for if the thing itself had no influence on the effect, neither could
the modifications of the thing have any influence. If the stars have no
THE FOUR EXPERIMENTAL METHODS. 289
power over the fortunes of mankind, it is implied in the very terms that
the conjunctions or oppositions of different stars can have no such power.
Although the most striking applications of the Method of Concomitant
Variations take place in the cases in which the Method of Difference,
strictly so called, is impossible, its use is not confined to those cases ; it
may often usof ally follow after the Method of Difference, to give addition-
al precision to a solution which that has found. When by the Method of
Difference it has first been ascertained that a certain object produces a
certain effect, the Method of Concomitant Variations may be usefully call-
ed in, to determine according to what law- the quantity or the different re-
lations of the effect follow those of the cause.
§ 7. The case in which this method admits of the most extensive em-
ployment, is that in which the variations of the cause are variations of
quantity. Of such variations we may in general affirm with safety, that
they will be attended not only with variations, but with similar variations,
of the effect : the proposition that njore of the cause is followed by more
of the effect, being a corollary from the principle of the Composition of
Causes, which, as we have seen, is the general rule of causation ; cases of
the opposite description, in which causes change their properties on being
conjoined with one another, being, on the contrary, special and exceptional.
Suppose, then, that when A changes in quantity, a also changes in quantity,
and in such a manner that we can trace the numerical relation which the
changes of the one bear to such changes of the other as take place within
our limits of observation. We may then, with certain precautions, safely
conclude that the same numerical relation will hold beyond those limits.
If, for instance, we find that when A is double, a is double; that when A is
treble or quadruple, a is treble or quadruple ; we may conclude that if A
were a half or a third, a would be a half or a third, and finally, that if A
were annihilated, a would be annihilated ; and that a is wholly the effect of
A, or wholly the effect of the same cause with A. And so with any other
numerical relation according to which A and a would vanish simultaneous-
ly ; as, for instance, if a were proportional to the square of A. If, on the
other hand, a is not wholly the effect of A, but yet varies when A varies, it
is probably a mathematical function not of A alone, but of A and something
else : its changes, for example, may be such as would occur if part of it re-
mained constant, or varied on some other principle, and the remainder va-
ried in some numerical relations to the variations of A. In that case, when
A diminishes, a will be seen to approach not toward zero, but toward some
other limit; and when the series of variations is such as to indicate what
that limit is, if constant, or the law of its variation, if variable, the limit
will exactly measure how much of a is the effect of some other and inde-
pendent cause, and the remainder will be the effect of A (or of the cause
of A).
These coaplusions, however, must not be drawn without certain precau-
tions. In the first place, the possibility of drawing them at all, manifestly
supposes that we are acquainted not only with the variations, but with the
absolute quantities both of A and a. If we do not know the total quan-
tities, we can not, of course, determine the real numerical relation according
to which those quantities vary. It is, therefore, an error to conclude, as
some have concluded, that because increase of heat expands bodies, that
is, increases the distance between their particles, therefore the distance is
wholly the effect of heat, and that if we could entirely exhaust the body of
19
290 INDUCTION.
its heat, the particles wonld be in complete contact. This is no more than
a guess, and of the most hazardous sort, not a legitimate induction : for
«ince we neither know how much heat there is in any body, nor what is
the real distance between any two of its particles, we can not judge whether
the contraction of the distance does or does not follow the diminution of
the quantity of heat according to such a numerical relation that the two
quantities would vanish simultaneously.
In contrast with this, let us consider a case in which the absolute quan-
tities are known ; the case contemplated in the first law of motion : viz.,
that all bodies in motion continue to move in a straight line with uniform
velocity until acted upon by some new force. This assertion is in open op-
position to first appearances ; all terrestrial objects, when in motion, grad-
ually abate their velocity, and at last stop ; which accordingly the ancients,
with their inductio per enumerationem simplicem, imagined to be the law.
Every moving body, however, encounters various obstacles, as friction, the
resistance of the atmosphere, etc., which we know by daily experience to
be causes capable of destroying motiooi. It was suggested that the whole
■of the retardation might be owing to these causes. How was this in-
•quired into ? If the obstacles could have been entirely removed, the case
would have been amenable to the Method of Difference. They could not
be removed, they could only be diminished, and the case, therefore, ad-
mitted only of the Method of Concomitant Variations. This accordingly
being employed, it was found that every diminution of the obstacles di-
minished the retardation of the motion : and inasmuch as in this case (un-
like the case of heat) the total quantities both of the antecedent and of the
consequent were known, it was practicable to estimate, with an approach
to accuracy, both the amount of the retardation and the amount of the
retarding causes, or resistances, and to judge how near they both were to
being exhausted ; and it appeared that the effect dwindled as rapidly, and
at each step was as far on the road toward annihilation, as the cause was.
The simple oscillation of a weight suspended from a fixed point, and
moved a little out of the perpendicular, which in ordinary circumstances
lasts but a few minutes, was prolonged in Borda's experiments to more than
thirty hours, by diminishing as much as possible the friction at the point
of suspension, and by making the body oscillate in a space exhausted as
nearly as possible of its air. There could therefore be no hesitation in as-
signing the whole of the retardation of motion to the influence of the ob-
stacles ; and since, after subducting this retardation from the total phenom-
enon, the remainder was a uniforni velocity, the result was the proposition
known as the first law of motion.
There is also another characteristic uncertainty affecting the inference
that the law of variation which the quantities observe within our limits of
■observation, will hold beyond those limits. There is, of course, in the first
instance, the possibility that beyond the limits, and in circumstances there-
fore of which we have no direct experience, some counteracting cause
might develop itself ; either a new agent or a new property of the agents
concerned, which lies dormant in the circumstances we are able to observe.
This is an element of uncertainty which enters largely into all our predic-
tions of effects ; but it is not peculiarly applicable to the Method of Con-
comitant Variations. The uncertainty, however, of which I am about to
speak, is characteristic of that method ; especially in the cases in which
the extreme limits of our observation are very narrow, in comparison with
the possible variations in the quantities of the phenomena. Any one who
THE FOUR EXPERIMENTAL METHODS. 291
has the slightest acquaintance with mathematics, is aware that very differ-
ent laws of variation may produce numerical results which differ but slight-
ly from one another within narrow limits; and it is often only when the
absolute amounts of variation are considerable, that the difference between
the results given by one law and by another becomes appreciable. When,
therefore, such variations in the quantity of the antecedents as we have the
means of observing are small in comparison with the total quantities, there
is much danger lest we should mistake the numerical law, and be led to
.miscalculate the variations which would take place beyond the limits ; a
miscalculation which would vitiate any conclusion respecting the depend-
•ence of the effect upon the cause, that could be founded on those varia-
"tions. Examples are not wanting of such mistakes. " The formulae," says
Sir John Herschel,* " which have been empirically deduced for the elas-
ticity of steam (till very recently), and those for the resistance of fluids, and
other similar subjects," when relied on beyond the limits of the observa-
tions from which they were deduced, " have almost invariably failed to sup-
port the theoretical structures which have been erected on them."
In this uncertainty, the conclusion we may draw from the concomitant
■variations of a and A, to the existence of an invariable and exclusive con-
nection between them, or to the permanency of the same numerical relation
between their variations when the quantities are much greater or smaller
than those which we have had the means of observing, can not be consider-
ed to rest on a complete induction. All that in such a case can be regard-
-Ed as proved on the subject of causation is, that there is some connection
between the two phenomena ; that A, or something which can influence A,
must be one of the causes which collectively determine a. We may, how-
■ever, feel assured that the relation which we have observed to exist be-
tween the variations of A and a, will hold true in all cases which fall be-
tween the same extreme limits ; that is, wherever the utmost increase or
■diminution in which the result has been found by observation to coincide
with the law, is not exceeded.
The four methods which it has now been attempted to describe, are the
only possible modes of experimental inquiry — of direct induction a poste-
riori, as distinguished from deduction : at least, I know not, nor am able to
imagine any others. And even of these, the Method of Residues, as we
have seen, is not independent of deduction; though, as it also requires
specific experience, it may, without impropriety, be included among meth-
ods of direct observation and experiment.
These, then, with such assistance as can be obtained from Deduction,
compose the available resources of the human mind for ascertaining the
laws of the succession of phenomena. Before proceeding to point out cer-
tain circumstances by which the employment of these methods is subjected
to an immense increase of complication and of diflSculty, it is expedient to
illustrate the use of the methods, by suitable examples drawn from actual
physical investigations. These, accordingly, wiU. form the subject of the
succeeding chapter.
* Discourse on the Study of Natural Philosophy, p. 179.
292 INDUCTION.
CHAPTER IX.
MISCELLANEOUS EXAMPLES OP THE FOtTE METHODS.
§ 1. I SHALL select, as a first example,' an interesting speculation of one
of the most eminent of theoretical chemists, Bai-on Liebig. The ob^ject in
view is to ascertain the immediate cause of the death produced by metal-
lic poisons.
Arsenious acid, and the salts of lead, bismuth, copper, and mercury, if
introduced into the animal organism, except in the smallest doses, destroy
life. These facts have long been known, as insulated truths of the lowest
order of generalization ; but it was reserved for Liebig, by an apt employ-
ment of the first two of our methods of experimental inquiry, to connect
these truths together by a higher induction, pointing out what property,
common to all these deleterious substances, is the really operating cause of
their fatal effect.
When solutions of these substances are placed in sufficiently close con-
tact with many animal products, albumen, milk, muscular fibre, and animal
membranes, the acid or salt leaves the water in which it was dissolved,
and enters into combination with the animal substance, which substance,
after being thus acted upon, is found to have lost its tendency to sponta-
neous decomposition, or putrefaction.
Observation also shows, in cases where death has been produced by
these poisons, that the parts of the body with which the poisonous sub-
stances have been brought into contact, do not afterward putrefy.
And, finally, when the poison has been supplied in too small a quantity
to destroy life, eschars are produced, that is, certain superficial portions of
the tissues are destroyed, which are afterward thrown off by the reparative
process taking place in the healthy parts.
These three sets of instances admit of being treated according to the
Method of Agreement. In all of them the metallic compounds are
brought into contact with the substances which compose the human or anif
mal body; and the instances do not seem to agree in any other circum-
stance. The remaining antecedents are as different, and even opposite, as
they could possibly be made; for in some the animal substances exposed
to the action of the poisons are in a state of life, in others only in a state
of organization, in others not even in that. And what i* the result which
follows in all the cases ? The conversion of the animal substance (by com-
bination with the poison) into a chemical compound, held together by so
powerful a force as to resist the subsequent action of the ordinary causes
of decomposition. Now, organic life (the necessary condition of sensitive
life) consisting in a continual state of decomposition and recomposition of
the different organs and tissues, whatever incapacitates them for this de-
composition destroys life. And thus the proximate cause of the death pro-
duced by this description of poisons is ascertained, as far as the Method
of Agreement can ascertain it.
Let us now bring our conclusion to the test of the Method of Difference.
Setting out from the cases already mentioned, in which the antecedent is
the presence of substances forming with the tissues a compound incapable
EXAMPLES OF THE FOUR METHODS. 293
of putrefaction, (and a fortiori incapable of the chemical actions which
constitute life), and the consequent' is death, either of the whole organism,
or of some portion of it ; let us compare with these cases other cases, as
much resembling them as possible, but in which that effect is not produced.
And, first, " many insoluble basic salts of arsenious acid are known not to
be poisonous. The substance called alkargen, discovered by Bunsen, which
contains a very large quantity of arsenic, and approaches very closely in
composition to the organic arsenious compounds found in the body, has
not the slightest injurious action upon the organism." "Now when these
substances are brought into contact with the tissues in any way, they do
not combine with them ; they do not arrest their progress to decomposi-
tion. As far, therefore, as these instances go, it appears that when the
effect is absent, it is by reason of the absence of that antecedent which we
had already good ground for considering as the proximate cause.
But the rigorous conditions of the Method of Difference are not yet sat-
isfied ; for we can not be- sure that these unpoisonous bodies agree with
the poisonous substances in every property, except the particular one of
entering into a difficultly decomposable compound with the animal tissues.
To render the method strictly applicable, we need an instance, not of a
different substance, but of one of the very same substances, in circum-
stances which would prevent it from forming, with the tissues, the sort
of compound in question; and then, if death does not follow, our case is
made out. Now such instances are afforded by the antidotes to these poi-
f sons. For example, in case of poisoning by arsenious acid, if hydrated
peroxide of iron is administered, the destructive agency is instantly check-
ed. Now this peroxide is known to combine with the acid, and form a
compound, which, being insoluble, can not act at all on animal tissues. So,
again, sugar is a well-known antidote to poisoning by salts of copper ; and
sugar reduces those salts either intp metallic copper, or into the red sub-
oxide, neither of which enters into combination with animal matter. The
disease called painter's colic, so common in manufactories of white-lead, is
unknown where the workmen are accustomed to take, as a preservative,
sulphuric acid lemonade (a. solution of sugar rendered acid by sulphuric
acid). Now diluted sulphuric acid has the property of decomposing aU
compounds of lead with organic matter, or of preventing them from being
formed.
There is another class of instances, of the nature required by the Method
of Difference, which seem at first sight to conflict with the theory. Solu-
ble.salts of silver, such for instance as the nitrate, have the same stiffening
antiseptic effect on decomposing animal substances as corrosive sublimate
and the most deadly metallic poisons ; and when applied to the external
parts of the body, the nitrate is a powerful caustic, depriving those parts of
all active vitality, and causing them to be thrown off by the neighboring
living structures, in the form of an eschar. The nitrate and the other
salts of silver ought, theii, it would seem, if the theory be correct, to be
poisonous ; yet they may be administered internally with perfect impunity.
From this apparent exception arises the strongest confirmation which the
theory has yet received. Nitrate of silver, in spite of its chemical proper-
ties, does not poison when introduced into the stomach ; but in the stom-
ach, as in all animal liquids, there is common salt ; and in the stomach
there is also free muriatic acid. These substances operate as natural anti-
dotes, combining with the nitrate, and if its quantity is not too great, im-
mediately converting it into chloride of silver, a substance very slightly
294 INDUCTION.
soluble, and therefore incapable of combining with the tissues, although to
the extent of its solubility it has a medicinal influence, though an entirely-
different class of organic actions.
The preceding instances have afforded an induction of a high order of
conclusiveness, illustrative of the two simplest of our four methods ; though
not rising to the maximum of certainty which the Method of Difference,,
in its most perfect exemplification, is capable of affording. For (let us
not forget) the positive instance and the negative one which the rigor of
that method requires, ought to differ only in the presence or absence of'
one single circumstance. Now, in the preceding argument, they differ in
the presence or absence not of a single circumstance, but of a single sub-
stance : and as every substance has innumerable properties, there is na
knowing what number of real differences are involved in what is nominally
and apparently only one difference. It is conceivable that the antidote,,
the peroxide of iron for example, may counteract the poison through some
other of its properties than that of forming an insoluble compound with it;,
and if so, the theory would fall to the ground, so far as it is supported by
that instance. This source of uncertainty, which is a serious hinderance to-
all extensive generalizations in chemistry, is, however, reduced in the pres-
ent case to almost the lowest degree possible, when we find that not only
one substance, but many substances, possess the capacity of acting as anti-
dotes to metallic poisons, and that all these agree in the property of form-
ing insoluble compounds with the poisons, while they can not be ascer-
tained to agree in any other property whatsoever. We have thus, in favor
of the theory, all the evidence which can be obtained by what we termed
the Indirect Method of Difference, or the Joint Method of Agreement and
Difference ; the evidence of which, though it never can amount to that of
the Method of Difference properly so called, may approach indefinitely near
to it.
§ 2. Let the object be* to ascertain the law of what is tei-med inducec^
electricity ; to find under what conditions any electrified body, whether
positively or negatively electrified, gives rise to a contrary electric state in
some other body adjacent to it.
The most familiar exemplification of the phenomenon to be investigated
is the following. Around the prime conductors of an electrical machine
the atmosphere to some distance, or any conducting surface suspended in
that atmosphere, is found to be in an electric condition opposite to that of
the prime conductor itself. Near and around the positive prime conductor
there is negative electricity, and near and around the negative prime con-
ductor there is positive electricity. "When pith balls are brought near to
either of the conductors, they become electrified with the opposite electric-
ity to it; either receiving a share from the already electrified atmosphere
by conduction, or acted upon by the direct inductive influence of the con-
ductor itself : they are then attracted by the conductor to which they are
in opposition ; or, if withdrawn in their electrified state, they will be at-
tracted by any other oppositely charged body. In like manner the hand,,
if brought near enough to the conductor, receives or gives an electric dis-
charge ; now we have no evidence that a charged conductor can be sud-
denly discharged unless by the approach of a body oppositely electrified.
* For this speculation, as for many other of my scientific illustrations, I am indebted to
Professor Bain, whose subsequent treatise on Logic abounds with apt illustrations of all the:
indnctive methods.
EXAMPLES OF THE FOUR METHODS. 295.
In the case, therefore, of the electric machine, it appears that the accumula-
tion of electricity in an insulated conductor is always accompanied by the
excitement of the contrary electricity in the surrounding atmosphere, and
in every conductor placed near the former conductor. It does not seem
possible, in this case, to produce one electricity by itself.
Let us now examine all the other instances which we can obtain, resem-
bling this instance in the given consequent, namely, the evolution of an op-
posite electricity in the neighboi'hood of an electrified body. As one re-
markable instance we have the Leyden jar; and after the splendid experi-
ments of Faraday in complete and final establishment of the substantial,
identity of magnetism and electricity, we may cite the magnet, both the
natural and the electro-magnet, in neither of which it is possible to produce-
one kind of electricity by itself, or to charge one pole without charging an
opposite pole with the contrary electricity at the same time. We can not
have a magnet with one pole : if we break a natural loadstone into a tliou-
sand pieces, each piece will have its two oppositely electrified poles com-
plete within itself. In the voltaic circuit, again, we can not have one cur-
rent without its opposite. In the oi'dinary electric machine, the glass cyl-
inder or plate, and the rubber, acquire opposite electricities.
From all these instances, treated by the Method of Agreement, a general
law appears to result. The instances embrace all the known modes in.
which a body can become charged with electricity ; and in all of them •
there is found, as a concomitant or consequent, the excitement of the op-
posite electric state in some other body or bodies. It seems to follow that
the two facts are invariably connected, and that the excitement of electric-
ity in any body has for one of its necessary conditions the possibility of
a simultaneous excitement of the opposite electricity in some neighbor-
ing body.
As the two contrary electricities can only be produced together, so they
can only cease together. This may be shown by an application of the Meth-
od of Difference to the example of the Leyden jar. It needs scarcely be-
here remarked that in the Leyden jar, electricity can be accumulated and
retained in considerable quantity, by the contrivance of having two conduct-
ing surfaces of equal extent, and parallel to each other through the whole
of that extent, with a non-conducting substance such as glass between them.
When one side of the jar is charged positively, the other is charged nega^
tively, and it was by virtue of this fact that the Leyden jar served just now
as an instance in our employment of the Method of Agreement. Now it
is impossible to discharge one of the coatings unless the other can be dis-
charged at the same time. A conductor held to the positive side can not con-
vey away any electricity unless an equal quantity be allowed to pass from,
the negative side : if one coating be perfectly insulated, the charge is safe..
The dissipation of one must proceed pari passu with that of the other.
The law thus strongly indicated admits of corroboration by the Method
of Concomitant Variations. The Leyden jar is capable of receiving a much
higher charge than can ordinarily be given to the conductor of an electi'ical
machine. Now in the case of the Leyden jar, the metallic surface which
receives the induced electricity is a conductor exactly similar to that which
receives the primary charge, and is therefore as susceptible of receiving-
and retaining the one electricity, as the opposite surface of receiving and
retaining the other ; but in the machine, the neighboring body which is ta
be oppositely electrified is the surrounding atmosphere, or any body casu-
ally brought near to the conductor ; and as these are generally much in-
296 INDUCTION.
ferior in their capacity of becoming electrified, to the conductor itself, thelt
limited power imposes a corresponding limit to the capacity of the con-
ductor for being charged. As the capacity of the neighboring body for
supporting the opposition increases, a higher charge becomes possible ; and
to this appears to be owing the great superiority of the Leyden jar.
A further and most decisive confirmation by the Method of Difference,
is to be found in one of Faraday's experiments in the course of his re-
searches on the subject of Induced Electricity.
Since common or machine electricity, and voltaic electricity, may be con-
sidered for the present purpose to be identical, Faraday wished to know
whether, as the prime conductor develops opposite electricity upon a con-
ductor in its vicinity, so a voltaic current running along a wire would in-
duce an opposite current upon another wire laid parallel to it at a short
•distance. Now this case is similar to the cases previously examined, in
every circumstance except the one to which we have ascribed the effect.
We found in the former instances that whenever electricity of one kind
was excited in one body, electricity of the opposite kind must be excited
in a neighboring body. But in Faraday's experiment this indispensable
•opposition exists within the wire itself. From the nature of a voltaic
•charge, the two opposite currents necessary to the existence of each pther
are both accommodated in one wire ; and there is no need of another wire
■ placed beside it to contain one of them, in the same way as the Leyden jar
must have a positive and a negative surface. The exciting cause can and
does produce all the effect which its laws require, independently of any
electric excitement of a neighboring body. Now the result of the experi-
ment with the second wire was, that no opposite current was produced.
There was an instantaneous effect at the closing and breaking of the vol-
taic circuit ; electric inductions appeared when the two wires were moved
to and from one another; but these are phenomena of a different class.
There was no induced electricity in the sense in which this is predicated
of the Leyden jar; there was no sustained current running up the one
wire while an opposite current ran down the neighboring wire; and this
alone would have been a true parallel case to the other. «
It thus appears by the combined evidence of the Method of Agreement,
the Method of Concomitant Variations, and the most rigorous form of the
Method of Difference, that neither of the two kinds of electricity can be
excited without an equal excitement of the other and opposite kind : that
both are effects of the same cause ; that the possibility of the one is a con-
dition of the possibility of the other, and the quantity of the one an im-
passable limit to the quantity of the other. A scientific result of consider-
able interest in itself, and illustrating those three methods in a manner
both characteristic and easily intelligible.*
§ 3. Our third example shall be extracted from Sir John Herschel's Dis-
* This view of the necessaiy co-existence of opposite excitements involves a great extension
of the original doctrine of two electricities. The early theorists assnmed that, when amber
was rubbed, the amber was made positive and the rubber negative to the same degree; but it
never occurred to them to suppose that the existence of the amber charge was dependent on
an opposite charge in the bodies with which the amber was contiguous, while the existence
of the negative charge on the rubber was equally dependent on a contrary state of the sur-
faces that might accidentally be confronted with it ; that, in fact, in a case ^f electrical ex-
citement by friction, four charges were the minimum that could exist. But this double elec-
trical action is essentially implied in the explanation now universally adopted in regard to
the phenomena of the common electric machine.
EXAMPLES OF THE FOUR METHODS. 297
course on the Study of I^atural Philosophy, a work replete with happily-
selected exemplifications of inductive processes from almost every depai't-
ment of physical science, and in which alone, of all books which I have met
with, the four methods of induction are distinctly recognized, though not
so clearly characterized and defined, nor their correlation so fully shown,
as has appeai-ed to me desirable. The present example is described by
Sir John Herschel as "one of the most beautiful specimens" which can be-
cited " of inductive experimental inquiry lying within a moderate com-
pass;" the theory of dew, first promulgated by the late Dr. Wells, and now
universally adopted by scientific authorities. The passages in inverted
commas are extracted verbatim from the Discourse.*
" Suppose dew were the phenomenon proposed, whose caTise we would
know. In the first place " we must determine precisely what we mean by
dew : what the fact really is whose cause we desire to investigate. " We
must separate dew from rain, and the moisture of fogs, and limit the ap-
plication of the term to what is really meant, which is the spontaneous ap-
pearance of moisture on substances exposed in the open air when no rain
or visible wet is falling." This answers to a preliminary operation which
will be characterized in the ensuing book, ti eating of operations subsidiary
to induclion.f
"Now, here we have analogous phenomena in the moisture which be-
dews a cold metal or stone when we breathe upon it ; that which appears
on a glass of water fresh from the well in hot weather ; that which appears
on the inside of windows when sudden rain or hail chills the external air %
that which runs down our walls when, after a long frost, a warm, moist
thaw comes on." Comparing these cases, we find that they all contain the
phenomenon which was proposed as the subject of investigation. Now
" all these instances agree in one point, the coldness of the object dewed,
in comparison with the air in contact with it." But there still remains the
most important case of all, that of nocturnal dew : does the same circum-
stance exist in this case? "Is it a fact that the object dewed is colder
than -the air? Certainly not, one would at first be inclined to say; for
what is to make it so ? But .... the experiment is easy : we have only ta
lay a thermometer in contact with the dewed substance, and hang one at a
little distance above it, out of reach of its influence. The experiment has.
been therefore made, the question has been asked, and the answer has been
invariably in the affirmative. Whenever an object contracts dew, it is-
colder than the air."
Here, then, is a complete application of the Method of Agreement, estab-
lishing the fact of an invariable connection between the deposition of dew
on a surface, and the coldness of that surface compared with the external
air. But which of these is cause, and which effect ? or are they both ef-
fects of something else? On this subject the Method of Agreement can
afford us no light : we must call in a more potent method. " We must
collect more facts, or, which comes to the same thing, vary the circum-
stances; since every instance in which the circumstances differ is a fresh
fact: and especially, we must note the contrary or negative cases, i. e.,
where no dew is produced :" a comparison between instances of dew and
instances of no dew, being the condition necessary to bring the Method of
Difference into play.
" Now, first, no dew is produced on the surface of polished metals, but
• Pp. 110, 111. t Infra, book iv., chap, ii., On Abstraction.
•298 INDUCTION*.
it is very copiously on glass, both exposed with their faces upward, and in
«ome cases the under side of a horizontal plate of glass is also dewed."
Here is an instance in which the effect is pi-oduced, and another instance in
which it is not produced ; but we can not yet pronounce, as the canon of
the Method of Difference requires, that the latter instance agrees with the
former in all its circumstances except one ; for the differences between
glass and polished metals are manifold, and the only thing we can as yet
be sure of is, that the cause of dew will be found among the circumstances
■by which the former substance is distinguished from the latter. But if
we could be sure that glass, and the various other substances on which dew
is deposited, have only one quality in common, and that polished metals
and the other substances on which dew is not deposited, have also nothing
in common but the one circumstance of not having the one quality which
the others have ; the requisitions of the Method of Difference would be
•completely satisfied, and we should recognize, in that quality of the sub-
«tances, the cause of dew. This, accordingly, is the path of inquiry which
is next to be pursued.
" In the cases of polished metal and polished glass, the contrast shows
«vidently that the substance has much to' do with the phenomenon ; there-
fore let the substance alone be diversified as much as possible, by exposing
polished surfaces of various kinds. This done, a scale of intensity becomes
obvious. Those polished substances are found to be most strongly dewed
which conduct heat worst ; while those which conduct heat well, resist dew
TOOSt effectually." The complication increases ; here is the Method of
Concomitant Variations called to our assistance ; and no other method was
practicable on this occasion ; for the quality of conducting heat could not
■be excluded, since all substances conduct heat in some degree. The conclu-
.sion obtained is, that cceteris paribus the deposition of dew is in some pro-
portion to the power which the body possesses of resisting the passage of
beat; and that this, therefore (or something connected with this), must be
at least one of the causes which assist in producing the deposition of dew
on the surface.
" But if we expose rough surfaces instead of polished, we sometimes find
this law interfered with. Thus, roughened iron, especially if painted over
or blackened, becomes dewed sooner than varnished paper; the kind of
■surface, therefore, has a great influence. Expose, then, the same material
in very diversified states, as to surface " (that is, employ the Method of Dif-
ference to ascertain concomitance of variations), " and another scale of in-
tensity becomes at once apparent ; those surfaces which part with their
heat most readily by radiation are found to contract dew most copiously."
Here, therefore, are the requisites ior a second employment of the Method
of Concomitant Variations ; which in this case also is the only method
available, since all substances radiate heat in some degree or other. The
•conclusion obtained by this new application of the method is, that cceteris
jaaribus the deposition of dew is also in some proportion to the power of
radiating heat; and that the quality of doing this abundantly (or some
■cause on which that quality depends) is another of the causes which pro-
mote the deposition of dew on the substance.
"Again, the influence ascertained to exist of substance and surface leads
us to consider that of texture : and here, again, we are presented on trial
with remarkable differences, and with a third scale of intensity, pointing
out substances of a close, firm texture, such as stones, metals, etc., as un-
favorable, but those of a loose one, as cloth, velvet, wool, eider-down, cotr-
EXAMPLES OF THE FOUR METHODS. 299
tot), etc., as eminently favorable to the contraction of dew." The Method
■of Concomitant Variations is here, for the third time, had recourse to;
and, as before, from necessity, since the texture of no substance is absolute-
ly firm or absolutely loose. Looseness of texture, therefore, or something
-which is the cause of that quality, is another circumstance which promotes
the deposition of dew; but this third course resolves itself into the first,
viz., the quality of resisting the passage of heat : for substances of loose
"texture " are precisely those which are best adapted for clothing, or for im-
peding the free passage of heat from the skin into the air, so as to allow
their outer surfaces to be very cold, while they remain warm within ;" and
this last is, therefore, an induction (from fresh instances) simply corrobora-
tive of a former induction.
It thus appears that the instances in which much dew is deposited, which
are very various, agree in this, and, so far as we are able to observe, in this
only, that they either radiate heat rapidly or conduct it slowly : qualities
between which there is no other circumstance of agreement than that by
virtue of either, the body tends to lose heat from the surface more rapidly
than it can be restored from within. The instances, on the contrary, in
which no dew, or but a small quantity of it, is formed, and which are also
€xtremely various, agree (as far as we can observe) in nothing except in
not having this same property. We seem, therefore, to have detected the
■characteristic difference between the substances on which dew is pro-
duced and those on which it is not produced. And thus have been real-
ized the requisitions of what we have termed the Indirect Method of Dif-
ference, or the Joint Method of Agreement and Difference. The example
afforded of this indirect method, and of the manner in which the data are
prepared for it by the Methods of Agreement and of Concomitant Varia-
tions, is the most important of all the illustrations of induction afforded by
this interesting speculation.
We might now consider the question, on what the deposition of dew de-
pends, to be completely solved, if we could be quite sure that the sub-
stances on which dew is produced differ from those on which it is not, in
nothing but in the property of losing heat from the surface faster than the
loss can be repaired from within. And though we never can have that
complete certainty, this is not of so much importance as might at first be
supposed ; for we have, at all events, ascertained that even if there be any
other quality hitherto unobserved which is present in all the substances
which conti-act dew, and absent in those which do not, this other property
must be one which, in all that great number of substances, is present or ab-
sent exactly where the property of being a better radiator than conductor
is present or absent; an extent of coincidence which affords a strong pre-
sumption of a community of cause, and a consequent invariable co-existence
between the two properties ; so that the property of being a better radiator
than conductor, if not itself the cause, almost certainly always accompanies
the cause, and for purposes of prediction, no error is likely to be commit-
ted by treating it as if it were really such.
Reverting now to an earlier stage of the inquiry, let us remember that
•we had ascertained that, in every instance where dew is formed, there is
actual coldness of the surface below the temperature of the surrounding
air ; but we were not sure whether this coldness was the cause of dew, or
its effect. This doubt we are now able to resolve. We have found that, in
every such instance, the substance is one which, by its own properties^ or
laws, would, if exposed in the night, become colder than the surrounding
300 INDUCTION.
air. The coldness, therefore, being accounted for independently of the dew,
while it is proved that there is a connection between the two, it must be
the dew which depends on the coldness ; or, in other words, the coldness i»
the cause of the dew.
This law of causation, already so amply established, admits, however, of
efficient additional corroboration in no less than three ways. First, by de-
duction fi'om the known laws of aqueous vapor when diffused through air
or any other gas; and though we have not yet come to the Deductive
Method, we will not omit what is necessary to render this speculation com-
plete. It is known by direct experiment that only a limited quantity of
water can remain suspended in the state of vapor at each degree of tem-
perature, and that this maximum grows less and less as the temperature
diminishes. From this it follows, deductively, that if there is already as
much vapor suspended as the air will contain at its existing temperature,
any lowering of that temperature will cause a portion of the vapor to be
condensed, and become water. But again, we know deductively, from the
laws of heat, that the contact of the air with a body colder than itself will
necessarily lower the temperature of the stratum of air immediately ap-
plied to its surface ; and will, therefore, cause it to part with a portion of
its water, which accordingly will, by the ordinary laws of gravitation or
cohesion, attach itself to the surface of the body, thereby constituting dew.
This deductive proof, it will have been seen, has the advantage of at once
proving causation as well as co-existence ; and it has the additional advan-
tage that it also accounts for the exceptions to the occurrence of the phe-
nomenon, the cases in which, although the body is colder than the air, yet
no dew is deposited ; by showing that this will necessarily be the case
when the air is so under-supplied with aqueous vapor, comparatively to its
temperature, that even when somewhat cooled by the contact of the cold-
er body it can still continue to hold in suspension all the vapor which was
previously suspended in it : thus in a very dry summer there are no dews,
in a very dry winter no hoar-frost. Here, therefore, is an additional con-
dition of the production of dew, which the methods we previously made
use of failed to detect, and which might have remained still undetected, if
recourse had not been had to the plan of deducing the effect from the as-
certained properties of the agents known to be present.
The second corroboration of the theory is by direct expei'iment, accord-
ing to the canon of the Method of Difference. We can, by cooling the sur-
face of any body, find in all cases some temperature (more or less inferior
to that of the surrounding air, according to its hygrometric condition) at
which dew will begin to be deposited. Here, too, therefore, the causation
is directly proved. We can, it is true, accomplish this only on a small
scale, but we have ample reason to conclude that the same operation, if
conducted in nature's great laboratory, would equally produce the effect.
And, finally, even on that great scale we are able to verify the result.
The case is one of those rare cases, as we have shown them to be, in which
nature works the experiment for us in the same manner in which we our-
selves perform it ; introducing into the previous state of things a single
and perfectly definite new circumstance, and manifesting the effect so rap-
idly that there is not time for any other material change in the pre-existing
circumstances. " It is observed that dew is never copiously deposited in
situations much screened from the open sky, and not at all in a cloudy
night; but if the clouds withdraw even for a few minutes, and leave a
dear opening, a deposition of dew presently begins, and goes on increas-
EXAMPLES OF THE FOUR METHODS. 301
ing Dew formed in clear intervals will often even evaporate again
when the sky becomes thickly overcast." The proof, therefore, is complete,
that the presence or absence of an uninterrupted communication with the
sky causes the deposition or non-deposition of dew. Now, since a clear sky
is nothing but the absence of clouds, and it is a known property of clouds, as
of all other bodies between which and any given object nothing intervenes
but an elastic fluid, that they tend to raise or keep up the superficial tem-
perature of the object by radiating heat to it, we see at once that the dis-
appearance of clouds will cause the surface to cool; so that nature, in this
■case, produces a change in the antecedent by definite and known means,
and the consequent follows accordingly : a natural experiment which satis-
fies the requisitions of the Method of Difference.*
The accumulated proof of which the Theory of Dew has been found
susceptible, is a striking instance of the fullness of assurance which the in-
ductive evidence of laws of causation may attain, in cases in which the in-
variable sequence is by no fneans obvious to a superficial view.
§ 4. The admirable physiological investigations of Dr. Brown-Sequard
afford bi'illiant examples of the application of the Inductive Methods to a
class of inquiries in which, for reasons which will presently be given, di-
rect induction takes place under peculiar difficulties and disadvantages.
As one of the most apt instances, I select his speculation (in the proceed-
ings of the Royal Society for May 16, 1861) on the relations between mus-
cular irritability, cadaveric rigidity, and putrefaction.
The law which Dr. Brown-Sequard's investigation tends to establish, is
the following : " The greater the degree of muscular irritability at the time of
death, the later the cadaveric rigidity sets in, and the longer it lasts, and the
later also putrefaction appears, and the slower it progresses." One would
say at first sight that the method here required must be that of Concomi-
tant Variations. But this is a delusive appearance, arising from the circum-
stance that the conclusion to be tested is itself a fact of concomitant varia-
tions. For the establishment of that fact any of the Methods may be put
in requisition, and it will be found that the fourth Method, though really
employed, has only a subordinate place in this particular investigation.
The evidences by which Dr. Brown-Sequard establishes the law may be
enumerated as follows :
1st. Paralyzed muscles have greater irritability than healthy muscles.
Now, paralyzed muscles are later in assuming the cadaveric rigidity than
healthy muscles, the rigidity lasts longer, and putrefaction sets in later, and
proceeds more slowly.
* I must, however, remark, that this example, which seems to militate against the assertion
we made of the comparative inapplicability of the Method of Difference to cases of pure ob-
servation, is really one of those exceptions which, according to a proverbial expression, prove
the general rule. For in this case, in which Nature, in her experiment, seems to have imi-
tated the type of the experiments made by man, she has only succeeded in producing the
likeness of man's most imperfect experiments ; namely, those in which, though he succeeds
in producing the phenomenon, he does so by employing complex means, which he is unable
perfectly to analyze, and can form, therefore, no siifiScient judgment what portion of the effects
may be due, not to the supposed cause, but to some unknown agency of the means by which
that cause was produced. In the natural experiment which we are speaking of, the means
used was the clearing off a canopy of clouds ; and we certainly do not know sufficiently in
what this process consists, or on what it depends, to be certain a priori that it might not oper-
ate upon the deposition of dew independently of any thermometric effect at the earth's surface.
Even, therefore, in a case so favorable as this to Nature's experimental talents, her experiment
is of little value except in corroboration of a conclusion already attained through other means.
302 INDUCTION.
Both these propositions had to be proved by experiment ; and for the
experiments which prove them, science is also indebted to Dr. Brown-S^-
qnard. The former of the two — that paralyzed muscles have greater irri-
tability than healthy muscles — he ascertained in various ways, but most
decisively by " comparing the duration of irritability in a paralyzed muscle
and in the corresponding healthy one of the opposite side, while they are
both submitted to the same excitation." He " often found, in experiment-
ing in that way, that the paralyzed muscle remained irritable twice, three
times, or even four times as long as the healthy one." This is a case of in-
duction by the Method of Difference. The two limbs, being those of the
game animal, were presumed to differ in no circumstance material to the
case except the paralysis, to the presence and absence of which, therefore,
the difference in the muscular irritability was to be attributed. This as-
sumption of complete resemblance in all material circumstances save one,
evidently could not be safely made in any one pair of experiments, because
the two legs of any given animal might be accidentally in very different
pathological conditions ; but if, besides taking pains to avoid any such dif-
ference, the experiment was repeated sufficiently often in different animals
to exclude the supposition that any abnormal circumstance could be pres-
ent in them all, the conditions of the Method of Difference were adequate-
ly secured.
In the same manner in which Dr. Brown-S'6quard proved that paralyzed
muscles have greater irritability, he also proved the correlative proposition
respecting cadaveric rigidity and putrefaction. Having, by section of the
roots of the sciatic nerve, a'hd again of a lateral half of the spinal cord,
produced paralysis in one hind leg of an animal while the other remained
healthy, he found that not only did muscular irritability last much longer
in the paralyzed limb, but rigidity set in later and ended later, and putre-
faction began later and was less rapid than on the healthy side. This is a
common case of the Method of Difference, requiring no comment. A fur-
ther and very important corroboration was obtained by the same method.
When the animal was killed, not shortly after the section of the nerve, but
a month later, the effect was reversed ; rigidity set in sooner, and lasted a
shorter time, than in the healthy muscles. But after this lapse of time, the
paralyzed muscles, having been kept by the paralysis in a state of rest, had
lost a great part of their irritability, and instead of more, had become less
irritable than those on the healthy side. This gives the ABC, abe, and
B C, 6 e, of the Method of Difference. One antecedent, increased irrita-
bility, being changed, and the other circumstances being the same, the con-
sequence did not follow ; and, moreover, when a new antecedent, contrary
to the first, was supplied, it was followed by a contrary consequent. This
instance is attended with the special advantage of proving that the re-
tardation and prolongation of the rigidity do not depend directly on the
paralysis, since that was the same in both the instances ; but specifically on
one effect of the paralysis, namely, the increased irritability ; since they
ceased when it ceased, and were reversed when it was reversed.
2d. Diminution of the temperature of muscles before death increases
their irritability. But diminution of their temperature also retards cadav-
eric rigidity and putrefaction.
Both these truths were first made known by Dr. Brown-Sequard himself,
through experiments which conclude according to the Method of Differ-
ence. There is nothing in the nature of the process requiring specific
analysis.
EXAMPLES OF THE FOUR METHOBS. SOS
3d. Muscular exercise, prolonged to exhaustion, diminishes the muscu-
lar irritability. This is a well-known truth, dependent on the most gener-
al laws of muscular action, and proved by experiments under the Method
of Difference, constantly repeated. Now, it lias been shown by observa-
tion that overdriven cattle, if killed before recovery from their fatigue,,
become rigid and putrefy in a surprisingly short time. A similar fact has
been observed in the case of animals hunted to death ; cocks killed during
or shortly after a fight ; and soldiers slain in the field of battle. These va^
rious cases agree in no circumstance, directly connected with the muscles,.
except that these have just been subjected to exhausting exercise. Under
the canon, therefore, of the Method of Agreement, it may be inferred that
there is a connection between the two facts. The Method of Agreement,
indeed, as has been shown, is not competent to prove causation. The pres-
ent case, however, is already known to be a case of causation, it being cer-
tain that the state of the body after death must somehow depend upon its.
state at the time of death. We are, therefore, warranted in concluding that
the single circumstance in which all the instances agree, is the part of the
antecedent which is the cause of that particular consequent.
4th. In proportion as the nutrition of muscles is in a good state, their
irritability is high. This fact also rests on the general evidence of the
laws of physiology, grounded on many familiar applications of the Method
of Difference. Now, in the case of those who die from accident or vio-
lence, with their muscles in a good state of nutrition, the muscular iri'ita-
bility continues long after death, rigidity sets in late, and persists long-
without the putrefactive change. On the contrary, in cases of disease in
which nutrition has been diminished for a long time before death, all these
effects are reversed. These are the conditions of the Joint Method of
Agreement and Difference. The cases of retarded and long continued
rigidity here in question agree only in being preceded by a high state of
nutrition of the muscles ; the cases of rapid and brief rigidity agree only
in being preceded by a low state of muscular nutrition ; a connection is,
therefore, inductively proved between the degree of the nutrition, and the
slowness and prolongation of the rigidity.
5th. Convulsions, like exhausting exercise, but in a still greater degree,
diminish the muscular irritability. Now, when death follows violent and
prolonged convulsions, as in tetanus, hydrophobia, some cases of cholera,
and certain poisons, rigidity sets in very rapidly, and after a very brief du-
ration, gives place to putrefaction. This is another example of the Meth-
od of Agreement, of the same character with No. 3.
6th. The series of instances which we shall take last, is of a more com-
plex character, and requires a more minute analysis.
It has long been observed that in some cases of death by lightning, ca-
daveric rigidity either does not take place at all, or is of such extremely
brief duration as to escape notice, and that in these cases putrefaction is
very rapid. In other cases, however, the usual cadaveric rigidity appears.
There must be some difference in the cause, to account for this difference
in the effect. Now, "death by lightning may be the result of, 1st, a syn-
cope by fright, or in consequence of a direct or reflex influence of light-
ning on the par vagum ; 2d, hemorrhage in or around the brain, or in the
lungs, the pericardium, etc. ; 3d, concussion, or some other alteration in
the brain ;" none of which phenomena have any known property capable ot
accounting for the suppression, or almost suppression, of the cadaveric ri-
gidity. But the cause of death may also be that the lightning produces
304 INDUCTION.
*' a violent convulsion of every muscle in the body," of which, if of suffi-
cient intensity, the known effect would be that "muscular irritability
ceases almost at once." If Dr. Brown-Sequard's generalization is a true
law, these will be the very cases in which rigidity is so much abridged as
to escape notice ; and the cases in which, on the contrary, rigidity takes
place as usual, will be those in which the stroke of lightning operates in
some of the other modes which have been enumerated. How, then, is this
brought to the test ? By experiments, not on lightning, which can not be
commanded at pleasure, but on the same natural agency in a manageable
form, that of artificial galvanism. Dr. Brown-S6quard galvanized the en-
tire bodies of animals immediately after death. Galvanism can not operate
in any of the modes iu which the stroke of lightning may have operated,
except the single one of producing muscular convulsions. If, therefore, af-
ter the bodies have been galvanized, the duration of rigidity is much short-
ened and putrefaction much accelerated, it is reasonable to ascribe the
same effects when produced by lightning to the property which galvanism
shares with lightning, and not to those which it does not. Now this Dr.
Brown-Sequard found to be the fact. The galvanic experiment was tried
with charges of very various degrees of strength ; and the more powerful the
charge, the shorter was found to be the duration of rigidity, and the more
«peedy and rapid the putrefaction. In the experiment in which the charge
was strongest, and the muscular irritability, most promptly destroyed, the
I'igidity only lasted fifteen minutes. On the principle, therefore, of the
Method of Concomitant Variations, it may be inferred that the duration
of the rigidity depends on the degree of the .irritability ; and that if the
charge had been as much stronger than Dr. Brown-S6qnard's strongest, as
a stroke of lightning must be stronger than any electric shock which we
can produce artificially, the rigidity would have been shortened in a corre-
sponding ratio, and might have disappeared altogether. This conclusion
having been arrived at, the case of an electi'ic shock, whether natural or
artificial, becomes an instance, in addition to all those already ascertained,
of correspondence between the irritability of the muscle and the duration
of rigidity.
All these instances are summed up in the following statement : " That
when the degree of muscular irritability at the time of death is considerar
ble, either in consequence of a good state of nutrition, as in persons who
die in full health from an accidental cause, or in consequence of rest, as in
cases of paralysis, or on account of the influence of cold, cadaveric rigidity
in all these cases sets in late and lasts long, and putrefaction appears late,
and progresses slowly ;" but " that when the degree of muscular irritability
at the time of death is slight, either in consequence of a bad state of nu-
trition, or of exhaustion from overexertion, or from convulsions caused by
disease or poison, cadaveric rigidity sets in and ceases soon, and putrefac-
tion appears and progresses quickly." These facts present, in all their
completeness, the conditions of the Joint Method of Agreement and Dif-
ference. Early and brief rigidity takes place in cases which agree only in
the circumstance of a low state of muscular irritability. Rigidity begins
late and lasts long in cases which agree only in the contrary circumstance,
of a muscular irritability high and unusually prolonged. It follows that
there is a connection through causation between the degree of muscular ir-
ritability after death, and the tardiness and prolongation of the cadaveric
rigidity-
This investigation places in a strong light the value and eflScacy of the
EXAMPLES OF THE FOUR METHODS. _ 305
Joint Method. For, as we have ah-eady seen, the defect of that Method is,
that like the Method of Agreement, of which it is only an improved form,
it can not prove causation. But in the present case (as in one of the steps
in the argument which led up to it) causation is already proved ; since
there could never be any doubt that the rigidity altogether, and the putre-
faction which follows it, are caused by the fact of death : the observations
and experiments on which this rests are too familiar to need analysis, and
fall under the Method of Difference. It being, therefore, beyond doubt
that the aggregate antecedent, the death, is the actual cause of the whole
train of consequents, whatever of the circumstances attending the death
can be shown to be followed in all its variations by variations in the effect
under investigation, must be the particular feature of the fact of death on
which that effect depends. The degree of muscular irritability at the
time of death fulfills this condition. The only point that could be brought
into question, would be whether the effect depended on the irritability it-
self, or on something which always accompanied the irritability : and this
doubt is set at rest by establishing, as the instances do, that by whatever
cause the high or low irritability is produced, the effect equally follows ;
and can not, therefore, depend upon the causes of irritability, nor upon the
other effects of those causes, which are as various as the causes them-
selves, but upon the irritability, solely.
§ 5. The last two examples will have conveyed to any one by whom
they have been duly followed, so clear a conception of the use and practi-
cal management of three of the four methods of experimental inquiry, as
to supersede the necessity of any further exemplification of them. The
remaining method, that of Residues, not having found a place in any of
the preceding investigations, I shall quote from Sir John Herschel some
examples of that method, with the remarks by which they are introduced.
" It is by this process, in fact, that science, in its pi-esent advanced state,
is chiefly promoted. Most of the phenomena which Nature presents are
very complicated ; and when the effects of all known causes are estimated
with exactness, and subducted, the residual facts are constantly appearing
in the form of phenomena altogether new, and leading to the most impor-
tant conclusions.
" For example : the return of the comet predicted by Professor Encke a
great many times in succession, and the general good agreement of its cal-
culated with its observed place during any one of its periods of visibility,
would lead us to say that its gravitation toward the sun and planets is the
sole and sufficient cause of all the phenomena of its orbitual motion ; but
when the effect of this cause is strictly calculated and subducted from the
observed motion, there is found to remain behind a residual phenomenon,
which would never have been otherwise ascertained to exist, which is a
small anticipation of the time of its re-appearance, or a diminution of its
periodic time, which can not be accounted for by gravity, and whose cause
is therefore to be inquired into. Such an anticipation would be caused by
the resistance of a medium disseminated through the celestial regions;
and as there are other good reasons for believing this to be a vera causa "
(an actually existing antecedent), " it has therefore been ascribed to such a
resistance.*
" M. Arago, having suspended a magnetic needle by a silk thread, and set
* In his subsequent work, Outlines of Astronomy (§ 570), Sir John Herschel suggests an-
■other possible explanation of the acceleration of the revolution of a comet.
20
306 INDUCTION.
it in vibration, observed, that it came much sooner to a state of rest when
suspended over a plate of copper, than when no such plate was beneath it^
Now, in both cases there were two verm causce" (antecedents known to-
exist) " why it should come at length to rest, viz., the resistance of the air,,
•which opposes, and at length destroys, all motions performed in it ;• and the
want of perfect mobility in the silk thread. But the effect of these causes
"being exactly known by the observation made in the absence of the cop-
per, and being thus allowed for and subducted, a residual phenomenon
appeared, in the fact that a retarding influence was exerted by the copper
itself;, and this fact, once ascertained, speedily led to the knowledge of
an entirely new and unexpected class of relations." This example belongs,.
however, not to the Method of Residues but to the Method of Difference,,
the law being ascertained by a direct comparison of the results of two ex-
periments, which differed in nothing but the presence or absence of the
" plate of copper. To have made it exemplify the Method of Residues, the
effect of the resistance of the air and that of the rigidity of the silk should
have been calculated a priori, irom the laws obtained by separate and fore-
gone experiments.
"Unexpected and peculiarly striking confirmations of inductive laws
frequently occur in the form of I'esidual phenomena, in the course of in-
vestigations of a widely different nature from those which gave rise to the
inductions themselves. A very elegant example may be cited in the unex-
pected confirmation of the law of the development of heat in elastic fluids-
by compression, which is afforded by the phenomena of sound. The in-
quiry into the cause of sound had led to conclusions respecting its mode
of propagation, from which its velocity in the air could be precisely cal-
culated. The calculations were performed; but, when compared with
fact, though the agreement was quite sufiicient to show the general cor-
rectness of the cause and mode of propagation assigned, yet the whole ve-
locity could not be shown to arise from this theory. There was still a
residual velocity to be accounted for, which placed dynamical philosophers
for a long time in great dilemma. At length Laplace struck on the happy
idea, that this might arise from the heat developed in the act of that con-
densation which necessarily takes place at every vibration by which sound
is conveyed. The matter was subjected to exact calculation, and the result
•was at once the complete explanation of the residual phenomenon, and a
striking confirmation of the general law of the development of heat by
compression, under circumstances beyond artificial imitation."
"Many of the new elements of chemistry have been detected in the-
investigation of residual phenomena. Thus Arfwedson discovered lithia
by perceiving an excess of weight in the sulphate produced from a small
portion of what he considered as magnesia present in a mineral he had an-
alyzed. It is on this principle, too, that the small concentrated residues of
great operations in the arts are almost sure to be the lurking-places of new
chemical ingredients : witness iodine, brome, selenium, and the new metals
accompanying platina in the experiments of WoUaston and Tennant. It
was a happy thought of Glauber to examine what every body else threw
away."*
"Almost all the greatest discoveries in Astronomy," says the same au-
thor,f " have resulted from the consideration of residual phenomena of a
quantitative or numerical kind It was thus that the grand discovery
* Discourse, pp. 156-8, and 171. t Outlines of Astronomy, § 856.
EXAMPLES or THE FOUR METHODS. 307
of the precession of the equinoxes resulted as a residual phenomenon, from
the imperfect explanation of the return of the seasons by the return of the
sun to the same apparent place among the fixed stars. Thus, also, aberra-
tion and nutation resulted as residual phenomena from that portion of the
changes of the apparent places of the fixed stars which was left unaccounted
for by precession. And thus again the apparent proper motions of the stars
are the observed residues of their apparent movements outstanding and
unaccounted for by strict calculation of the effects of precession, nutation,
and aberration. The nearest approach which human theories can make to
perfection is to diminish this residue, this caput mortuum of observation,
as it may be considered, as much as practicable, and, if possible, to reduce
it to nothing, either by showing that something has been neglected in our
estimation of known causes, or Ify reasoning upon it as a new fact, and on
the principle of the inductive philosophy ascending from the effect to its
cause or causes."
The disturbing effects mutually produced by the earth and planets upon
each other's motions were first brought to light as residual phenomena, by the
difference which appeared between the observed places of those bodies, and
the places calculated on a consideration solely of their gravitation toward the
sun. It was this which determined astronomers to consider the law of gravi-
tation, as obtaining between all bodies whatever, and therefore between all
particles of matter ; their first tendency having been to regard it as a force
acting only between each planet or satellite and the central body to whose
system it belonged. Again, the catastrophists, in geology, be their opinion
right or wrong, support it on the plea, that after the effect of all causes now
in operation has been allowed for, there remains in the existing constitu-
tion of the earth a large residue of facts, proving the existence at former
periods either of other forces, or of the same forces in a much greater de-
gree of intensity. To add one more example : those who assert, what no
one has shown any real ground for believing, that there is in one human
individual, one sex, or one race of mankind over another, an inherent and
inexplicable superiority in mental faculties, could only substantiate their
proposition by subtracting from the differences of intellect which we in
fact see, all that can be traced by known laws either to the ascertained
differences of physical organization, or to the differences which have ex-
isted in the outward circumstances in which the subjects of the comparison
have hitherto been placed. What these causes might fail to account for
would constitute a residual phenomenon, which and which alone would be
evidence of an ulterior original distinction, and the measure of its amount.
But the asserters of such supposed differences have not provided them-
selves with these necessary logical conditions of the establishment of their
doctrine.
The spirit of the Method of Residues being, it is hoped, sufficiently in-
telligible from these examples, and 'the other three methods having already
been so fully exemplified, we may here close our exposition of the four
methods, considered as employed in the investigation of the simpler and
more elementary order of the combinations of phenomena.
§ 6. Dr. Whewell has expressed a very unfavorable opinion of the utili-
ty of the Four Methods, as well as of the aptness of the examples by which
I have attempted to illustrate them. His words are these :*
* Philosophy of Discover]/, pp. 263, 264.
308 INDUCTION.
" Upon these methods, the obvious thing to remark is, that they take for
granted the very thing which is most difficult to discover, the reduction of
the phenomena to formulae such as are here presented to us. When we
have any set of complex facts offered to us ; for instance, those which were
offered in the cases of discovery which I have mentioned — the facts of the
planetary paths, of falling bodies, of refracted i"ays, of cosmical motions, of
chemical analysis ; and when, in any of these cases, we would discover the
law of nature which governs them, or, if any one chooses so to term it, the
■ feature in which all the cases agree, where are we to look for our A, B, C,
and a,h,c? Nature does not present to us the cases in this form; and
how are we to reduce them to this form ? You say when we find the com-
bination of A B C with a bo and A B D with ah d, then we may draw our
inference. Granted ; but when and whei'e &re we to find such combina-
tions ? Even now that the discoveries are made, who will point out to us
what are the A, B, C, and a, b, c, elements of the cases which have just been
enumerated ? Who will tell us which of the methods of inquiry those
historically real and successful inquiries exemplify ? Who will carry these
formulae through the history of the sciences, as they have really grown up,
and show us that these four methods have been operative in their forma-
tion; or that any light is thrown upon the steps of their progress by refer-
ence to these formulae ?"
He adds that, in this work, the methods have not been applied " to a
large body of conspicuous and undoubted examples of discovery, extending
along the whole history of science ;" which ought to have been done in or-
der that the methods might be shown to possess the " advantage " (which
he claims as belonging to his own) of being those " by which all great dis-
coveries in science have really been made." — (P. 277.)
There is a striking similarity between the objections here made against
Canons of Induction, and what was alleged, in the last century, by as able
men as Dr. Whewell, against the acknowledged Canon of Ratiocination.
Those who protested against the Aristotelian Logic said of the Syllogism,
what Dr. Whewell says of the Inductive Methods, that it " takes for grant-
ed the very thing which is most difficult to discover, the reduction of the
argument to formulae such as are here presented to us." The grand diffi-
culty, they said, is to obtain your syllogism, not to judge of its correctness
when obtained. On the matter of fact, both they and Dr. Whewell are
right. The greatest difficulty in both cases is, first, that of obtaining the
evidence, and next, of reducing it to the form which tests its conclusive-
ness. But if we try to reduce it without knowing what it is to be reduced
to, we are not likely to make much progress. It is a more difficult thing
to solve a geometrical problem, than to judge whether a proposed solution
is correct : but if people were not able to judge of the solution when found,
they would have little chance of finding it. And it can not be pretended
that to judge of an induction when found is perfectly easy, is a thing for
which aids and instruments are superfluous ; for erroneous inductions, false
inferences from experience, are quite as common, on some subjects much
commoner than true ones. The business of Inductive Logic is to provide
rules and models (such as the Syllogism and its rules are for ratiocination)
to which if inductive arguments conform, those arguments are conclusive,
and not otherwise. This is what the Four Methods profess to be, and
what I believe they are universally considered to be by experimental phi-
losophers, who had practiced all of them long before any one sought to re-
duce the practice to theory.
EXAMPLES OF THE FOUR METHODS. 309
The assailants of the Syllogism had also anticipated Dr.Whewell in the
other branch of his argument. They said that no discoveries were ever
made by syllogism ; and Dr. Whewell says, or seems to say, that none were
ever made by the Four Methods of Induction. To the former objectors,
Archbishop Whately very pertinently answered, that their argument, if
good at all, was good against the reasoning process altogether ; for vehat-
ever can not be reduced to syllogism, is not reasoning. And Dr. Whewell's
argument, if good at all, is good against all inferences from experience. In
saying that no discoveries were ever made by the Four Methods, he affirms
that none were ever made by observation and experiment ; for assuredly if
any were, it was by processes reducible to one or other of those methods.
This difference .between us accounts for the dissatisfaction which my ex-
amples give him ; for I did not select them with a view to satisfy any one
who required to be convmced that observation and experiment are modes
of acquiring knowledge : i contess that in the choice of them I thought
only of illustration, and oi facilitating the conception of the Methods by
concrete instances. If it had been my object to justify the processes thein-
selves as means of investigation, there would have been no need to look
far off, or make use of recondite or complicated instances. As a specimen
of a truth ascertained by the Method of Agreement, I might have chosen
the proposition, " Dogs bark." This dog, and that dog, and the other dog,
answer to A B C, A D E, A F G. The circumstance of being a dog an-
swers to A. Barking answers to a. As a truth made known by the Meth-
od of Difference, " Fire burns " might have suificed. Before I touch the
fire I am not burned ; this is B C : I touch it, and am burned'; this is A B
C, a B C.
Such familiar experimental processes are not regarded as inductions by
Dr. Whewell ; but they are perfectly homogeneous with those by which,
even on his own showing, the pyramid of science is supplied with its base.
In vain he attempts to escape from this conclusion by laying the most ar-
bitrary restrictions on the choice of examples admissible as instances of
Induction : they must neither be such as are still matter of discussion
(p. 265), nor must any of them be drawn from mental and social subjects
(p. 269), nor from ordinary observation and practical life (pp. 241-247).
They must be taken exclusively from the generalizations by which scientific
thinkers have ascended to great and comprehensive laws of natural phe-
nomena. Now it is seldom possible, in these complicated inquiries, to go
much beyond the initial steps, without calling in the instrument of Deduc-
tion, and the tempoi-ary aid of hypothesis ; as I myself, in common with
Dr. Whewell, have maintained against the purely empirical school. Since,
therefore, such cases could not conveniently be selected to illustrate the
principles of mere observation and experiment. Dr. Whewell is misled by
their absence into representing the Experimental Methods as serving no
purpose in scientific investigation ; forgetting that if those methods had
not supplied the first generalizations, there would have been no materials
for his own conception of Induction to work upon.
His challenge, however, to point out which of the four methods are exem-
plified in certain important cases of scientific inquiry, is easily answered.
"The planetary paths," as far as they are a case of induction at all,* fall
under the Method of Agreement. The law of " falling bodies," namely,
that they describe spaces proportional to the squares of the times, was his-
* See, on this point, the second chapter of the present book.
310 INDUCTION.
torically a deduction from the first law of motion ; but the experiments by
which it was verified, and by which it might have been discovered, were
examples of the Method of Agreement; and the apparent variation from
the true law, caused by the resistance of the air, was cleared up by experi.
ments in vacuo, constituting an application of the Method of Difference.
The law of " refracted i-ays " (the constancy of the ratio between the sines
of incidence and of refraction for each refracting substance) was ascertained
by direct measurement, and therefore by the Method of Agreement. The
" cosmical motions " were determined by highly complex processes of
thought, in which Deduction was predominant, but the Methods of Agree-
ment and of Concomitant Variations had a large part in establishing the
empirical laws. Every case without exception of " chemical analysis " con-
stitutes a well-marked example of the Method of Difference. To any one
acquainted with the subjects — to Dr. Whewell himself, there would not be
the smallest difficulty in setting out " the A B C and abc elements " of
these cases.
If discoveries are ever made by observation and experiment without De-
duction, the four methods are methods of discovery : but even if they were
not methods of discovery, it would not be the less true that they are the
sole methods of Proof ; and in that character, even the results of deduction
are amenable to them. The great generalizations which begin as Hypo-
theses, must end by being proved, and are in reality (as will be shown
hereafter) proved, by the Four Methods. Now it is with Proof, as such,
that Logic is principally concerned. This distinction has indeed no chance
of finding favor with Dr. Whewell; for it is the peculiarity of his system,
not to recognize, in cases of Induction, any necessity for proof. If, after
assuming an hypothesis and carefully collating it with facts, nothing is
brought to light inconsistent with it, that is, if experience does not c?isprove
it, he is content : at least until a simpler hypothesis, equally consistent with
experience, presents itself. If this be Induction, doubtless there is no ne-
cessity for the four methods. But to suppose that it is so, appears to me a
radical misconception of the nature of the evidence of physical truths.
So real and practical is the need of a test for induction, similar to the
syllogistic test of ratiocination, that inferences which bid defiance to the
most elementary notions of inductive logic are put forth without misgiv-
ing by persons eminent in physical science, as soon as they are off the
ground on which they are conversant with the facts, and not reduced to
judge only by the arguments; and as for educated persons in general, it
may be doubted if they are better judges of a good or a bad induction
than they were before Bacon wrote. The improvement in the results of
thinking has seldom extended to the processes ; or has reached, if any proc-
ess, that of investigation only, not that of proof. A knowledge of many
laws of nature has doubtless been arrived at, by framing hypotheses and
finding that the facts corresponded to them; and many errors have been
got rid of by coming to a knowledge of facts which were inconsistent with
them, but not by discovering that the mode of thought which led to the
errors was itself faulty, and might have been known to be such independ-
ently of the facts which disproved the specific conclusion. Hence it is,
that while the thoughts of mankind have on many subjects worked them-
selves practically right, the thinking power remains as weak as ever : and
on all subjects on which the facts which would check the result are not ac-
cessible, as in what relates to the invisible world, and even, a.a has been
seen lately, to the visible world of the planetary regions, men oi the great-
PLURALITY OF CAUSES. 3U
<e8t scientific acquirements argue as pitiably as the merest ignoramus. For
though they have made many sound inductions, they have not learned from
them (and Dr. Whewell thinks there is no necessity that they should learn)
the principles of inductive evidence.
CHAPTER X.
OF PLURALITY OF CAUSES, AKD OP THE INTBEMIXTUEE OP EPPECTS.
§ 1. In the preceding exposition of the four methods of observation
-and experiment, by which we contrive to distinguish among a mass of co-
existent phenomena the particular efEect due to a given cause, or the par-
ticular cause which gave birth to a given effect, it has been necessary to
suppose, in the first instance, for the sake of simplification, that this ana-
lytical operation is encumbered by no other difficulties than what are essen-
tially inherent in its nature ; and to represent to ourselves, therefore, every
•effect, on the one hand as connected exclusively with a single cause, and
on the other hand as incapable of being mixed and confounded with any
other co-existent effect. We have regarded abode, the aggregate of
the phenomena existing at any moment, as consisting of dissimilar facts,
a, h, c, d, and e, for each of which one, and only one, cause needs be sought;
the difficulty being only that of singling out this one cause from the mul-
titude of antecedent circumstances, A,B,C,D, and E. The cause indeed
may not be simple ; it may consist of an assemblage of conditions ; but we
have supposed that there was only one possible assemblage of conditions
from which the given effect could result.
If such were the fact, it would be comparatively an easy task to investi-
:gate the laws of nature. But the supposition does not hold in either of
its parts. In the first place, it is not true that the same phenomenon is
always produced by the same cause: the effect a may sometimes arise
irom A, sometimes from B. And, secondly, the effects of different causes
-are often not dissimilar, but homogeneous, and marked out by no assign-
able boundaries from one another : A and B may produce not a and b, but
•different portions of an effect a. The obscurity and difficulty of the inves-
tigation of the laws of phenomena is singularly increased by the necessi-
ty of adverting to these two circumstances : Intermixture of Effects, and
^Plurality of Causes. To the latter, being the simpler of the two considera-
tions, we shall first direct our attention.
It is not true, then, that one effect must be connected with only one
cause, or assemblage of conditions ; that each phenomenon can be pro-
duced only in one way. There are often several independent modes in
which the same phenomenon could have originated. One fact may be the
-consequent in several invariable sequences ; it may follow, with equal uni-
formity, any one of several antecedents, or collections of antecedents.
Many causes may produce mechanical motion; many causes may produce
some kinds of sensation ; many causes may produce death. A given effect
may really be produced by a certain cause, and yet be perfectly capable of
being produced without it.
/ § 2. One of the principal consequences of this fact of Plurality of Causes
is, to render the first of the inductive methods, that of Agreement, uncer-
312 INDUCTION.
tain. To illustrate that method, we supposed two instances, ABC follow-
ed by a 6 c, and A D E followed by ade. From these instances it might
apparently be concluded that A is an invariable antecedent of a, and even
that it is the unconditional invariable antecedent, or cause, if we could be
sure that there is no other antecedent common to the two cases. That this
difficulty may not stand in the way, let us suppose the two cases positive-
ly ascertained to have no antecedent in common except A. The moment,
however, that we let in the possibility of a plurality of causes, the conclu-
sion fails. For it involves a tacit supposition, that a must have been pro-
duced in both instances by the same cause. If there can possibly have
been two causes, those two may, for example, be C and E : the one may
have been the cause of a in the former of the instances, the other in the
latter, A having no influence in either case.
Suppose, for example, that two great artists or great philosophers, that
two extremely selfish or extremely generous characters, were compared
together as to the circumstances of their education and history, and the
two cases were found to agree only in one circumstance : would it follow-
that this one circumstance was the cause of the quality which characterized
both those individuals ? Not at all ; for the causes which may produce
any type of character are very numerous ; and the two persons might
equally have agreed in their character, though there had been no manner
of resemblance in their previous history.
This, therefore, is a characteristic imperfection of the Method of Agree-
ment, from which imperfection the Method of Difference is free. For if
we have two instances, ABC and B C, of which B C gives h c, and A being
added converts it into ab c,\t is certain that in this instance at least, A was
either the cause of a, or an indispensable portion of its cause, even though
the cause which produces it in other instances may be altogether different.
Plurality of Causes, therefore, not only does not diminish the reliance due
to the Method of Difference, but does not even render a greater number
of observations or experiments necessary : two instances, the one positive
and the other negative, are still sufficient for the most complete and rigor-
ous induction. Not so, however, with the Method of Agreement. The
conclusions which that yields, when the number of instances compared is
small, are of no real value, except as, in the character of suggestions, they
may lead either to experiments bringing them to the test of the Method
of Difference, or to reasonings which may explain and verify them de-
ductively.
It is only when the instances, being indefinitely multiplied and varied,
continue to suggest the same result, that this result acquires any high de-
gree of independent value. If there are but two instances, ABC and
ADE, though these instances have no antecedent in common except A, yet
as the effect may possibly have been produced in the two cases by differ-
ent causes, the result is at most only a slight probability in favor of A ;
there may be causation, but it is almost equally probable that there was
only a coincidence. But the oftener we repeat the observation, varying
the circumstances, the more we advance toward a solution of this doubt.
For if we try A F G, A H K, etc., all unlike one another except in contain-
ing the circumstance A, and if we find the effect a entering into the re-
sult in all these cases, we must suppose one of two things, either that it is
caused by A, oi- that it has as many different causes as there are instances.
With each addition, therefore, to the number of instances, the presump-
tion is s<-"5ngthened in favor of A. The inquirer, of course, will not neg-
PLUEALITY OF CAUSES. 313
lect, if an opportunity present itself, to exclude A from some one of these
combinations, from A H K for instance, and by trying H K separately, ap-
peal to the Method of DifEerence in aid of the Method of Agreement. By
the Method of DifEerence alone can it be ascertained that A is the cause
of a; but that it is either the cause, or another effect of the same cause,
may be placed beyond any reasonable doubt by the Method of Agreement,
provided the instances are very numei'ous as well as sufficiently various.
After how great' a multiplication, then, of varied instances, all agreeing
in no other antecedent except A, is the supposition of a plurality of causes
sufficiently rebutted, and the conclusion that a is connected with A divest-
ed of the characteristic imperfection, and reduced to a virtual certainty ?
This is a question which we can not be exempted from answering: but
the consideration of it belongs to what is called the Theory of Probability,
which will form the subject of a chapter hereafter. It is seen, however, at
once, that the conclusion does amount to a practical certainty after a suffi-
cient number of instances, and that the method, therefore, is not radically
vitiated by the characteristic imperfection. The result of these considera-
tions is only, in the first place, to point out a new source of inferiority in
the Method of Agreement as compared with other modes of investigation,
and new reasons for never resting contented with the results obtained by
it, without attempting to confirm them either by the Method of Difference,
or by connecting them deductively with some law or laws already ascer-
tained by that superior method. And, in the second place, we learn from
this the true theory of the value of mere number of instances in inductive
inquiry. The Plurality of Causes is the only reason why mere number is
of any importance. The tendency of unscientific inquirers is to rely too
much on number, without analyzing the instances ; without looking closely
enough into their nature to ascertain what circumstances are or are not
eliminated by means of them. Most people hold their conclusions with a
degree of assurance proportioned to the mere mass of the experience on
which they appear to rest; not considering that by the addition of in-
stances to instances, all of the same kind, that is, differing from one another
only in points ali'eady recognized as immaterial, nothing whatever is add-
ed to the evidence of the conclusion. A single instance eliminating some
antecedent which existed in all the other cases, is of more value than the
greatest multitude of instances which are reckoned by their number alone.
It is necessary, no doubt, to assure ourselves, by repetition of the observa^
tion or experiment, that no error has been committed concerning the indi-
vidual facts observed ; and until we have assured ourselves of this, instead
of varying the circumstances, we can not too scrupulously repeat the same
experiment or observation without any change. But when once this as-
surance has been obtained, the multiplication of instances which do not ex-
clude any more circumstances is entirely useless, provided there have been
already enough to exclude the supposition of Plurality of Causes.
It is of importance to remark, that the peculiar modification of the
Method of Agreement, which, as partaking in some degree of the nature
of the Method of Difference, I have called the Joint Method of Agreement
and Difference, is not affected by the characteristic imperfection now
pointed out. For, in the joint method, it is supposed not only that the in-
stances in which a is, agree only in containing A, but also that the in-
stances in which a is not, agree only in not containing A. Now, if this be
80, A must be not only the cause of a, but the only possible cause : for if
there wei-e another, as for example B, then in the instances in which a is
314 INDUCTION.
not, B must have been absent as well as A, and it wonld not be true that
these instances agree only in not containing A. This, therefore, consti-
tutes an immense advantage of the joint method over the simple Method
of Agreement. It may seem, indeed, that the advantage does not belong
so much to the joint method, as to one of its two premises (if they may be
so called), the negative premise. The Method of Agreement, when applied
to negative instances, or those in which a phenomenon does not take place,
is certainly free from the characteristic imperfection which affects it in the
affirmative case. The negative premise, it might therefore be supposed,
could be worked as a simple case of the Method of Agreement, without re-
quiring an affirmative premise to be joined with it. But though this is.
true in principle, it is generally altogether impossible to work the Method
of Agreement by negative instances without positive ones : it is so much-
more difficult to exhaust the field of negation than that of affirmation.
For instance, let the question be what is the cause of the transparency of
bodies; with what prospect of success could we set ourselves to inquire
directly in what the multifarious substances which are not transparent
agree? But we might hope much sooner to seize some point of resem-
blance among the comparatively few and definite species of objects whiclv
are transparent ; and this being attained, we should quite naturally be put
upon examining whether the absence of this one circumstance be not pre-
cisely the point in which all opaque substances will be found to resemble.
The Joint Method of Agreement and Difference, therefore, or as I have,
otherwise called it, the Indirect Method of Difference (because, like the
Method of Difference properly so-called, it proceeds by ascertaining how and
n what the cases where the phenomenon is present differ from those in which
t is absent) is, after the Direct Method of Difference, the most powerful
)f the remaining instruments of inductive investigation ; and in the sciences-
which depend on pure observation, with little or no aid from experiment^
this method, so well exemplified in the speculation on the cause of dew, is.
the primary resource, so far as direct appeals to experience are concerned.
§ 3. We have thus far treated Plurality of Causes only as a possible sup-
position, which, until removed, renders our inductions uncertain ; and have
Dnly considered by what means, where the plurality does not really exist,,
sve may be enabled to disprove it. But we must also consider it as a case
ictnally occurring in nature, and which, as often as it does occur, our
methods of induction ought to be capable of ascertaining and establishing-
For this, however, there is required no peculiar method. When an effect
s really producible by two or more causes, the process for detecting them
.8 in no way different from that by which we discover single causes. They
nay (first) be discovered as separate sequences, by separate sets of in-
stances. One set of observations or experiments shows that the sun is a
5ause of heat, another that friction is a source of it, another that percus-
sion, another that electricity, another that chemical action is such a source.
3r (secondly) the plurality may come to light in the course of collating a
mmber of instances, when we attempt to find some circumstance in which,
.hey all agree, and fail in doing so. We find it impossible to trace, in all
.he cases in which the effect is met with, any common circumstance. We
ind that we can eliminate all the antecedents; that no one of them is
)resent in all the instances, no one of them indispensable to the effect.
)n closer scrutiny, however, it appears that though no one is always pres-
int. one or other of several always is. If, on further analysis, we can de-
" INTERMIXTURE OF EFFECTS. 315
tect in these any common element, we may be able to ascend from them
to some one cause which is the really operative circumstance in them all.
Thus it is now thought that in the production of heat by friction, percus-
sion, chemical action, etc., the ultimate source is one and the same. But if
(as continually happens) we can not take this ulterior step, the different
antecedents must be set down provisionally as distinct causes, each suffi-
cient of itself to produce the effect.
We here close our remarks on the Plurality of Causes, and proceed to
the still more peculiar and more complex case of the Intermixture of Ef-
fects, and the interference of causes with one another : a case constituting
the principal part of the complication' and difficulty of the study of nature ;
and with which the four only possible methods of directly inductive inves-
tigation by observation and experiment, are, for the most part, as will ap-
pear presently, quite unequal to cope. The instrument of Deduction alone
is adequate to unravel the complexities proceeding from this source ; and
the four methods have little more in their power than to supply premises
for, and a verification of, our deductions.
§ 4. A concurrence of two or more causes, not separately producing each
its own effect, but interfering with or modifying the effects of one anoth-
er, takes place, as has already been explained in two different ways. In
the one, which is exemplified by the joint operation of different forces in
mechanics, the separate effects of all the causes continue to be produced,
but are compounded with one another, and disappear in one total. In the
other, illustrated by the case- of chemical action, the separate effects cease
entirely, and are succeeded by phenomena altogether different, and govern-
ed by different laws.
Of these cases the former is by far the more frequent, and this case it is
■which, for the most part, eludes the grasp of our experimental methods.
The other and exceptional case is essentially amenable to them. When the
laws of the original agents cease entirely, and a phenomenon makes its
appearance, which, with reference to those laws, is quite heterogeneous ;
when, for example, two gaseous substances, hydrogen and oxygen, on be-
ing brought together, throw off their peculiar properties, and produce the
substance called water; in such cases the new fact may be subjected to
experimental inquiry, like any other phenomenon ; and the elements which
are said to compose it may be considered as the mere agents of its pro-
duction— the conditions on which it depends, the facts which make up its
cause.
The effects of the new phenomenon, the properties of water, for instance,
are as easily found by experiment as the effects of any other cause. But
to discover the cause of it, that is, the particular conjunction of agents
from which it results, is often difficult enough. In the first place, the ori-
gin and actual production of the phenomenon are most frequently inacces-
sible to our observation. If we could not have learned the composition of
water until we found instances in which it was actually produced from
oxygen and hydrogen, we should have been forced to wait until the casual
thought struck some one of passing an electric spark through a mixture
of the two gases, or inserting a lighted taper into it, merely to try what
would happen. Besides, many substances, though they can be analyzed,
can not by any known artificial means be recompounded. Further, even
if we could have ascertained, by the Method of Agreement, that oxygen
and hydrogen were both present when water is produced, no experimenta'
316 INDUCTION.
tion on oxygen and hydrogen separately, no knowledge of their laws, could
have enabled us deductively to infer that they would produce water. We
require a specific experiment on the two combined.
tinder these difficulties, we should generally have been indebted for our
knowledge of the causes of this class of effects, not to any inquiry direct-
ed specifically toward that end, but either to accident, or to the gradual
progress of experimentation on the different combinations of which the
producing agents are susceptible; if it were not for a peculiarity belonging
to effects of this description, that they often, under some particular com-
bination of circumstances, reproduce their causes. If water results from
the juxtaposition of hydrogen and oxygen whenever this can be made suf-
ficiently close and intimate, so, on the other hand, if water itself be placed
in certain situations, hydrogen and oxygen are reproduced from it: an
abrupt termination is put to the new laws, and the agents re-appear sepa-
rately with their own properties as at first. What is called chemical anal-
ysis is the process of searching for the causes of a phenomenon among its
effects, or rather among the effects produced by the action of some other
causes upon it.
Lavoisier, by heating mercury to a high temperature in a close vessel
containing air, found that the mercury increased in weight, and became
what was then called red precipitate, while the air, on being examined
after the experiment, proved to have lost weight, and to have become in-
capable of supporting life or combustion. When red precipitate was ex-
posed to a still greater heat, it became mercury again, and gave off a gas
which did support life and flame. Thus the agents which by their com-
bination produced red precipitate, namely, the mercury and the gas, re-
appear as effects resulting from that precipitate when acted upon by heat.
So, if we decompose water by means of iron filings, we produce two effects,
rust and hydrogen. Now rust is already known, by experiments upon the
component substances, to be an effect of the union of iron and oxygen :
the iron we ourselves supplied, but the oxygen must have been produced
From the water. The result, therefore, is that water has disappeared, and
bydrogen and oxygen have appeared in its stead ; or, in other words, the
sriginal laws of these gaseous agents, which had been suspended by the
iuperinduction of the new laws called the properties of water, have again
started into existence, and the causes of water are found among its effects.
Where two phenomena, between the laws or properties of which, con-
sidered in themselves, no connection can be traced, are thus reciprocally
sause and effect, each capable in its turn of being produced from the oth-
3r, and each, when it produces the other, ceasing itself to exist (as water
.8 produced from oxygen and hydrogen, and oxygen and hydrogen are re-
sroduced from water) ; this causation of the two phenomena by one an-
>ther, each being generated by the other's destruction, is properly trans-
rormation. The idea of chemical composition is an idea of transformation,
3ut of a ti-ansformation which is incomplete; since we consider the oxy-
gen and hydrogen to be present in the water as oxygen and hydrogen, and
sapable of being discovered in it if our senses were sufficiently keen: a
opposition (for it is no more) grounded solely on the fact that the weight
)f the water is the sum of the separate weights of the two ingredients. If
-here had not been this exception to the entire disappearance, in the com-
Dound, of the laws of the separate ingredients ; if the combined agents had
lot, in this one particular of weight, preserved their own laws, and produced
I joint result equal to the sum of their separate results ; we should never,
INTEEMIXTURE OF EFFECTS. 317
probably, have had the notion now implied by the words chemical compo-
sition ; and, in the facts of water produced from hydrogen and oxygen,
and hydrogen and oxygen produced from water, as the transformation
would have been complete, we should have seen only a transformation.
In these cases, where the heteropathic effect (as we called it in a former
chapter)* is but a transformation of its cause, or in other words, where
the effect and its cause are reciprocally such, and mutually convertible into
each other; the problem of finding the cause resolves itself into the far
easier one of finding an effect, which is the kind of inquiry that admits of
being prosecuted by direct experiment. But there are other cases of
heteropathic effects to which this mode of investigation is not applicable.
Take, for instance, the heteropathic laws of mind ; that portion of the phe-
nomena of our mental nature which are analogous to chemical rather than
to dynamical phenomena ; as when a complex passion is formed by the co-
alition of several elementary impulses, or a complex emotion by several
simple pleasures or pains, of which it is the result without being the ag-
gregate, or in any respect homogeneous with them. The product, in these
cases, is generated by its various factors ; but the factors can not be re-
produced from the product ; just as a youth can grow into an old man,
but an old man can not grow into a youth. We can not ascertain from
what simple feelings any of our complex states of mind are generated, as
we ascertain the ingredients of a chemical compound, by making it, in its
turn, generate them. We can only, therefore, discover these laws by the
slow process of studying the simple feelings themselves, and ascertaining
synthetically, by experimenting on the various combina,tions of which they
are susceptible, what they, by their mutual action upon one another, are
capable of generating.
§ 5. It might have been supposed that the other, and apparently simpler
variety of the mutual interference of causes, where each cause continues
to produce its own proper effect according to the same laws to which it
conforms in its separate state, would have. presented fewer difficulties to
the inductive inquirer than that of which we have just finished the consid-
eration. It presents, however, so far as direct induction apart from de-
duction is concerned, infinitely greater difficulties. When a concurrence
of causes gives rise to a new effect, bearing no relation to the separate
effects of those causes, the resulting phenomenon stands forth undisguised,
inviting attention to its peculiarity, and presenting no obstacle to our rec-
ognizing its presence or absence among any number of surrounding phe-
nomena. It admits, therefore, of being easily brought under the canons of
Induction, provided instances can be obtained such as those canons require ;
and the non-occurrence of such instances, or the want of means to pro-
duce them artificially, is the real and only difficulty in such investigations;
a difficulty not logical but in some sort.physical. It is otherwise with cases
of what, in a preceding chapter, has been denominated the Composition of
Causes. There, the effects of the separate causes do not terminate and give
place to others, thereby ceasing to form any part of the phenomenon to be
investigated ; on the contrary, they still take place, but are intermingled
with, and disguised by, the homogeneous and closely allied effects of other
causes. They are no longer a, b, c, d, e, existing side by side, and continu-
ing to be separately discernible ; they are -fa, —a, -J 6, —6, 2 5, etc ; some of
* Ante, chap. tU., § 1.
318 INDUCTION.
which cancel one another, while many others do not appear distingnisha-
bly, but merge in one sum ; forming altogether a result, between which
and the causes whereby it was produced there is often an insurmountable
difficulty in tracing by observation any fixed relation whatever.
The general idea of the Composition of Causes has been seen to be, that
though two or more laws interfere with one another, and apparently frus-
trate or modify one another's operation, yet in reality all are fulfilled, the
collective effect being the exact sum of the effects of the causes taken sepa-
rately. A familiar instance is that of a body kept in equilibrium by two
equal and contrary forces. One of the foi'ces if acting alone would carry
the body in a given time a certain distance to the west, the other if acting
alone would carry it exactly as far toward the east; and the result is the
same as if it had been first carried to the west as far as the one force would
carry it, and then back towai'd the east as far as the other would carry
it — that is, precisely the same distance ; being ultimately left where it was
found at first.
All laws of causation are liable to be in this manner counteracted, and
seemingly frustrated, by coming into conflict with other laws, the separate
result of which is opposite to theirs, or more or less inconsistent with it.
And hence, with almost every law, many instances in which it really is
entirely fulfilled, do not, at first sight, appear to be cases of its operation
at all. It is so in the example just adduced : a force in mechanics means
neither more nor less than a cause of motion, yet the sum of the effects of
two causes of motion may be rest. Again, a body solicited by two forces
in directions making an angle with one another, moves in the diagonal;
and it seems a paradox to say that motion in the diagonal is the sum of two
motions in two other lines. Motion, however, is but change of place, and
at every instant the body is in the exact place it would have been in if the
forces had acted during alternate instants instead of acting in the same
instant (saving that if we suppose two forces to act successively which are
in truth simultaneous we must of course allow them double the time). It
is evident, therefore, that each force has had, during each instant, all the
effect which belonged to it; and that the modifying influence which one
of two concurrent causes is said to exercise with respect to the other may
be considered as exerted not over the action of the cause itself, but over
the effect after it is completed. For all purposes of predicting, calcula-
ting, or explaining their joint result, causes which compound their effects
may be treated as if they produced simultaneously each of them its own
effect, and all these effects co-existed visibly.
Since the laws of causes are as really fulfilled when the causes are said
to be counteracted by opposing causes, as when they are left to their own
undisturbed action, we must be cautious not to express the laws in such
terms as would render the assertion of their being fulfilled in those cases a
contradiction. If, for instance, it were stated as a law of nature that a
body to which a force is applied moves in the direction of the force, with a
velocity proportioned to the force directly, and to its own mass inversely;
when in point of fact some bodies to which a force is applied do not move
at all, and those which do move (at least in the region of our earth) are,
from the very first, retarded by the action of gravity and other resisting
forces, and at last stopped altogether ; it is clear that the general proposi-
tion, though it would be true under a certain hypothesis, would not ex-
press the facts as they actually occur. To accommodate the expression of
the law to the real phenomena, we must say, not that the object moves, but
INTERMIXTURE OF EFFECTS. 319
that it tetids to move, in the direction and with the velocity specified.
We miglit, indeed, guard our expression in a different mode, by saying
that the body moves in that manner unless prevented, or except in so far
•as prevented, by some counteracting cause. But the body does not only
move in that manner unless counteracted ; it tends to move in that manner
even when counteracted ; it still exerts, in the original direction, the same
■energy of movement as if its first impulse had been undisturbed, and pro-
duces, by that energy, an exactly equivalent quantity of effect. This is
true even when the force leaves the body as it found it, in a state of abso-
lute rest ; as when we attempt to raise a body of three tons' weight with
a force equal to one ton. For if, while we are applying this force, wind or
water or any other agent supplies an additional force just exceeding two
tons, the body will be raised ; thus proving that the force we applied ex-
erted its full effect, by neutralizing an equivalent portion of the weight
which it was insufficient altogether to overcome. And if, while we are
exerting this force of one ton upon the object in a direction contrary to
that of gravity, it be put into a scale and weighed, it will be found to have
lost a ton of its weight, or, in other words, to press downward with a force
•only equal to the difference of the two forces.
These facts are correctly indicated by the expression tendency. All laws
■of causation, in consequence of their liability to be counteracted, require to
be stated in words affirmative of tendencies only, and not of actual results.
In those sciences of causation which have an accurate nomenclature, there
■are special words which signify a tendency to the particular effect with
which the science is conversant ; thus pressure, in mechanics, is synony-
mous with tendency to motion, and forces are not reasoned on as causing
actual motion, but as exerting pressure. A similar improvement in termi-
nology would be very salutary in many other branches of science.
The habit of neglecting this necessary element in the precise expression
of the laws of nature, has given birth to the popular prejudice that all gen-
eral truths have exceptions ; and much unmerited distrust has thence ac-
crued to the conclusions of science, when they have been submitted to the
judgment of minds insufficiently disciplined and cultivated. The rough
generalizations suggested by common observation usually have exceptions ;
but principles of science, or, in other words, laws of causation, have not.
■"What is thought to be an exception to a principle" (to quote words used
on a different occasion), " is always some other and distinct principle cut-
ting into the former ; some other force which impinges* against the first
■force, and deflects it from its direction. There are not a law and an excep-
tion ■to that law, the law acting in ninety-nine cases, and the exception in
■one. There are two laws, each possibly acting in the whole hundred cases,
and bringing about a common effect by their conjunct operation. If the
force which, being the less conspicuous of the two, is called the disturbing
force, prevails sufficiently over the other force in some one case, to consti-
tute that case what is commonly called an exception, the same disturbing
force probably acts as a modifying cause in many other cases which no one
will call exceptions.
"Thus if it were stated to be a law of nature that all heavy bodies fall
to the ground, it would probably be said that the resistance of the atmos-
phere, which prevents a balloon from falling, constitutes the balloon an ex-
* It seems hardly necessary to say that the word impinae. as a general term to express col-
lision of forces, is here used by a figure of speech, and not as expressive of any theory respect-
ing the nature of foi'ce.
320 INDUCTION.
ception to that pretended law of nature. But the real law is, that all heavy
bodies tend to fall ; and to this there is no exception, not even the sun and
moon ; for even they, as every astronomer knows, tend toward the earth,
with a force exactly equal to that with which the earth tends toward them.
The resistance of the atmosphere might, in the particular case of the bal-
loon, from a misapprehension of what the law of gravitation is, be said to
prevail over the law ; but its disturbing effect is quite as real in every
other case, since though it does not prevent, it retards the fall of all bodies
whatever. The rule, and the so-called exception, do not divide the cases
between them ; each of them is a comprehensive rule extending to all cases.
To call one of these concurrent principles an exception to the other, is su-
perficial, and contrary to the correct principles of nomenclature and ar-
rangement. An effect of precisely the same kind, and arising from the
same cause, ought not to be placed in two different categories, merely as
there does or does not exist another cause preponderating over it."*
§ 6. We have now to consider according to what method these complex
effects, compounded of the effects of many causes, are to be studied ; how
we are enabled to trace each effect to the concurrence of causes in which
it originated, and ascertain the conditions of its recurrence — the circum-
stances in which it may be expected again to occur. The conditions of a
phenomenon which arises from a composition of causes, may be investi-
gated either deductively or experimentally.
The case, it is evident, is naturally susceptible of the deductive mode of
investigation. The law of an effect of this description is a result of the
laws of the separate causes on the combination of which it depends, and is,
therefore, in itself capable of being deduced from these laws. This is call-
ed the method a priori. The other, or a posteriori method, professes to
proceed according to the canons of experimental inquiry. Considering
the whole assemblage of concurrent causes which produced the phenome-
non, as one single cause, it attempts to ascertain the cause in the ordinary
manner, by a comparison of instances. This second method subdivides
itself into two different varieties. If it merely collates instances of the
effect, it is a method of pure observation. If it operates upon the causes,
and tries different combinations of them, in hopes of ultimately hitting the
precise combination which will produce the given total effect, it is a method
of experiment.
In order more completely to clear up the nature of each of these three
methods, and determine which of them deserves the preference, it will be
expedient (conformably to a favorite maxim of Lord Chancellor Eldon, to
which, though it has often incurred philosophical ridicule, a deeper phi-
losophy will not refuse its sanction) to "clothe them in circumstances."
"We shall select for this purpose a case which as yet furnishes no very brill-
iant example of the success of any of the three methods, but which is all
the more suited to illustrate the difficulties inherent in them. Let the sub-
ject of inquiry be, the conditions of health and disease in the human body;
or (for greater simplicity) the conditions of recovery from a given disease ;
and in order to narrow the question still more, let it be limited, in the first
instance, to this one inquiry: Is, or is not, some particular medicament
(mercury, for instance) a remedy for the given disease.
Now, the deductive method would set out from known properties of
* Essays on some Unsettled Questions of Political Economy, Essay V.
INTERMIXTURE OF EFFECTS. 321
mercury, and known laws of the human body, and by reasoning from these,
would attempt to discover whether mercury will act upon the body when
in the morbid condition supposed, in such a manner as would tend to re-
store health. The experimental method would simply administer mercury
in as many cases as possible, noting the age, sex, temperament, and other
peculiarities of bodily constitution, the particular form or variety of the
disease, the particular stage of its progress, etc., remarking in which of
these cases it was attended with a salutary effect, and with what circum-
stances it was on those occasions combined. The method of simple obser-
vation would compare instances of recovery, to find whether they agreed
in having been preceded by the administration of mercury ; or would com-
pare instances of recovery with instances of failure, to find cases which,
agreeing in all other respects, differed only in the fact that mercury had
been administered, or that it had not.
§ 7. That the last of these three modes of investigation is applicable to
the case, no one has ever seriously contended. No conclusions of value on
a subject of such intricacy ever were obtained in that way. The utmost
that could result would be a vague general impression for or against the
eflScacy of mercury, of no avail for guidance unless confirmed by one of the
other two methods. Not that the results, which this method strives to ob-
tain, would not be of the utmost possible value if they could be obtained.
If all the cases of recovery which presented themselves, in an examination
extending to a great number of instances, were cases in which mercury had
been administered, we might generalize with confidence from this expe-
rience, and should have obtained a conclusion of real value. But no such
basis for generalization can we, in a case of this description, hope to obtain.
The reason is that which we have spoken of as constituting the character-
istic imperfection of the Method of Agreement, Plurality of Causes. Sup-
posing even that mercury does tend to cure the disease, so many other
causes, both natural and artificial, also tend to cure it, that there are sure
to be abundant instances of recovery in which mercury has not been ad-
ministered, unless, indeed, the practice be to administer it in all cases ; on.
which supposition it will equally be found in the cases of failure.
When an effect results from the union of many causes, the share which
each has in the determination of the effect can not in general be great,
and the effect is not likely, even in its presence or absence, still less in its
variations, to follow, even approximately, any one. of the causes. Recov-
ery from a disease is an event to which, in every case, many influences
must concur. Mercury may be one such influence ; but from the very fact
that there are many other such, it will necessarily happen that although
mercury is administered, the patient, for want of other concurring influ-
ences, will often not recover, and that he often will recover when it is
not administered, the other favorable influences being suflSciently powerful
without it. Neither, therefore, will the instances of recovery agree in the
administration of mercury, nor will the instances of failure agree in its
non - administration. It is much if, by multiplied and accurate returns
from hospitals and the like, we can collect that there are rather more re-
coveries and rather fewer failures when mercury is administered than when
it is not ; a result of very secondary value even as a guide to practice, and
almost worthless as a contribution to the theory of the subject.*
* It is justly remarked by Professor Bain, that though the Methods of Agreement and Dif-
ference are not applicable to these cases, they are not wholly inaccessible' to the Method of
21
322 INDUCTION.
§ 8. The inapplicability of the method of simple observation to ascertain
the conditions of effects dependent on many concurring causes, being thus
recognized, we shall next inquire whether any greater benefit can be ex-
pected from the other branch of the a posteriori method, that which pro-
ceeds by directly trying different combinations of causes, either artificially
produced or found in nature, and taking notice what is their effect; as, for
example, by actually trying the effect of mercury in as many different cir-
cumstances as possible. This method differs from the one which we have
just examined in turning our attention directly to the causes or agents,
instead of turning it to the effect, recovery from the disease. And since,
as a general rule, the effects of causes are far more accessible to our study
than the causes of effects, it is natural to think that this method has a
much better chance of proving successful than the former.
The method now under consideration is called the Empirical Method ;
and in order to estimate it fairly, we must suppose it to be completely, not
incompletely, empirical. We must exclude from it every thing which par-
takes of the nature not of an experimental but of a deductive operation.
If, for instance, we try experiments with mercury upon a person in health,
in order to ascertain the general laws of its action upon the human body,
and then reason from these laws to determine how it will act upon persons
affected with a particular disease, this may be a really effectual method ;
but this is deduction. The experimental method does not derive the law
of a complex case from the simpler laws which conspire to produce it, but
makes its experiments directly upon the complex case. We must make
entire abstraction of all knowledge of the simpler tendencies, the modi
operandi of mercury in detail. Our experimentation must aim at obtain-
ing a direct answer to the specific question. Does or does not mercury tend
to cure the particular disease ?
Let us see, therefore, how far the case admits of the observance of those
rules of experimentation which it is found necessary to observe in other
cases. When we devise an experiment to ascertain the effect of a given
agent, there are certain precautions which we never, if we can help it, omit.
In the first place, we introduce the agent into the midst of a set of circum-
stances which we have exactly ascertained. It needs hardly be remarked
how far this condition is from being realized in any case connected with
the phenomena of life ; how far we are from knowing what are all the cir-
cumstances which pre-exist in any instance in which mercury is adminis-
tered to a living being. This difficulty, however, though insuperable in
Concomitant Variations. " If a cause happens to vary alone, the eflFeot will also vary alone :
% cause and effect may be thus singled out under the greatest complications. Thus, when the
appetite for food increases with the cold, we have a strong evidence of connection between
these two facts, although other circumstances may operate in the same direction. The as-
signing of the respective parts of the sun and moon in the action of the tides may be effected,
to a certain degree of exactness, by the variations of the amount according to the positions
if the two attractive bodies. By a series of experiments of Concomitant Variations, directed
to ascertain the elimination of nitrogen from the human body under varieties of muscular ex-
jrcise. Dr. Parkes obtained the remarkable conclusion, that a muscle grows during exercise,
ind loses bulk during the subsequent rest." {Logic, ii., 83.)
It is, no doubt, often possible to single out the influencing causes from among a great num-
ber of mere concomitants, by noting what are the antecedents, a variation in which is followed
ay a variation in the effect. But when there are many influencing causes, no one of then,
greatly predominating over the >rest, and especially when some of these are continually ohan-
^ng, it is scarcely ever possible to trace such a relation between the variations of the effect
md those of any one cause as would enable us to assign to that cause its real share in the
3roduction of the effect.
INTERMIXTURE OF EFFECTS. 323
anost cases, may not be so in all ; there are sometimes concurrences of
jnany causes, in which we yet know accurately what the causes are. More-
over, the difficulty may be attenuated by sufficient multiplication of experi-
ments, in circumstances rendering it improbable that any of the unknown
■causes should exist in them all. But when we have got clear of this ob-
iStacle, we encounter another still more serious. In other cases, when we
intend to try an experiment, we do not reckon it enough that there be no
circumstance in the case the presence of which is unknown to us. We re-
quire, also, that none of the circumstances which we do know shall have
■effects susceptible of being confounded with those of the agents whose
properties we wish to study. We take the utmost pains to exclude all
causes capable of composition with the given cause ; or, if forced to let in
.any such causes, we take care to make them such that we can compute
and allow for their influence, so that the effect of the given cause may, af-
ter the subduotion of those other effects, be apparent as a residual phe-
nomenon.
These precautions are inapplicable to such cases as we are now consid-
•ering. The mercury of our experiment being tried with an unknown mul-
titude (or even let it be a known multitude) of other influencing circum-
stances, the mere fact of their being influencing circumstances implies that
they disguise the effect of the mercury, and preclude us from knowing
whether it has any effect or not. Unless we already knew what and how
much is owing to every other circumstance (that is, unless we suppose the
very problem solved which we are considering the means of solving), we
«an not tell that those other circumstances may not have produced the
■whole of the effect, independently or even in spite of the mercury. The
Method of Dift'ei'ence, in the ordinary mode of its use, namely, by com-
paring the state of things following the experiment with the state which
preceded it, is thus, in the case of intermixture of effects, entirely unavail-
ing ; because other causes than that whose effect we are seeking to deter-
mine have been operating during the transition. As for the other mode
of employing the Method of Difference, namely, by comparing, not the
same case at two different periods, but different cases, this in the present
instance is quite chimerical. In phenomena so complicated it is question-
able if two cases, similar in all respects but one, ever occurred ; and were
^ they to occur, we could not possibly know that they were so exactly
similar.
Any thing like a scientific use of the method of experiment, in these com-
plicated cases, is therefore out of the question. We can generally, even in
the most favorable cases, only discover by a succession of trials, that a cer-
tain cause is very often followed by a certain effect. For, in one of these
conjunct effects, the portion which is determined by any one of the in-
fluencing agents, is usually, as we before renjarked, but small ; and it must
be a more potent cause than most, if even the tendency which it really ex-
erts is not thwarted by other tendencies in nearly as many cases as it is ful-
filled. Some causes indeed there are which are more potent than any
counteracting causes to which they are commonly exposed ; and according-
ly there are some truths in medicine which are sufficiently proved by direct
experiment. Of these the most familiar are those that relate to the efficacy
of the substances known as Specifics for particular diseases, " quinine,
colchicum, lime-juice, cod-liver oil,"* and a few others. Even these are
* Bain's Logic, ii., 360.
324 INDUCTION.
not invariably followed by success ; but they succeed in so large a propor-
tion of cases, and against such powerful obstacles, that their tendency to
restore health in the disorders for which they are prescribed may be re-
garded as an experimental truth.*
If so little can be done by the experimental method to determine the
conditions of an effect of many combined causes, in the case of medical
science ; still less is this method applicable to a class of phenomena more
complicated than even those of physiology, the phenomena of politics and
history. There, Plurality of Causes exists in almost boundless excess, and
effects are, for the most part, inextricably interwoven with one another. To
add to the embarrassment, most of the inquiries in political science relate
to the production of effects of a most comprehensive description, such as
the public wealth, public security, public morality, and the like : results
liable to be affected directly or indirectly either in plus or in minus by
nearly every fact which exists, or event which occurs, in human society.
The vulgar notion, that the safe methods on political subjects are those of
Baconian induction — that the true guide is not general reasoning, but spe-
cific experience — will one day be quoted as among the most unequivocal
marks of a low state of the speculative faculties in any age in which it is
accredited. Nothing can be more ludicrous than the sort of parodies on
experimental reasoning which one is accustomed to meet with, not in pop*
ular discussion only, but in grave treatises, when the affairs of nations
are the theme. " How," it is asked, " can an institution be bad, when the
country has prospered under it?" "How can such or such causes have
contributed to the prosperity of one country, when another has prospered
without them ?" Whoever makes use of an argument of this kind, not in-
tending to deceive, should be sent back to learn the elements of some one
of the more easy physical- sciences. Such reasoners ignore the fact of
Plurality of Causes in the very case which affords the most signal example
of it. So little could be concluded, in such a case, from any possible colla-
tion of individual instances, that even the impossibility, in social phenomena,
of making artificial experiments, a circumstance otherwise so prej udioial to
directly inductive inquiry, hai-dly affords, in this case, additional reason of
regret. For even if we could try experiments upon a nation or upon the
human race, with as little scruple as M. Magendie tried them on dogs and
rabbits, we should never succeed in making two instances identical in every
respect except the presence or absence of some one definite circumstance.
The nearest approach to an experiment in the philosophical sense, which
takes place in politics, is the introduction of a new operative element into
national affairs l)y some special and assignable measure of government,
such as the enactment or repeal of a particular law. But where there are
so many influences at work, it requires some time for the influence of any
new cause upon national phenomena to become apparent; and as the causes
operating in so extensive a sphere are not only infinitely numerous, but in
a state of perpetual alteration, it is always certain that before the effect of
* What is said in the text on the applicability of the experimental methods to resolve par-
ticular questions of medical treatment, does not detract from their efficacy in ascertaining the
general laws of the animal or human system. The functions, for example, of the different
classes of nerves have been discovered, and probably could only have been discovered, by ex-
periments on living animals. Observation and experiment are the ultimate basis of all knowl-
edge : from them we obtain the elementary laws of life, as we obtain all other elementary truths.
It is in dealing with the complex combinations that the experimental methods are for the most,
part illusory, and the deductive mode of investigation must be invoked to disentangle the com-
plexity.
THE DEDUCTIVE METHOD. 325
the new cause becomes conspicuous enough to be a subject of induction, so
many of the other influencing circumstances will have changed as to vitiate
the experiment.*
Two, therefore, of the three possible methods for the study of phenomena
resulting from the composition of many causes, being, from the very nature
of the case, inefficient and illusory, there remains only the third — that which
considers the causes separately, and infers the effect from the balance of
the different tendencies which produce it : in short, the deductive, or a pri-
ori method. The more particular consideration of this intellectual process
requires a chapter to itself.
CHAPTER XI,
OF THE DEDUCTIVE METHOD.
§ 1. The mode of investigation which, from the proved inapplicability
of direct methods of observation and experiment, remains to us as the
main source of the knowledge we possess or can acquire respecting the
conditions and laws of recurrence, of the more complex phenomena, is
called, in its most general expression, the Deductive Method ; and consists
of three operations : the first, one of direct induction ; the second, of ra-
tiocination ; the third, of verification.
I call the first step in the process an inductive operation, because there
must be a direct induction as the basis of the whole ; though in many par-
ticular investigations the place of the induction may be supplied by a prior
deduction ; but the premises of this prior deduction must have been de-
rived from induction.
The problem of the Deductive Method is, to find the law of an effect,
from the laws of the different tendencies of which it is the joint result.
The first requisite, therefore, is to know the laws of those tendencies ; the
law of each of the concurrent causes : and this supposes a previous proc-
ess of observation or experiment upon each cause separately ; or else a pre-
vious deduction, which also must depend for its ultimate premises on ob-
servation or experiment. Thus, if the subject be social or historical phe-
nomena, the premises of the Deductive Method must be the laws of the
■causes which determine that class of phenomena ; and those causes are hu-
man actions, together with the general outward circumstances under the
* Professor Bain, though concurring generally in the views expressed in this chapter, seems
to estimate more highly than I do the scope for specific experimental evidence in politics.
{Logic, ii., 333-337.) There are, it is true, as he remarks (p. 336), some cases "when an
agent suddenly introduced is almost instantaneously followed by some other changes, as when
the announcement of a diplomatic rupture between two nations is followed the same day by a
derangement of the money-market." But this experiment would be quite inconclusive merely
as an experiment. It can only seiTe, as any experiment may, to verify the conclusion of a
deduction. Unless we already knew by our knowledge of the motives which act on business
men, that the prospect of war tends to derange the money-market,' we should never have been
able to prove a connection between the two facts, unless after having ascertained historically
that the one followed the other in too great a number of instances to be consistent with their
having been recorded with due precautions. Whoever has carefully examined any of the at-
tempts continually made to prove economic doctrines by such a recital of instances, knows
well how futile they are. It always turns out that the circumstances of scarcely any of the
cases have been fully stated ; and that cases, in equal or greater numbers, have been omitted
which would have tended to an opposite conclusion.
326 INDUCTION.
influence of which mankind are placed, and which constitute man's posi-
tion on the earth. The Deductive Method, applied to social phenomena,
must begin, therefore, by investigating, or must suppose to have been al-
ready investigated, the laws of human action, and those properties of out-
ward things by which the actions of human beings in society are deter-
mined. Some of these general truths will naturally be obtained by obser-
vation and experiment, others by deduction : the moi"e complex laws of
human action, for example, may be deduced from the simpler ones; but
the simple or elementary laws will always, and necessarily, have been ob-
tained by a directly inductive process.
To ascertain, then, the laws of each separate cause' which takes a share-
in producing the effect, is the first desideratum of the Deductive Method.
To know what the causes are which must be subjected to this process of
study, may or may not be difficult. In the case last mentioned, this first
condition is of easy fulfillment. That social phenomena depend on the acts-
and mental impressions of human beings, never could have been a matter
of any doubt, however imperfectly it may have been known either by what
laws those impressions and actions are governed, or to what social conse-
quences their laws naturally lead. Neither, again, after physical science
had attained a certain development, could there be any real doubt where to
look for the laws on which the phenomena of life depend, since they must
be the mechanical and chemical laws of the solid and fluid substances com-
posing the organized body and the medium in which it subsists, together
with the peculiar vital laws of the different tissues constituting the organic
structure. In other cases, really far more simple than these, it was much
less obvious in what quarter the causes were to be looked for: as in the
case of the celestial phenomena. Until, by combining the laws of certain
causes, it was found that those laws explained all the facts which experi-
ence had proved concerning the heavenly motions, and led to predictions
which it always verified, mankind never knew that those were the causes.
But whether we are able to put the question before, or not until after, we
have become capable of answering it, in either case it must be answered j
the laws of the different causes must be ascertained, before we can proceed
to deduce from them the conditions of the effect.
The mode of ascertaining those laws neither is, nor can be any other
than the fourfold method of experimental inquiry, already discussed. A
few remai-ks on the application of that method to cases of the Composition
of Causes are all that is requisite.
It is obvious that we can not expect to find the law of a tendency by
an induction from cases in which the tendency is counteracted. The laws
of motion could never have been brought to light from the observation of
bodies kept at rest by the equilibrium of opposing forces. Even where the
tendency is not, in the ordinary sense of the word, counteracted, but only
modified, by having its effects compounded with the effects arising from
some other tendency or tendencies, we are still in an unfavorable position
for tracing, by means of such cases, the law of the tendency itself. It
would have been scarcely possible to discover the law that every body in
motion tends to continue moving in a straight line, by an induction from
instances in which the motion is deflected into a curve, by being corapound-
sd with the effect of an accelerating force. Notwithstanding the resources
afforded in this description of cases by the Method of Concomitant Varia-
tions, the principles of a judicious experimentation prescribe that the law
jf each of the tendencies should be studied, if possible, in cases in which
THE DEDUCTIVE METHOD. 327
that tendency operates alone, or in combination with no agencies but those-
of which the effect can, from previous knowledge, be calculated and allow-
ed for.
Accordingly, in the cases, unfortunately very numerous and important,,
in which the causes do not suffer themselves to be separated and observed
apart, there is much difficulty in laying down with due certainty the induc-
tive foundation necessary to support the deductive method. This difficulty"
is most of all conspicuous in the case of physiological phenomena ; it being
seldom possible to separate the different agencies which collectively com-
pose an organized body, without destroying the very phenomena which it
is our object to investigate :
following life, in creatures we dissect,
We lose it, in the moment we detect.
And for this reason I am inclined to the opinion that physiology (greatly
and rapidly progressive as it now is) is embarrassed by greater natural dif-
ficulties, and is probably susceptible of a less degree of ultimate perfec- ,
tion, than even the social science ; inasmuch as it is possible to study the
laws and operations of one human mind apart from other minds, much les*
imperfectly than we can study the laws of one organ or tissue of the hu-
man body apart from the other organs or tissues.
It has been judiciously remarked that pathological facts, or, to speak in-
common language, diseases in their different forms and degrees afford in
the case of physiological investigation the most valuable equivalent to ex-
perimentation properly so called ; inasmuch as they often exhibit to us a
definite disturbance in some one organ or organic function, the remaining
organs and functions being, in the first instance at least, unaffected. It is-
true that from the perpetual actions and reactions which are going on
among all parts of the organic economy, there can be no prolonged disturb-
ance in any one function without ultimately involving many of tjie othei'S ;
and when once it has done so, the experiment for the most part loses its
scientific value. All depends on observing the early stages of the derange-
ment ; which, unfortunately, are of necessity the least marked. If, how-
ever, the organs and functions not disturbed in the first instance become
affected in a fixed order of succession, some light is thereby thrown upon,
the action which one organ exercises over another: and we occasionally
obtain a series of effects which we can refer with some confidence to the-
original local derangement ; but for this it is necessary that we should know
that the original derangement was local. If it was what is termed consti-
tutional ; that is, if we do not know in what part of the animal economy it
took its rise, or the precise nature of the disturbance which took place in
that part, we are unable to determine which of the various derangements
was cause and which effect ; which of them were produced by one another,
and which by the direct, though perhaps tardy, action of the original cause.
Besides natural pathological facts, we can produce pathological facts ar-
tificially : we can try experiments, even in the popular sense of the term,
by subjecting the living being to some external agent, such as the mercury
of our former example, or the section of a nerve to ascertain the function*
of different parts of the nervous system. As this experimentation is not.
intended to obtain a direct solution of any practical question, but to dis-
cover general laws, from which afterward the conditions of any particular
effect may be obtained by deduction, the best cases to select are those of
which the circumstances can be best ascertained : and such are generally
328 INDUCTION.
not those in which there is any practical object in view. The experiments
are best tried, not in a state of disease, which is essentially a changeable
state, but in the condition of health, comparatively a fixed state. In the
one, unusual agencies are at work, the results of which we have no means
of predicting: in the other, the course of the accustomed physiological
phenomena would, it may generally be presumed, remain undisturbed, were
it not for the disturbing cause which we introduce.
Such, with the occasional aid of the Method of Concomitant Variations
(the latter not less encumbered than the more elementary methods by the
peculiar difficulties of the subject), are our inductive resources for ascer-
taining the laws of the causes considered separately, when we have it not
in our power to make trial of them in a state of actual separation. The
insufficiency of these resources is so glaring, that no one can be surprised
at the backward state of the science of physiology ; in which indeed our
knowledge of causes is so imperfect, that we can neither explain, nor could
without specific experience have predicted, many of the facts which are
certified to us by the most ordinary observation. Fortunately, we are
much better informed as to the empirical laws of the phenomena, that is,
the uuifoi-mities respecting which we can not yet decide whether they are
oases of causation, or mere results of it. Not only has the order in which
the facts of organization and life successively manifest themselves, from
the first germ of existence to death, been found to be uniform, and very
accurately ascertainable ; but, by a great application of the Method of
Concomitant Variations to the entii'e facts of comparative anatomy and
physiology, the characteristic organic structure corresponding to each class
of functions has been determined with considerable precision. Whether
these organic conditions are the whole of the conditions, and in many cases
whether they are conditions at all, or mere collateral effects, of some com-
mon cause, we are quite ignorant; nor are we ever likely to know, unless
we could construct an organized body and try whether it would live.
Under such disadvantages do we, in cases of this description, attempt
the initial, or inductive step, in the application of the Deductive Method to
complex phenomena. But such, fortunately, is not the common case. lu
general, the laws of the causes on which the effect depends may be obtain-
ed by an induction from comparatively simple instances, or, at the worst,
by deduction from the laws of simpler causes, so obtained. By simple in-
stances are meant, of course, those in which the action of each cause was
not intermixed or interfered with, or not to any great extent, by other
causes whose laws were unknown. And only when the induction which
furnished the premises to the Deductive method rested on such instances
has the application of such a method to the ascertainment of the laws of a
complex effect, been attended with brilliant results.
§ 2. When the laws of the causes have been ascertained, and the first
stage of the great logical operation now under discussion satisfactorily ac-
complished, the second part follows ; that of determining from the laws of
the causes what effect any given combination of those causes will produce.
This is a process of calculation, in the wider sense of the term ; and very
often involves processes of calculation in the narrowest sense. It is a
ratiocination ; and when our knowledge of the causes is so perfect as to
extend to the exact numerical laws which they observe in producing their
■effects, the ratiocination may reckon among its premises the theorems ol
the science of number, in the whole immense extent of that science. Not
THE DEDUCTIVE METHOD. 329
only are the most advanced trutbs of mathematics often required to enable
us to compute an effect, the numerical law of which we already know ; but,
even by the aid of those most advanced truths, we can go but a little way.
In so simple a case as the common problem of three bodies gravitating to-
ward one another, with a force directly as their mass and inversely as the
square of the distance, all the resources of the calculus have not hitherto
sufficed to obtain any general solution, but an approximate one. In a case
a little more complex, but still one of the simplest which arise in practice,
that of the motion of a projectile, the causes which affect the velocity and
range (for example) of a cannon-ball may be all known and estimated : the
force of the gunpowder, the angle of elevation, the density of the air, the
strength and direction of the wind ; but it is one of the most difficult of
mathematical problems to combine all these, so as to determine the effect
resulting from their collective action.
Besides the theorems of number, those of geometiy also come in as
premises, where the effects take place in space, and involve motion and ex-
tension, as in mechanics, optics, acoustics, astronomy. But when the com-
plication increases, and the effects are under the influence of so many and
such shifting causes as to give no room either for fixed numbers, or for
straiglit lines and regular curves (as in the case of physiological, to say
nothing of mental and social phenomena), the laws of number and exten-
sion are applicable, if at all, only on that large scale on which precision of
details becomes unimportant. Although these laws play a conspicuous
part in the most striking examples of the investigation of nature by the
Deductive Method, as for example in the Newtonian theory of the celestial
motions, they are by no means an indispensable part of every such process.
All that is essential in it is reasoning from a general law to a particular
case, that is, determining by means of the particular circumstances of that
case, what result is required in that instance to fulfill the law. Thus in
the Torricellian experiment, if the fact that air has weight had been pre-
viously known, it would have been easy, without any numerical data, to
deduce from the general law of equilibrium, that the mercury would stand
in the tube at such a height that the column of mercury would exactly bal-
ance a column of the atmosphere of equal diameter; because, otherwise,,
equilibrium would not exist.
By such ratiocinations from the separate laws of the causes, we may, ta
a certain extent, succeed in answering either of the following questions:
Given a certain combination of causes, what effect will follow ? and, What
combination of causes, if it existed, would produce a given effect?. In
the one case, we determine the effect to be expected in any complex cir-
cumstances of which the different elements are known : in the other case
we learn, according to what law — under what antecedent conditions — a
given complex effect will occur.
§ 3. But (it may here be asked) are not the same arguments by which
the methods of direct observation and experiment were set aside as illuso-
ry when applied to the laws of complex phenomena, applicable with equal
force against the Method of Deduction ? When in every single instance a
multitude, often an unknown multitude, of agencies, are clashing and com-
bining, what security have we that in our computation a priori we have
taken all these into our reckoning? How many must we not generally be
ignorant of? Among those which we know, how probable that some have
been overlooked ; and, even were all included, how vain the pretense of
330 INDUCTION.
summing up the effects of many causes, unless we know accurately the
numerical law of each — -a condition in most cases not to be fultiUed; and
■even when it is fulfilled, to make the calculation transcends, in any but
very simple cases, the utmost power of mathematical science with all its
most modern improvements.
These objections have real weight, and would be altogether unanswer-
able, if there were no test by which, when we employ the Deductive Meth-
od, we might judge whether an error of any of the above descriptions had
been committed or not. Such a test, however, there is : and its application
forms, under the name of Verification, the third essential component part
■of the Deductive Method ; without which all the results it can give have
little other value than that of conjecture. To warrant reliance on the gen-
■eral conclusions arrived at by deduction, these conclusions must be found,
on careful comparison, to accord with the results of direct observation
wherever it can be had. If, when we have experience to compare with
them, this experience confirms them, we may safely trust to them in other
■cases of which our specific experience is yet to come. But if our deduc-
tions have led to the conclusion that from a particular combination of
■causes a given effect would result, then in all known cases where that com-
bination can be shown to have existed, and where the effect has not follow-
ed, we must be able to show (or at least to make a probable surmise) what
frustrated it : if we can not, the theory is imperfect, and not yet to be re-
iied upon. Nor is the verification complete, unless some of the cases in
which the theory is borne out by the observed result are of at least
-equal complexity with any other cases in which its application could be
■called for.
If direct observation and collation of instances have furnished us with any
•empirical laws of the effect (whether true in all observed cases, or only true
for the most part), the most effectual verification of which the theory .could
be susceptible, would be, that it led deductively to those empirical laws;
that the uniformities, whether complete or incomplete, which were observed
to exist among the phenomena, were accounted for by the laws of the causes
— were such as could not but exist if those be really the causes by which
the phenomena are produced. Thus it was very reasonably deemed an es-
sential requisite of any true theoi-y of the causes of the celestial motions,
that it should lead by deduction to Kepler's laws ; which, accordingly, the
Newtonian theory did.
In order, thei-efore, to facilitate the verification of theories obtained by
■deduction, it is important that as many as possible of the empirical laws
of the phenomena should be ascertained, by a comparison of instances, con
formably to the Method of Agreement: as well as (it must be added) that
the phenomena themselves should be described, in the most comprehensive
AS well as accurate manner possible; by collecting from the observation
of parts, the simplest, possible correct expressions for the corresponding
wholes : as when the series of the observed places of a planet was first
■expressed by a circle, then by a system of epicycles, and subsequently by
nn ellipse.
It is worth remarking, that complex instances which would have been
■of no use for the discovery of the simple laws into which we ultimately
■analyze their phenomena, nevertheless, when they have served to verify the
analysis, become additional evidence of the laws themselves. Although
we could not have got at the law from complex cases, still when the law,
got at otherwise, is found to be in accordance with the result of a complex
THE DEDUCTIVE METHOD. 331
case, that case becomes a new experiment on the law, and helps to confirm,
what it did not assist to discover. It is a new trial of the principle in a
difEerent set of circumstances; and occasionally serves to eliminate some
circumstance not previously excluded, and the exclusion of vphich might
require an experiment impossible to be executed. This was strikingly
conspicuous in the example formerly quoted, in which the difference be-
tween the observed and the calculated velocity of sound was ascertained to
result from the heat extricated by the condensation which takes place in
each sonorous vibration. This was a trial, in new circumstances, of the
law of the development of heat by compression ; and it added materially
to the proof of the universality of that law. Accordingly, any law of na-
ture is deemed to have gained in point of certainty, by being found to
explain some complex case which had not previously been thought of in
connection with it; and this indeed is a consideration to which it is the
habit of scientific inquirers to attach rather too much value than too little.
To the Deductive Method, thus characterized in its three constituent
parts. Induction, Ratiocination, and Verification, the human mind is in-
debted for its most conspicuous triumphs in the investigation of nature.
To it we owe all the theories by which vast and complicated phenomena
are embraced under a few simple laws, which, considered as the laws of
those great phenomena, could never have been detected by their direct
study. We may form some conception of what the method has done for
us from the case of the celestial motions : one of the simplest among the
greater instances of the Composition of Causes, since (except in a few cases
not of primary importance) each of the heavenly bodies may be consider-
ed, without material inaccuracy, to be never at one time influenced by the
attraction of more than two bodies, the sun and one other planet or satel-
lite ; making, with the reaction of the body itself, and the force generated
by the body's own motion and acting in the direction of the tangent, only
four different agents on the concurrence of which the motions of that body
depend ; a much smaller number, no doubt, than that by which any other
of the great phenomena of nature is determined or modified. Yet how
could we ever have ascertained the combination of forces on which the
motions of the earth and planets are dependent, by merely comparing the
orbits or velocities of different planets, or the different velocities or posi-
tions of the same planet? Notwithstanding the regularity which mani-
fests itself in those motions, in a degree so rare among the effects of con-
currence of causes ; and although the periodical recurrence of exactly the
same effect, affords positive proof that all the combinations of causes which
occur at all, recur periodically ; we should not have known what the causes
were, if the existence of agencies precisely similar on our own earth had
not, fortunately, brought the causes themselves within the reach of experi-
mentation under simple circumstances. As we shall have occasion to an-
alyze, further on, this great example of the Method of Deduction, we shall
not occupy any time with it here, but shall proceed to that secondary ap-
plication of the Deductive Method, the result of which is not to prove laws
of phenomena, but to explain them.
832 INDUCTION.
CHAPTER XII.
OV THE EXPLANATION OF LAWS OP NATUBE.
§ 1. The deductive operation by which we derive the law of an effect
from the laws of the causes, the concurrence of which gives rise to it, may
be undertaken either for the purpose of discovering the law, or of explain-
ing a law already discovered. The word explanation occurs so continual-
ly, and holds so important a place in philosophy, that a little time spent in
fixing the meaning of it will be profitably employed.
An individual fact is said to be explained, by pointing out its cause, that
is, by stating the law or laws of causation, of which its production is an
instance. Thus, a confiagration is explained, when it is proved to have
arisen from a spark falling into the midst of a heap of combustibles. And
in a similar manner, a law or uniformity in nature is said to be explained,
when another law or laws a7-e pointed out, of which that law itself is but a
case, and from which it could be deduced.
§ 2. There are three distinguishable sets of circumstances in which a law
of causation may be explained from, or, as it also is often expressed, re-
solved into, other laws.
The first is the case already so fully considered ; an intermixture of laws,
producing a joint effect equal to the sum of the effects of the causes taken
separately. The law of the complex effect is explained, by being resolved
into the separate laws of the causes which contribute to it. Thus, the law
of the motion of a planet is resolved into the law of the acquired force,
which tends to produce a uniform motion in the tangent, and the law of
the centripetal force, which tends to produce an accelerating motion toward
the sun ; the real motion being a compound of the two.
It is necessary here to remark, that in this resolution of the law of a
complex effect, the laws of which it is compounded are not the only ele-
ments. It is resolved into the laws of the separate causes, together with
the fact of their co-existence. The one is as essential an ingredient as the
other ; whether the object be to discover the law of the effect, or only to
explain it. To deduce the laws of the heavenly motions, we require not
only to know the law of a rectilineal and that of "a gravitative force, but the
existence of both these forces in the celestial regions, and even their rela-
tive amount. The complex laws of causation are thus resolved into two
distinct kinds of elements : the one, simpler laws of causation, the other
(in the aptly selected expression of Dr. Chalmers) collocations; the colloca-
tions consisting in the existence of certain agents or powers, in certain
circumstances of place and time. We shall hereafter have occasion to re-
turn to this distinction, and to dwell on it at such length as dispenses with
the necessity of further insisting on it here. The first mode, then, of the
explanation of Laws of Causation, is when the law of an effect is resolved
into the various tendencies of which it is the result, together with the laws
of those tendencies.
§ 3. A second case is when, between what seemed the cause and what
EXPLANATION OF LAWS. 333
was supposed to be its effect, farther observation detects an intermediate
link ; a fact caused by the antecedent, and in its turn causing the conse-
quent ; so that the cause at first assigned is but the remote cause, operating
through the intermediate phenomenon. A seemed the cause of C, but it
subsequently appeared that A was only the cause of B, and that it is B
which was the cause of C. For example : mankind were aware that the
act of touching an outward object caused a sensation. It was subsequent-
ly discovered that after we have touched the object, and before we ex-
perience the sensation, some change takes place in a kind of thread called
a nerve, which extends from our outward organs to the brain. Touching
the object, therefore, is only the remote cause of our sensation ; that is, not
the cause, properly speaking, but the cause of the cause ; the real cause of
the sensation is the change in the state of the nerve. Future experience
may not only give us more knowledge than we now have of the particular
nature of this change, but may also interpolate another link : between the
contact (for example) of the object with our outward organs, and the pro-
duction of the change of state in the nerve, there may take place some
electric phenomenon, or some phenomenon of a nature not resembling the
effects of any known agency. Hitherto, however, no such intermediate
link has been discovered ; and the touch of the object must be considered,
provisionally, as the proximate cause of the affection of the nerve. The
sequence, therefore, of a sensation of touch on contact with an object is
ascertained not to be an ultimate law ; it is resolved, as the phrase is, into
two other laws — the law that contact with an object produces an affection
of the nerve, and the law that an affection of the nerve produces sensation.
To take another example : the more powerful acids corrode or blacken
organic compounds. This is a case of causation, but of remote causation ;
and is said to be explained when it is shown that there is an intermediate
link, namely, the separation of some of the chemical elements of the organ-
ic structure from the rest, and their entering into combination with the
acid. The acid causes this separation of the elements, and the separation
of the elements causes the disorganization, and often the charring of the
structure. So, again, chlorine extracts coloring matters (whence its efficacy
in bleaching) and purifies the air from infection. This law is resolved into
the two following laws : Chlorine has a powerful affinity for bases of all
kinds, particularly metallic bases and hydrogen : such bases are essential
elements of coloring matters and contagious compounds, which substances,
therefore, are decomposed and destroyed by chlorine.
§ 4. It is of importance to remark, that when a sequence of phenomena
is thus resolved into other laws, they are always laws more general than
itself. The law that A is followed by C, is less general than either of the
laws which connect B with C and A with B. This will appear from very
simple considerations.
All laws of causation are liable to be counteracted or fustrate'd, by the
non-fulfillment of some negative condition ; the tendency, therefore, of B
to produce C may be defeated. Now the law that A produces B, is equal-
ly fulfilled whether B is followed by C or not ; but the law that A pro-
duces C by means of B, is of course only fulfilled when B is really followed
by C, and is, therefore, less general than the law that A produces B. It is
also less general than the law that B produces C. For B may have other
causes besides A; and as A produces C only by means of B, while B pro-
duces C, whether it has itself been produced by A or by any thing else, the
334 INDUCTION.
second law embraces a greater number of instances, covers as it were a
greater space of ground, than the first.
Thus, in our former example, the law that the contact of an object
causes a change in the state of the nerve, is more general than the law
that contact with an object causes sensation, since, for aught we know, the
change in the nerve may equally take place when, from a counteracting
cause, as, for instance, strong mental excitement, the sensation does not
follow ; as in a battle, where wounds are sometimes received without any
consciousness of receiving them. And again, the law that change in the
state of a nerve produces sensation, is more general than the law that con-
tact with an object produces sensation ; since the sensation equally follows
the change in the nerve when not produced by contact with an object, but
by some other cause ; as in the well-known case, when a person who has
lost a limb feels the same sensation which he has been accustomed to call
a pain in the limb.
Not only are the laws of more immediate sequence into which the law
of a remote sequence is resolved, laws of greater generality than that law
is, but (as a consequence of, or rather as implied in, their greater general-
ity) they are more to be relied on ; there are fewer chances of their being
ultimately found not to be universally true. From the moment when the
sequence of A and C is shown not to be immediate, but to depend on an
intervening phenomenon, then, however constant and invariable the se-
quence of A and C has hitherto been found, possibilities arise of its failure,
exceeding those which can effect either of the more immediate sequences,
A, B, and B, C. The tendency of A to produce C may be defeated by
whatever is capable of defeating either the tendency of A to produce B,
or the tendency of B to produce C ; it is, therefore, twice as liable to failure
as either of those more elementary tendencies ; and the generalization that
A is always followed by C, is twice as likely to be found erroneous. And
so of the converse generalization, that C is always preceded and caused by
A ; which will be erroneous not only if there should happen to be a sec-
ond immediate mode of production of C itself, but moreover if there be
a second mode of production of B, the immediate antecedent of C in the
sequence.
The resolution of the one generalization into the other two, not only
shows that there are possible limitations of the former, from which its two
elements are exempt, but shows also where these are to be looked for. As
soon as we know that B intervenes between A and C, we also know that
if there be cases in which the sequence of A and C does not hold, these are
most likely to be found by studying the effects or the conditions of the
phenomenon B.
It appears, then, that in the second of the three modes in which a law
may be resolved into other laws, the latter are more general, that is, extend
to more cases, and are also less likely to require limitation from subsequent
experience, than the law which they serve to explain. They are more near-
ly unconditional; they are defeated by fewer contingencies; they are a
nearer approach to the universal truth of nature. The same observations
are still more evidently true with regard to the first of the three modes of
resolution. When the law of an effect of combined forces is resolved into
the separate laws of the causes, the nature of the case implies that the law
of the effect is less general than the law of any of the causes, since it only
holds when they are combined ; while the law of any one of the causes
holds good both then, and also when that cause acts apart from the rest..
EXPLANATION OF LAWS. 335
It is also manifest tbat the complex law is liable to be oftenev unfulfilled
than any one of the simpler laws of which it is the result, since every con-
tingency which defeats any of the laws prevents so much of the effect as
depends on it, and thereby defeats the complex law. The mere rusting, for
example, of some small part of a great machine, often suffices entirely to
prevent the effect which ought to result from the joint action of all the
parts. The law of the effect of a combination of causes is always subject
to the whole of the negative conditions which attach to the action of all
the causes severally.
There is another and an equally strong reason why the law of a complex
effect must be less general than the laws of the causes which conspire to
produce it. The same causes, acting according to the same laws, and differ-
ing only in the proportions in which they are combined, often produce ef-
fects which differ not merely in quantity, but in kind. The combination
of a centripetal with a projectile force, in the proportions which obtain in
all the planets and satellites of our solar system, gives rise to an elliptical
motion ; but if the ratio of the two forces to each other were slightly al-
tered, it is demonstrated that the motion produced would be in a circle, or
a parabola, or an hyperbola ; and it is thought that in the case of some
comets one of these is probably the fact. Yet the law of the parabolic mo-
tion would be resolvable into the very same simple laws into which that of
the elliptical motion is resolved, namely, the law of the permanence of rec-
tilineal motion, and the law of gravitation. If, therefore, in the course of
ages, some circumstance were to manifest itself which, without defeating
the law of either of those forces, should merely alter their proportion to
one another (such as the shock of some solid body, or even the accumula-
ting effect of the resistance of the medium in which astronomers have been
led to surmise that the motions of the heavenly bodies take place), the el-
liptical motion might be changed into a motion in some other conic section j
and the complex law, that the planetary motions take place in ellipses, would
be deprived of its universality, though the discovery would not at all de-
tract from the universality of the simpler laws into which that complex law
is resolved. The law, in short, of each of the concurrent causes remains
the same, however their collocations may vary; but the law of their joint
effect varies with every difference in the collocations. There needs no more
to show how much more general the elementary laws must be than any of
the complex laws which are derived from them.
§ 5. Besides the two modes which have been treated of, there is a third
mode in which laws are resolved into one another ; and in this it is self-ev-
ident that they are resolved into laws more general than themselves. This
third mode is the suhsumption (as it has been called) of one law under an-
other ; or (what comes to the same thing) the gathering up of several laws
into one more general law which includes them all. The most splendid ex-
ample of this operation was when terrestrial gravity and the central force
of the solar system were brought together under the general law of gravi-
tation. It had been proved antecedently that the earth and the other plan-
ets tend to the sun ; and it had been known from the earliest times that
terrestrial bodies tend toward the earth. These were similar phenomena;
and to enable them both to be subsumed under one law, it was only neces-
sary to prove that, as the effects were similar in quality so also they, as to
quantity, conform to the same rules. This was first shown to be true of
the moon, which agreed with terrestrial objects not only in tending to a
336 INDUCTION.
centre, bnt in the fact that this centre was the earth. The tendency of the
moon toward the earth being ascertained to vary as the inverse square of
the distance, it was deduced from this, by direct calculation, that if the moon
were as near to the earth as terrestrial objects are, and the acquired force
in the direction of the tangent were suspended, the moon would fall toward
the earth through exactly as many feet in a second as those objects do by
virtue of their weight. Hence the inference was irresistible, that the moon
also tends to the earth by virtue of its weight : and that the two phenome-
na, the tendency of the moon to the earth and the tendency of terrestrial
objects to the earth, being not only similar in quality, but, when in the
same circumstances, identical in quantity, are cases of one and the same
law of causation. But the tendency of the moon to the earth, and the tend-
ency of the earth and planets to the sun, were already known to be cases
of the same law of causation ; and thus the law of all these tendencies, and
the law of terrestrial gravity, were recognized as identical, and were sub-
sumed under one general law, that of gravitation.
In a similar manner, the laws of magnetic phenomena have more recently
been subsumed under known laws of electricity. It is thus that the most
general laws of nature are usually arrived at : we mount to them by suc-
cessive steps. For, to arrive by correct induction at laws which hold un-
der such an immense variety of circumstances, laws so general as to be in-
dependent of any varieties of space or time which we are able to observe,
requires for the most part many distinct sets of experiments or observa-
tions, conducted at different times and by different people. One part of
the law is first ascertained, afterward another part : one set of observations
teaches us that the law holds good under some conditions, another that it
holds good under other conditions, by combining which observations we
find that it holds good under conditions much more general, or even uni-
versally. The general law, in this case, is literally the sum of all the partial
ones ; it is a recognition of the same sequence in different sets of instances ;
and may, in fact, be regarded as merely one step in the process of elimi-
nation. The tendency of bodies toward one another, which we now call
gravity, had at first been observed only on the earth's surface, where it
manifested itself only as a tendency of all bodies toward the earth, and
might, therefore, be ascribed to a peculiar property of the earth itself : one of
the circumstances, namely, the proximity of the earth, had not been elimi-
nated. To eliminate this circumstance required a fresh set of instances in
other parts of the universe : these we could not ourselves create ; and
though natui-e had created them for us, we were placed in very unfavorable
circumstances for observing them. To make these observations, fell nat-
urally to the lot of a different set of persons from those who studied ter-
restrial phenomena; and had, indeed, been a matter of great interest at
a time when the idea of explaining celestial facts by terrestrial laws was
looked upon as the confounding of an indefeasible distinction. When,
however, the celestial motions were accurately ascertained, and the deduc-
tive processes performed, from which it appeared that their laws and
those of terrestrial gravity corresponded, those celestial observations be-
came a set of instances which exactly eliminated the circumstance of prox-
imity to the earth ; and proved that in the original case, that of terrestrial
objects, it was not the earth, as such, that caused the motion or the press-
ure, but the circumstance common to that case with the celestial instances,
namely, the presence of some great body within certain limits of dis-
tance.
EXPLANATION OF LAWS. 337
§ 6. There are, then, three modes of explaining laws of causation, or,
whi«h is the same thing, resolving them into other laws. First, when the
law of an effect of combined causes is resolved into the separate laws of
the causes, together with the fact of their combination. Secondly, when
the law which connects any two links, not proximate, in a chain of causa-
tion, is resolved into the laws which connect each with the intermediate
links. Both of these are cases of resolving one law into two or more ; in
the third, two or more are resolved into one : when, after the law has been
shown to hold good in several different classes of cases, we decide that
what is true in each of these classes of cases, is true under some more gen-
eral supposition, consisting of what all those classes of cases have in com-
mon. We may here remark that this last operation involves none of the
uncertainties attendant on induction by the Method of Agreement, since we
need not suppose the result to be extended by way of inference to any new class
of cases different from those by the comparison of which it was engendered.
In all these three processes, laws are, as we have seen, resolved into laws
more general than themselves ; laws extending to all the cases which the
former extended to, and others besides. In the first two modes they are
also resolved into laws more certain, in other words, more universally true
than themselves ; they are, in fact, proved not to be themselves laws of na-
tui-e, the character of which is to be universally true, but results of laws of
nature, which may be only true conditionally, and for the most part. No
difference of this sort exists in the third case ; since here the partial laws
are, in fact, the very same law as the general one, and any exception to
them would be an exception to it too.
By all the three processes, the range of deductive science is extended ;
since the laws, thus resolved, may be thenceforth deduced demonstratively
from the laws into which they are resolved. As already remarked, the
same deductive process which proves a law or fact of causation if un-
known, serves to explain it when known.
The word explanation is here used in its philosophical sense. What is
called explaining one law of nature by another, is but substituting one
mystery for another ; and does nothing to render the general course of na-
ture other than mysterious : we can no more assign a why for the more
extensive laws than for the partial ones. The explanation may substitute
a mystery which has become familiar, and has grown to seem not mysteri-
ous, for one which is still strange. And this is the meaning of explanation,
in common parlance. But the process with which we are here concerned
often does the very contrary : it resolves a phenomenon with which we are
familiar into one of which we previously knew little or nothing ; as when
the common fact of the fall of heavy bodies was resolved into the tendency
of all particles of matter toward one another. It must be kept constantly
in view, therefore, that in science, those who speak of explaining any phe-
nomenon mean (or should mean) pointing out not some more familiar, but
merely some more general, phenomenon, of which it is a partial exemplifica-
tion ; or some laws of causation which produce it by their joint or succes-
sive action, and from which; therefore, its conditions may be determined
deductively. Every such operation brings us a step nearer toward answer-
ing the question which was stated in a previous chapter as comprehending
the whole problem of the investigation of nature, viz. : what are the fewest
assumptions, which being granted, the order of nature as it exists would
be the result? What are the fewest general propositions from which all
the uniformities existing in nature could be deduced ?
22
338 INDUCTION,
The laws, thus explained or resolved, are sometimes said to be accounted
for; but the expression is incorrect, if taken to mean any thing more than
what has been already stated. In minds not habituated to accurate think-
ing, there is often a confused notion that the general laws are the causes of
the partial ones ; that the law of general gravitation, for example, causes
the phenomenon of the fall of bodies to the earth. But to assert this-
would be a misuse of the word cause : terrestrial gravity is not an effect of
general gravitation, but a case of it ; that is, one kind of the particular in-
stances in which that general law obtains. To account for a law of nature-
means, and can mean, nothing more than to assign other laws more general,,
together with collocations, which laws and collocations being supposed, the
partial law follows without any additional supposition.
CHAPTER XIII.
MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE.
§ 1. The most striking example which the history of science presents,
of the explanation of laws of causation and other uniformities of sequence
among special phenomena, by resolving them into laws of greater simplic-
ity and generality, is the great Newtonian generalization; respecting
which typical instance, so much having already been said, it is suflScient to
call attention to the great number and variety of the special observed uni-
formities, which are in this case accounted for, either as particular cases, or
as consequences, of one very simple law of universal nature. The simple
fact of a tendency of every particle of matter toward every other particle^
vai'ying inversely as the square of the distance, explains the fall of bodies
to the earth, the revolutions of the planets and satellites, the motions (so
far as known) of comets, and all the various regulai'ities which have been
observed in these special phenomena ; such as the elliptical orbits, and the
variations from exact ellipses; the relation between the solar distances of
the planets and the duration of their revolutions ; the precession of the
equinoxes ; the tides, and a vast number of minor astronomical truths.
Mention has also been made in the preceding chapter of the explanation
of the phenomena of magnetism from laws of electricity ; the special laws
of magnetic agency having been affiliated by deduction to observed laws
of electric action, in which they have ever since been considered to be in-
cluded as special cases. An example not so complete in itself, but even
more fertile in consequences, having been the starting-point of the really
scientific study of physiology, is the afliliation, commenced by Bichat, and
carried on by subsequent biologists, of the properties of the bodily organs,
to the elementary properties of the tissues into which they are anatomical-
ly decomposed.
Another striking instance is afforded by Dalton's generalization, com-
monly known as the atomic theory. It had been known from the very
commencement of accurate chemical observation, that any two bodies com-
bine chemically with one another in only a' certain number of proportions ;
but those proportions were in each case expressed by a percentage — so-
many parts (by weight) of each ingredient, in 100 of the compound (say
35 and a fraction of one element, 64 and a fraction of the other) ; in which
mode of statement no relation was perceived between the proportion itt
EXAMPLES OF THE EXPLANATION OF LAWS. 339
■which a given element combines with one substance, and that in which it
combines with others. The great step made by Dalton consisted in per-
ceiving that a unit of weight might be established for each substance,
such that by supposing the substance to enter into all its combination^ in
the ratio either of that unit, or of some low multiple of that unit, all the
different proportions, previously expressed by percentages, were found to
result. Thus 1 being assumed as the unit of hydrogen, if 8 were then
taken as that of oxygen, the combination of one unit of hydrogen with one
unit of oxygen would produce the exact proportion of weight between the
two substances which is known to exist in water ; the combination of one
unit of hydrogen with two units of oxygen would produce the proportion
which exists in the other compound of the same two elements, called perox-
ide of hydrogen ; and the combinations of hydrogen and of oxygen with
all other substances, would correspond with the supposition that those ele-
ments enter into combination by single units, or twos, or threes, of the
numbers assigned to them, 1 and 8, and the other substances by ones or
twos or threes of other determinate numbers proper to each. The result
is that a table of the equivalent numbers, or, as they are called, atomic
weights, of all the elementary substances, comprises in itself, and scientific-
ally explains, all the proportions in which any substance, elementary or
compound, is found capable of entering into chemical combination with
any other substance whatever.
§ 2. Some interesting cases of the explanation of old uniformities by
newly ascertained laws are afforded by the researches of Professor Gra-
ham. That eminent chemist was the first who drew attention to the dis-
tinction which may be made of all substances into two classes, termed by
him crystalloids and colloids; or rather, of all states of matter into the
crystalloid and the colloidal states, for many substances are capable of ex-
isting in either. When in the colloidal state, their sensible properties are
very different from those of the same substance when crystallized, or when
in a state easily susceptible of crystallization. Colloid substances pass with
extreme diflSculty and slowness into the crystalline state, and are extreme-
ly inert in all the ordinary chemical relations. Substances in the colloid
state are almost always, when combined with water, more or less viscous or
gelatinous. The most prominent examples of the state are certain animal
and vegetable substances, particularly gelatine, albumen, starch, the gums,
caramel, tannin, and some others. Among substances not of organic origin,
the most notable instances are hydrated silicic acid, and hydrated alumina,
with other metallic peroxides of the aluminous class.
Now it is found, that while colloidal substances are easily penetrated by
water, and by the solutions of crystalloid substances, they are very little
penetrable by one another : which enabled Professor Graham to introduce
a highly effective process (termed dialysis) for separating the crystalloid
substances contained in any liquid mixture, by passing them through a
thin septum of colloidal matter, which does not suffer any thing colloidal
to pass, or suffers it only in very minute quantity. This property of col-
loids enabled Mr. Graham to account for a number of special results of
observation, not previously explained.
For instance, " while soluble crystalloids are always highly sapid, soluble
colloids are singularly insipid," as might be expected ; for, as the sentient
extremities of the nerves of the palate " are probably protected by a col-
loidal membrane," impermeable to other colloids, a colloid, when tasted,
340 INDUCTION.
probably never reaches those nerves. Again, " it has been observed that
vegetable gum is not digested in the stomach ; the coats of that organ
dialyse the soluble food, absorbing crystalloids, and rejecting all colloids."
One of the mysterious processes accompanying digestion, the secretion of
free muriatic acid by the coats of the stomach, obtains a probable hypo-
thetical explanation through the same law. Finally, much light is thrown
upon the observed phenomena of osmose (the passage of fluids outward
and inward through animal membranes) by the fact that the membranes
are colloidal. In consequence, the water and saline solutions contained in
the animal body pass easily and rapidly through the membranes, while the
substances directly applicable to nutrition, which are mostly colloidal, are
detained by them.*
The property which salt possesses of preserving animal substances from
putrefaction is resolved by Liebig into two more general laws, the strong
attraction of salt for water, and the necessity of the presence of water as a
condition of putrefaction. The intermediate phenomenon which is inter-
polated between the remote cause and the effect, can here be not merely
inferred but seen ; for it is a familiar fact, that flesh upon which salt has
been thrown is speedily found swimming in brine.
The second of the two factors (as they may be ternied) into which the
preceding law has been resolved, the necessity of water to putrefaction,
itself affords an additional example of the Resolution of Laws. The law
itself is proved by the Method of Difference, since flesh completely dried
and kept in a dry atmosphere does not putrefy ; as we see in the case of
dried provisions and human bodies in very dry climates. A deductive
explanation of this same law results from Liebig's speculations. The
puti'efaction of animal and other azotized bodies is a chemical process, by
which they are gradually dissipated in a gaseous form, chiefly in that of
carbonic acid and ammonia ; now to convert the carbon of the animal sub-
stance into carbonic acid requires oxygen, and to convert the azote into
ammonia requires hydrogen, which are the elements of water. The ex-
treme rapidity of the putrefaction of azotized substances, compared with
the gradual decay of non-azotized bodies (such as wood and the like) by
the action of oxygen alone, he explains from the general law that sub-
stances are much more easily decomposed by the action of two different
affinities upon two of their elements than by the action of only one.
§ 3. Among the many important properties of the nervous system which
have either been first discovered or strikingly illustrated by Dr. Brown-
Sequard, I select the reflex influence of the nervous system on nutrition
and secretion. By reflex nervous action is meant, action which one part
of the nervous system exerts over another part, without any intermediate
action on the brain, and consequently without consciousness ; or which, if
it does pass through the brain, at least produces its effects independently
of the will. There are many experiments which prove that irritation of a
nerve in one part of the body may in this manner excite powerful action
in another part ; for example, food injected into the stomach through a
divided oesophagus, nevertheless produces secretion of saliva ; warm water
injected into the bowels, and various other irritations of the lower intes-
tines, have been found to excite secretion of the gastric juice, and so forth.
* Vide Memoir by Thomas Graham, F.R.S., Master of the Mint, "On Liquid Diffusion
applied to Analysis," in the Philosophical Transacticms for 1862, reprinted in the Journal of
the Chemical Society, and also separately as a pamphlet.
EXAMPLES OF THE EXPLANATION OF LAWS. 34]
The reality of the power being thus proved, its agency explains a great
variety of apparently anomalous phenomena ; of which I select the follow-
ing from Dr. Brown-S^quard's Lectures on the Nervous System:
The production of tears by irritation of the eye, or of the mucous mem-
brane of the nose ;
The secretions of the eye and nose increased by exposure of other parts
of the body to cold ; '
Inflammation of the eye, especially when of traumatic origin, very fre-
quently excites a similar affection in the other eye, which may be cured by
section of the intervening nerve ;
Loss of sight sometimes produced by neuralgia, and has been known
to be at once cured by the extirpation (for instance) of a carious tooth ;
Even cataract has been produced in a healthy eye by cataract in the
other eye, or by neuralgia, or by a wound of the frontal nerve ;
The well-known phenomenon of a sudden stoppage of the heart's action,
and consequent death, produced by irritation of some of the nervous ex-
tremities; e.g-., by drinking very cold water, or by a blow on the abdo-
men, or other sudden excitation of the abdominal sympathetic nerve,
though this nerve may be irritated to any extent without stopping the
heai't's action, if a section be made of the communicating nerves ;
The extraordinary effects produced on the internal organs by an exten-
sive burn on the surface of the body, consisting in violent inflammation
of the tissues of the abdomen, chest, or head, which, when death ensues
from this kind of injury, is one of the most frequent causes of it;
Paralysis and anfesthesia of one part of the body from neuralgia in an-
other part ; and muscular atrophy from neuralgia, even when there is no
paralysis ;
Tetanus produced by the lesion of a nerve. Dr. Brown-S6quard thinks
it highly probable that hydrophobia is a phenomenon of a similar nature ;
Morbid changes in the nutrition of the brain and spinal cord, manifest-
ing themselves by epilepsy, chorea, hysteria, and other diseases, occasioned
by lesion of some of the nervous extremities in remote places, as by worms,
calculi, tumors, carious bones, and in some cases even by very slight irri-
tations of the skin.
§ 4. From the foregoing and similar instances, we may see the impor-
tance, when a law of nature previously unknown has been brought to light,
or when new light has been thrown upon a known law by experiment, of
examining all cases which present the conditions necessary for bringing
that law into action ; a process fertile in demonstrations of special laws
previously unsuspected, and explanations of others already empirically
known.
For instance, Faraday discovei-ed by experiment, that voltaic electricity
could be evolved from a natural magnet, provided a conducting body were
set in motion at right angles to the direction of the magnet; and this he
found to hold not only of small magnets, but of that great magnet, the
earth. The law being thus established experimentally, that electricity is
evolved, by a magnet, and a conductor moving at right angles to the direc-
tion of its poles, we may now look out for fresh instances in which these
conditions meet. Wherever a conductor moves or revolves at right angles
to the direction of the earth's magnetic poles, there we may expect an evo-
lution of electricity. In the northern regions, where the polar direction is
Dearly perpendicular to the horizon, all horizontal motions of conductors
342 INDUCTION.
will produce electricity; horizontal wheels, for example, made of metal;
likewise all running streams will evolve a current of electricity, which will
circulate round them ; and the air thus charged with electricity may be
one of the causes of the Aurora Borealis. In the equatorial regions, on
the contrary, upright wheels placed parallel to the equator will originate a
voltaic circuit, and water-falls will naturally become electric.
For a second example, it has been proved, chiefly by the researches of
Professor Graham, that gases have a strong tendency to permeate animal
membranes, and diffuse themselves through the spaces which such mem-
branes inclose, notwithstanding the presence of other gases in those spaces.
Proceeding from this general law, and reviewing a variety of cases in which
gases lie contiguous to membranes, we are enabled to demonstrate or to
explain the following more special laws: 1st. The human or animal body,
when surrounded with any gas not already contained within the body,
absorbs it rapidly ; such, for instance, as the gases of putrefying matters :
which helps to explain malaria. 2d. The carbonic acid gas of effervescing
drinks, evolved in the stomach, permeates its membranes, and rapidly spreads
through the system. 3d. Alcohol taken into the stomach passes into vapor,
and spreads through the system with great rapidity (which, combined with
the high combustibility of alcohol, or in other words its ready combination
with oxygen, may perhaps help to explain the bodily warmth immediately
consequent on drinking spirituous liquors). 4th. In any state of the body
in which peculiar gases are formed within it, these will rapidly exhale
through all parts of the body ; and hence the rapidity with which, in certain
states of disease, the surrounding atmosphere becomes tainted. 5th. The
putrefaction of the interior parts of a carcass will proceed as rapidly as
that of the exterior, from the ready passage outward of the gaseous prod-
ucts. 6th. The exchange of oxygen and carbonic acid in the lungs is not
prevented, but rather promoted, by the intervention of the membrane of
the lungs and the coats of the blood-vessels between the blood and the air.
It is necessary, however, that there should be a substance in the blood with
which the oxygen of the air may immediately combine ; otherwise, instead
of passing into the blood, it would permeate the whole organism : and it is
necessary that the carbonic acid, as it is formed in the capillaries, should
also find a substance in the blood with which it can combine ; otherwise it
would leave the body at all points, instead of being discharged through
the lungs.
§ 5. The following is a deduction which confirms, by explaining, the em-
pirical generalization, that soda powders weaken the human system. These
powders, consisting of a mixture of tartaric acid with bicarbonate of soda,
from which the carbonic acid is set free, must pass into the stomach as
tartrate of soda. Now, neutral tartrates, citrates, and acetates of the al-
kalis are found, in their passage through the system, to be changed into
carbonates; and to convert a tartrate into a carbonate requires an addi-
tional quantity of oxygen, the abstraction of which must lessen the oxygen
destined for assimilation with the blood, on the quantity of which the
vigorous action of the human system partly depends.
The instances of new theories agreeing with and explaining old empiri-
cisms, are innumerable. All the just remarks made by experienced per-
sons on human character and conduct, are so many special laws, which
the general laws of the human mind explain and resolve. The empirical
generalizations on which the operations of the arts have usually beea
EXAMPLES OF THE EXPLANATION OF LAWS. 343
founded, are continually justified and confirmed on the one hand, or cor-
rected and improved on the other, by the discovery of the simpler scientific
laws on which the efficacy of those operations depends. The effects of the
Totation of crops, of the various manures, and other processes of improved
agriculture, have been for the first time resolved in our own day into known
laws of chemical and organic action, by Davy, Liebig, and others. The
processes of the medical art are even now mostly empirical : their efficacy
is concluded, in each instance, from a special and most precarious experi-
mental genei'alizatiou : but as science advances in discovering the simple
laws of chemistry and physiology, progress is made in ascertaining the in-
termediate links in the series of phenomena, and the more general laws on
which they depend ; and thus, while the old processes are either exploded,
■or their efficacy, in so far as real, explained, better processes, founded ou
"the knowledge of proximate causes, are continually suggested and brought
into use.* Many even of the truths of geometry were generalizations from
•experience before they were deduced from first principles. The quadra-
ture of the cycloid is said to have been first effected by measurement, or
rather by weighing a cycloidal card, and comparing its weight with that
•of a piece of similar card of known dimensions.
§ 6. To the foregoing examples from physical science, let us add another
■from mental. The following is one of the simple laws of mind : Ideas of
■a pleasurable or painful character form associations more easily and strong-
ly than other ideas, that is, they become associated after fewer repetitions,
and the association is more durable. This is an experimental law, ground-
ed on the Method of Difference. By deduction from this law, many of the
more special laws which experience shows to exist among particular men-
tal phenomena may be demonstrated and explained : the_ease_andj;ap2d-
ity^or Jnstance,-with- which thoughts- connected with our passions or_QUE
more cheris^donterests are excited, and the finnjipld _v?hich the^iactaxe-
■latuIgTo them have on our inemory; the vivid recollection we retain of
min5te circumstances which accompanied any object or event that deeply
interested us, and of the times and places in which we have been very
Jiappy or very miserable ; the horror with which we view the accidental
instrument of any occurrence which shocked us, or the locality where it
took place and the pleasure we derive from any memorial of past enjoy-
ment ; all these effects being proportional to the sensibility of the individ-
■ual mind, and to the consequent intensity of the pain or pleasure from
which the association originated. It has been suggested by the able writer
•of a biographical sketch of Dr. Priestley in a monthly periodical,! that the
same elementary law of our mental constitution, suitably followed out,
would explain a variety of mental phenomena previously inexplicable, and
in particular some of the fundamental diversities of human character and
-genius. Associations being of two sorts, either between synchronous, or
* It was an old generalization in surgery, that tight bandaging had a tendency to prevent
■or dissipate local inflammation. This sequence, being, in the progress of physiological knowl-
edge, resolved into more general laws, led to the important surgical invention made by Dr.
Arnott, the treatment of local inflammation and tumors by means of an equable pressure,
■produced by a bladder partially filled with air. The pressure, by keeping back the blood
from the part, prevents the inflammation, or the tvfmor, from being nourished : in the case of
inflammation, it removes the stimulus, which the organ is unfit to receive ; in the case of tu-
mors, by keeping ba<;k the nutritive fluid, it causes the absorption of matter to exceed the
supply, and the diseased mass is gradually absorbed and disappears.
t Since ackno\vledged and reprinted in Mr. Martineau's Miscellatdes.
344 INDUCTION.
between successive impressions; and the influence of the law which venders
associations stronger in proportion to the pleasurable or painful character
of the impressions, being felt with peculiar force in the synchronous class
of associations ; it is remarked by the writer referred to, that in minds of
strong organic sensibility synchronous associations will be likely to pre-
dominate, producing a tendency to conceive things in pictures and in the
concrete, richly clothed in attributes and circumstances, a mental habit
which is commonly called Imagination, and is one of the peculiarities of
the painter and the poet ; while persons of more moderate susceptibility
to pleasure and pain will have a tendency to associate facts chiefly in the
order of their succession, and such persons, if they possess mental superior-
ity, will addict themselves to history or science rather than to creative art.
This interesting speculation the author of the present work has endeavored,
on another occasion, to pursue further, and to examine how far it will avail
toward explaining the peculiarities of the poetical temperament.* It is
at least an example which may serve, instead of many others, to show the
extensive scope which exists for deductive investigation in the important
and hitherto so imperfect Science of Mind.
§ 7. The copiousness with which the discovery and explanation of special
laws of phenomena by deduction from simpler and more general ones has
here been exemplified, was prompted by a desire to characterize clearly, and
place in its due position of importance, the Deductive Method ; which, in the
present state of knowledge, is destined henceforth irrevocably to predom-
inate in the course of scientific investigation. A revolution is peaceably
and progressively effecting itself in philosophy, the reverse of that to which
Bacon has iittached his name. That great man changed the method of
the sciences from deductive to experimental, and it is now rapidly revert-
ing from experimental to deductive. But the deductions which Bacon
abolished were from premises hastily snatched up, or arbitrarily assumed.
The principles were neither established by legitimate canons of experi-
mental inquiry, nor the results tested by that indispensable element of a
rational Deductive Method, verification by specific experience. Between
the primitive method of Deduction and that which I have attempted to
characterize,. there is all the difference which exists between the Aristotelian
physics and the Newtonian-theory of the heavens.
_ It would, however, be a mistake to expect that those great generaliza-
tions, from which the subordinate truths of the more backward sciences
will probably at some future period be deduced by reasoning (as the
truths of astronomy are deduced from the generalities of the Newtonian
theory), will be found in all, or even in most cases, among truths now
known and admitted. "We may rest assured, that many of the most gen-
eral laws of nature are as yet entirely unthought of; and that many others^
destined hereafter to assume the same character, are known, if at all, only
as laws or properties of some limited class of phenomena; just as electric-
ity, now recognized as one of the most universal of natural agencies, was
once known only as a curious property which certain substances acquired
by friction, of first attracting and then repelling light bodies. If the theo-
ries of heat, cohesion, crystallization, and chemical action are destined, as
there can be little doubt that they are, to become deductive, the truths
which will then be regarded as the principia of those sciences would prob-
* Dissertations and Discussions, vol. i. , fourth paper.
HYPOTHESES. 345
ably, if now announced, appear quite as novel* as the law of gravitation
appeared to the contemporaries of Newton ; possibly even more so, since
Newton's law, after all, was but an extension of the law of weight — that is,
of a generalization familiar from of old, and which already comprehended
a not inconsiderable body of natural phenomena. The general laws of a
similarly commanding character, which we still look forward to the dis-
covery of, may not always find so much of their foundations already laid.
These general truths will doubtless make their first appearance in the
character of hypotheses ; not proved, nor even admitting of proof, in the
first instance, but assumed as premises for the purpose of deducing from
them the known laws of concrete phenomena. But this, though their ini-
tial, can not be their final state. To entitle an hypothesis to be received
as one of the truths of nature, and not as a mere technical help to the hu-
man faculties, it must be capable of being tested by the canons of legiti-
mate induction, and must actually have been submitted to that test. When
this shall have been done, and done successfully, premises will have been
obtained from which all the other propositions of the science will thence-
forth be presented as conclusions, and the science will, by means of a new
and unexpected Induction, be rendered Deductive.
CHAPTER XIV.
OF THE LIMITS TO THE EXPLANATION OP LAWS OF NATUEE ; AND OP
HYPOTHESES.
§ 1. The preceding considerations have led us to recognize a distinc-
tion between two kinds of laws, or observed uniformities in nature : ulti-
mate laws, and what may be termed derivative laws. Derivative laws are
8uch as are deducible from, and may, in any of the modes which we have
pointed out, be resolved into, other and more general ones. Ultimate laws
are those which can not. We are not sure that any of the uniformities
with which we are yet acquainted are ultimate laws ; but we know that
there must be ultimate laws ; and that every resolution of a derivative law
into more general laws brings us nearer to them.
■ Since we are continually discovering that uniformities, not previously
known to be other than ultimate, are derivative, and resolvable into more
general laws; since (in other words) we are continually discovering the
explanation of some sequence which was previously known only as a fact ;
it becomes an interesting question whether there are any necessary limits
to this philosophical operation, or whether it may proceed until all the uni-
form sequences in nature are resolved into some one universal law. For.
this seems, at first sight, to be the ultimatum toward which the progress
of induction by the Deductive Method, resting on a basis of observation
and experiment, is tending. Projects of this kind were universal in the
infancy of philosophy; any speculations which held out a less brilliant
prospect being in these early times deemed not worth pursuing. And the
idea receives so much apparent countenance from the nature of the most
remarkable achievements of modern science, that speculators are even now
frequently appearing, who profess either to have solved the problem, or to
suggest modes in which it may one day be solved. Even where pretensions
* Written before the rise of the new views respecting the relation of heat to mechanical
force ; but confirmed rather than contradicted by them.
346 INDUCTION.
of this magnitude are not made, the character of the solutions which are
given or sought of particular classes of phenomena, often involves eucb
conceptions of what constitutes explanation, as would render the notion of
explaining all phenomena whatever by means of some one cause or law^
perfectly admissible.
§ 2. It is, therefore, useful to remark that the ultimate Laws of Nature
can not possibly be less numerous than the distinguishable sensations or
other feelings of our nature; those, I mean, which are distinguishable
from one another in quality, and not merely in quantity or degree. For
example : since there is a phenomenon sui generis, called color, which our
consciousness testifies to be not a particular degree of some other phenom-
enon, as heat or odor or motion, but intrinsically unlike all others, it fol-
lows that there are ultimate laws of color ; that though the facts of color
may admit of explanation, they never can be explained from laws of heat
or odor alone, or of niiotion alone, but that, however far the explanation may
be carried, there will always remain in it a law of color. I do not mean,
that it might not possibly be shown that some other phenomenon, some
chemical or mechanical action, for example, invariably precedes, and is the-
cause of, every phenomenon of color. But though this, if proved, would
be an important extension of our knowledge of nature, it would not explain
how or why a motion, or a chemical action, can produce a sensation of
color; and, however diligent might be our scrutiny of the phenomena,
whatever number of hidden links we might detect in the .chain of causa-
tion terminating in the color, the last link would still be a law of color, not
a law of motion, nor of any other phenomenon whatever. Nor does this-
observation apply only to color, as compared with any other of the great
classes of sensations ; it applies to every particular color, as compared with>
others. White color can in no manner be explained exclusively by the
laws of the production of red color. In any attempt to explain it, we can.
not but introduce, as one element of the explanation, the proposition that
some antecedent or other produces the sensation of white.
The ideal limit, therefore, of the explanation of natural phenomena (to-
ward which as toward other ideal limits we are constantly tending, with-
out the prospect of ever completely attaining it) would be to show that
each distinguishable variety of our sensations, or other states of conscious-
ness, has only one sort of cause ; that, for example, whenever we perceive
a white color, there is some one condition or set of conditions which is al-
ways present, and the presence of which always produces in us that sensa-
tion. As long as there are several known modes of production of a phe-
nomenon (several different substances, for instance, which have the property
of whiteness, and between which we can not trace any other resemblance)
so long it is not impossible that one of these modes of production may
be resolved into another, or that all of them, may be resolved into some
more general mode of production not hitherto recognized. But when the
modes of production are reduced to one, we can not, in point of simplifica-
tion, go any further. This one may not, after all, be the ultimate mode;. •
there may be other links to be discovered between the supposed cause and.
the efBeet; but we can only further resolve the known law, by introducing^
some other law hitherto unknown, which will not diminish the number of
ultimate laws.
In what cases, accordingly, has science been most successful in explaining
phenomena, by resolving their complex laws into laws of gi-eater simplicity
HYPOTHESES 347
and generality? Hitherto chiefly in cases of the propagation of various
phenomena through space ; and, first and principally, the most extensive
and important of all facts of that description, mechanical motion. Now
this is exactly what might be expected from the principles here laid down.
Not only is motion one of the most universal of all phenomena, it is also
(as might be expected from that circumstance) one of those which, appar-
ently at least, are produced in the greatest number of ways ; but the phe-
nomenon itself is always, to our sensations, the same in every respect but
degree. Differences of duration or of velocity, are evidently differences in
degree only; and differences of direction in space, which alone has any
semblance of being a distinction in kind, entirely disappear (so far as our
sensations are concerned) by a change in our own position ; indeed, the
very same motion appears to us, according to our position, to take place in
every variety of direction, and motions in every different direction to take
place in the same. And again, motion in a straight line and in a curve are
no otherwise distinct than that the one is motion continuing in the same
direction, the other is motion which at each instant changes its direction.
There is, therefore, according to the principles I have stated, no absurdity
in supposing that all motion may be produced in one and the same way,
by the same kind of cause. Accordingly, the greatest achievements in phys-
ical science have consisted in resolving one observed law of the production
of motion into the laws of other known modes of production, or the laws
of several such modes into one more general mode ; as when the fall of
bodies to the earth, and the motions of the planets, were brought under
the one law of the mutual attraction of all particles of matter; when the
motions said to be produced by magnetism were shown to be produced by
electricity ; when the motions of fluids in a lateral direction, or even con-
trary to the direction of gravity, were shown to be produced by gravity;
and the Uke. There is an abundance of distinct causes of motion still un-
resolved into "one another : gravitation, heat, electricity, chemical action,
nervous action, and so forth ; but whether the efforts of the present gener-
ation of savants to resolve all these different modes of production into one
are ultimately successful or not, the attempt so to resolve them is perfect-
ly legitimate. For, though these various causes produce, in other respects,
sensations intrinsically different, and are not, therefore, capable of being
resolved into one another, yet, in so far as they all produce motion, it is
quite possible that the immediate antecedent of the motion may in all these
different cases be the same ; nor is it impossible that these various agencies
themselves may, as the new doctrines assert, all of them have for their own
immediate antecedent modes of molecular motion.
We need not extend our illustration to other cases, as, for instance, to the
propagation of light, sound, heat, electricity, etc., through space, or any of
the other phenomena which have been found susceptible of explanation by
the resolution of their observed laws into more general laws. Enough has
been said to display the difference between the kind of explanation and
resolution of laws which is chimerical, and that of which the accomplish-
ment is the great aim of science ; and to show into what sort of elements
the resolution must be effected, if at all.*
«
* As is well remarked by Professor Bain, in the very valuable chapter of his Logic which
treats of this subject (ii., 121), "scientific explanation and inductive generalization being the
same thing, the limits of Explanation are the limits of Induction, " and " the limits to induct-
ive generalization are the limits to the agreement or community of facts. Induction sup-
poses similarity among phenomena; and when such similarity is discovered, it reduces the
348 INDUCTION.
§ 3. As, however, there is scarcely any one of the principles of a true
method of philosophizing which does not require to be guarded against
errors on both sides, I must enter a caveat against another misapprehen-
sion, of a kind directly contrary to the preceding; M. Comte, among other
occasions on which he has condemned, with some asperity, any attempt to
explain phenomena which are "evidently primordial" (meaning, apparent-
ly, no more than that every peculiar phenomenon must have at least one
peculiar and therefore inexplicable law), has spoken of the attempt to fur-
nish any explanation of the color belonging to each substance, "la couleur
^lementaire propre k chaque substance," as essentially illusory. "No one,"
says he, "in our time attetnpts to explain the particular specific gravity of
each substance or of each structure. Why should it be otherwise as to
the specific color, the notion of which is undoubtedly no less primordial ?"*
Now although, as he elsewhere observes, a color must always remain a
different thing from a weight or a sound, varieties of color might neverthe-
less follow, or correspond to, given varieties of weight, or sound, or some
other phenomenon as different as these are from color itself. It is one
question what a thing is, and another what it depends on ; and though to
ascertain the conditions of an elementary phenomenon is not to obtain any
new insight into the nature of the phenomenon itself, that is no_ reason
against attempting to discover the conditions. The interdict against en-
deavoring to reduce distinctions of color to any common principle, would
have held equally good against a like attempt on the subject of distinctions
of sound ; which nevertheless have been found to be immediately preceded
and caused by distinguishable varieties in the vibrations of elastic bodies ;
though a sound, no doubt, is quite as different as a color is from any mo-
tion of particles, vibratory or otherwise. "We might add, that, in the case
of colors, there are strong positive indications that they are not ultimate
phenomena under a common statement. The similarity of terrestrial gravity to celestial at-
traction enables the two to be expressed as one phenomenon. The similarity between cap-
illary attraction, solution, the operation of cements, etc., leads to their being regarded not as
a plurality, but as a unity, a single causative link, the operation of a single agency If
it be asked whether we can merge gravity itself in some still higher law, the answer must de-
pend upon the facts. Are there any other forces, at present held distinct from gravity, that
we may hope to make fraternize with it, so as to join in constituting a higher unity ? Gravity
is an attractive force ; and another great attractive force is cohesion, or the force that binds
together the atoms of solid matter. Might we, then, join these two in a still higher unity, ex-
pressed under a more comprehensive law ? Certainly we might, but not to any advantage.
The two kinds of force agree in the one point, attraction, but they agree in no other ; indeed,
in the manner of the attraction, they differ widely ; so widely that we should have to state
totally distinct laws for each. Gravity is common to all matter, and equal in amount in equal
masses of matter, whatever be the kind ; it follows the law of the diffusion of space from a
point (the inverse square of the distance); it extends to distances unlimited; it is indestructi-
ble and invariable. Cohesion is special for each separate substance ; it decreases according
to distance much more rapidly than the inverse square, vanishing entirely at very small dis-
tances. Two such forces have not sufficient kindred to be generalized into one force ; the
generalization is only illusory ; the statement of the difference would still make two forces ;
while the consideration of one would not in any way simplify the phenomena of the other, as
happened in the generalization of gravity itself."
To the impassable limit of the explanation of laws of nature, set forth in the text, must
therefore be added a further limitation. Although, when the phenomena to be explained are
not, in their own nature, generically distinct, the attempt to refer them to the same cause is
scientifically legitimate ; yet to the success of the attempt it is indispensable that the cause
should be shown to be capable of producing them according to the same law. Otherwise the
unity of cause is a mere guess, and the generalization only a nominal one, which, even if ad-
mitted, would not diminish the number of ultimate laws of nature.
* Cours de Philosophie Positive, ii., 656.
HYPOTHESES. 349
properties of the different kinds of substances, but depend on conditions
capable of being superinduced upon all substances ; since there is no sub-
stance which can not, according to the kind of light thrown upon it, be
made to assume almost any color; and since almost every change in the
mode of aggregation of the particles of the same substance is attended
with alterations in its color, and in its optical properties generally.
The really weak point in the attempts which have been made to account
for colors by the vibrations of a fluid, is not that the attempt itself is un-
philosophical, but that the existence of the fluid, and the fact of its vibra-
tory motion, are not. proved, but are assumed, on no other ground than
the facility they are supposed to afford of explaining the phenomena. And
this consideration leads to the important question of the proper use of -
scientific hypotheses, the connection of which with the subject of the ex-
planation of the phenomena of nature, and of the necessary limits to that
explanation, need not be pointed out.
§ 4. An hypothesis is any supposition which we make (either without
actual evidence, or on evidence avowedly insufficient) in order to endeavor
to deduce from it conclusions in accordance with facts which are known to
be real; under the idea that if the conclusions to which the hypothesis
leads are known truths, the hypothesis itself either must be, or at least is
likely to be, true. If the hypothesis relates to the cause or mode of pro-
duction of a phenomenon, it will serve, if admitted, to explain such facts as
are found capable of being deduced from it. And this explanation is the
purpose of many, if not most hypotheses. Since explaining, in the scien-
tific sense, means resolving a uniformity which is not a law of causation,
into the laws of causation from which it results, or a complex law of causa-
tion into simpler and more general ones from which it is capable of being
deductively inferred, if there do not exist any known laws which fulfill
this requirement, we may feign or imagine some which would fulfill it;
and this is making an hypothesis.
An hypothesis being a mere supposition, there are no other limits to
hypotheses than those of the human imagination ; we may, if we please,
imagine, by way of accounting for an effect, some cause of a kind utterly
unknown, and acting according to a law altogether fictitious. But as hy-
potheses of this sort would not have any of the plausibility belonging to
those which ally themselves by analogy with known laws of nature, and be-
sides would not supply the want which arbitrary hypotheses are generally
invented to satisfy, by enabling the imagination to repi-esent to itself an
obscure phenomenon in a familiar light, there is probably no hypothesis
in the history of science in which both the agent itself and the law of its
operation were fictitious. Either the phenomenon assigned as the cause is
real, but the law according to which it acts merely supposed ; or the cause
is fictitious, but is supposed to produce its effects according to laws similar
to those of some known class of phenomena. An instance of the first kind
is afforded by the different suppositions made respecting the law of the
planetary central force, anterior to the discovery of the true law, that the
force varies as the inverse square of the distance; which also suggested
itself to Newton, in the first instance, as an hypothesis, and was verified
by proving that it led deductively to Kepler's laws. Hypotheses of the
second kind are such as the vortices of Descartes, which were fictitious,
but were supposed to obey the known laws of rotatory motion ; or the
two rival hypotheses respecting the nature of light, the one ascribing
350 INDUCTION.
the phenomena to a fluid emitted from all luminous bodies, the Wher (now
generally received) iattributing them to vibratory motions among the par-
ticles of an ether pervading all space. Of the existence of either fluid
there is no evidence, save the explanation they are calculated to afford of
some of the phenomena; but they are supposed to produce their effects
according to known laws: the ordinary laws of continued locomotion in
the one case, and in the other those of the propagation of undulatory
movements among the particles of an elastic fluid.
According to the foregoing remarks, hypotheses are invented to enable
the Deductive Method to be earlier applied to phenomena. But* in order to
discover the cause of any phenomenon by the Deductive Method, the proc-
ess must consist of three parts : induction, ratiocination, and verification.
Induction (the place of which, however, may be supplied by a prior deduc-
tion), to ascertain the laws of the causes ; ratiocination, to compute from
those laws how the causes will operate in the particular combination known
to exist in the case in hand ; verification, by comparing this calculated ef-
fect with the actual phenomenon. No one of these three parts of the
process can be dispensed with. In the deduction which proves the iden-
tity of gravity with the central force of the solar system, all the three are
found. First, it is proved from the moon's motions, that the earth at-
tracts her with a force varying as the inverse square of the distance. This
(though partly dependent on prior deductions) corresponds to the first, or
purely inductive, step : the ascertainment of the law of the cause. Second-
ly, from this law, and from the knowledge previously obtained of the
moon's mean distance from the earth, and of the actual amount of her de-
flection from the tangent, it is ascertained with what rapidity the earth's
attraction would cause the moon to fall, if she were no further off, and no
more acted upon by extraneous forces, than terrestrial bodies are : that is
the second step, the ratiocination. Finally, this calculated velocity being
compared with the observed velocity with which all heavy bodies fall,
by mere gravity, toward the surface of the earth (sixteen feet in the first
second, forty-eight in the second, and so forth, in the ratio of the odd num-
bers, 1, 3, 5, etc.), the two quantities are found to agree. The order in
which the steps are here presented was not that of their discovery ; but it is
their correct logical order, as portions of the proof that the same attraction
of the earth which causes the moon's motion causes also the fall of heavy
bodies to the earth : a proof which is thus complete in all its parts.
Now, the Hypothetical Method suppresses the first of the three steps,
the induction to ascertain the law; and contents itself with the other two
operations, ratiocination and verification ; the law which is reasoned from
being assumed instead of proved.
This process may evidently be legitimate on one supposition, namely, if
the nature of the case be such that the final step, the verification, shall
amount to, and fulfill the conditions of, a complete induction. We want
to be assured that the law we have hypothetically assumed is a true one ;
and its leading deductively to true results will afford this assurance, pro-
vided the case be such that a false law can not lead to a true result ; pro-
vided no law, except the very one which we have assumed, can lead deduct-
ively to the same conclusions which that leads to. And this proviso is
often realized. For example, in the very complete specimen of deduction
which we just cited, the original major premise of the ratiocination, the
* Vide supra, book iii., chap. xi.
HYPOTHESES. 36 X
law of the attractive force, was ascertained in this mode; by this legitimate
•employment of the Hypothetical Method. Newton began by an assump-
tion that the force which at each instant deflects a planet from its rectilin-
eal course, and makes it describe a curve round the sun, is a force tending
directly toward the sun. He then proved that if this be so, the planet will
describe, as we know by Kepler's first law that it does describe, equal areas
in equal times ; and, lastly, he proved that if the force acted in any other
■direction whatever, the planet would not describe equal areas in equal
times. It being thus shown that no other hypothesis would accord with
the facts, the assumption was proved ; the hypothesis became an inductive
truth. Not only did Newton ascertain by this hypothetical process the
direction of the deflecting force ; he proceeded in exactly the same manner
to ascertain the law of variation of the quantity of that force. He assumed
that the force varied inversely as the square of the distance ; showed that
from this assumption the remaining two of Kepler's laws might be de-
duced ; and, finally, that any other law of variation would give results in-
consistent with those laws, and inconsistent, therefore, with the real mo-
tions of the planets, of which Kepler's laws were known to be a correct
■expression.
I have said that in this case the verification fulfills the conditions of an
induction; but an induction of what sort? On examination we find that
it conforms to the canon of the Method of Difference. It affords the two
instances, ABC, abc, and B C, be. A represents central force ; A B C,
the planets plus a central force ; B C, the planets apart from a central
force. The planets with a central force give a, areas proportional to the
times; the planets without a central force give 6c (a set of motions) -with-
out a, or with something else instead of a. This is the Method of DifiEer-
■ence in all its strictness. It is true, the two instances which the method
requires are obtained in this case, not by experiment, but by a prior de-
duction. But that is of no consequence. It is immateiial what is the
nature of the evidence from which we derive the assurance that ABC
will produce abc, and BC only be; it is enough that we have that as-
surance. In the present case, a process of reasoning furnished Newton
with the very instances which, if the nature of the case had admitted of it,
he would have sought by experiment.
It is thus perfectly possible, and indeed is a very common occui-rence,
that what was an hypothesis at the beginning of the inquiry becomes a
proved law of nature before its close. But in order that this should hap-
pen, we must be able, either by deduction or experiment, to obtain both the
instances which the Method of Difference requires. That we are able from
the hypothesis to deduce the known facts, gives only the affirmative in-
stance, A B C, a 6 c. It is equally necessary that we should be able to ob-
tain, as Newton did, the negative instance BC, 6c/ by showing that no
antecedent, except the one assumed in the hypothesis, would in conjunc-
tion with B C produce a.
Now it appears to me that this assurance can not be obtained, when the
cause assumed in the hypothesis is an unknown cause imagined solely to
account for a. When we are only seeking to determine the precise law of
a cause already ascertained, or to distinguish the particular agent which is
in fact the cause, among several agents of the same kind, one or other of
•which it is already known to be, we may then obtain the negative instance.
An inquiry which of the bodies of the solar system causes by its attraction
some particular irregularity in the orbit or periodic time of some satellite
352 INDUCTION.
or comet, would be a case of the second description, lifewton's was a case
of the first. If it had not been previously known that the planets were
hindered from moving in straight lines by some force tending toward the
interior of their orbit, though the exact direction was doubtful ; or if it
had not been known that the force increased in some proportion or other
as the distance diminished, and diminished as it increased, Newton's ar-
gument would not have proved his conclusion. These facts, however, be-
ing already certain, the range of admissible suppositions was limited to
the various possible directions of a line, and the various possible numerical
relations between the variations of the distance, and the variations of the
attractive force. Now among these it was easily shown that different sup-
positions could not lead to identical consequences.
Accordingly, Newton could not have performed his second great scien-
tific operation : that of identifying terrestrial gravity with the central force
of the solar system by the same hypothetical method. When the law of
the moon's attraction had been proved from the data of the moon itself,
then, on finding the same law to accord with the phenomena of terrestrial
gravity, he was warranted in adopting it as the law of those phenomena
likewise ; but it would not have been allowable for him, without any lunar
data, to assume that the moon was attracted toward the earth with a force
as the inverse square of the distance, merely because that ratio would
enable him to account for terrestrial gravity; for it would have been im-
possible for him to prove that the observed law of the fall of heavy bodies
to the earth could not result from any force, save one extending to the
moon, and proportional to the inverse square.
It_ appears, then, to be a condition of the most genuinely scientific hy-
pothesis, that it be not destined always to remain an hypothesis, but be of
such a nature as to be either proved or disproved by comparison with ob-
served facts. This condition is fulfilled when the effect is already known to
depend on the very cause supposed, and the hypothesis relates only to the
precise mode of dependence ; the law of the variation of the effect according
to the variations in the quantity or in the i-elations of the cause. With these
may be classed the hypotheses which do not make any supposition with re-
gard to causation, but only with regard to the law of correspondence between
facts which accompany each other in their variations, though there may be
no relation of cause and effect between them. Such were the different
false hypotheses which Kepler made respecting the law of the refraction
of light. It was known that the direction of the line of refraction varied
with every variation in the direction of the line of incidence, but it was
not known how; that is, what changes of the one corresponded to the dif-
ferent changes of the other. In this case any law different from the true
one must have led to false results. And, lastly, we must add to these all
hypothetical modes of merely representing or describing phenomena ; such
as the hypothesis of the ancient astronomers that the heavenly bodies
moved in circles ; the various hypotheses of eccentrics, deferents, and epi-
cycles, which were added to that original hypothesis; the nineteen false
hypotheses which Kepler made and abandoned respecting the form of the
planetary orbits; and even the doctrine in which he finally rested, that
those orbits are ellipses, which was but an hypothesis like the rest until
verified by facts.
In all these cases, verification is proof ; if the supposition accords with
the phenomena thei-e needs no other evidence of it. But in order that this
may be the case, T conceive it to be necessary, when the hypothesis relates
HYPOTHESES. 353
to causation, that the supposed cause should not only be a real phenomenon,
something actually existing in nature, but should be already known to ex-
ercise, or at least to be capable of exercising, an influence of some sort over
the effect. In any other case, it is no sufficient evidence of the truth of the
hypothesis that we are able to deduce the real phenomena from it.
Is it, then, never allowable, in a scientific hypothesis, to assume a cause,
but only to ascribe an assumed law to a known cause ? I do not assert
this. I only say, that in the latter case alone can the hypothesis be received
as true merely because it explains the phenomena. In the former case it
may be very useful by suggesting a line of investigation which may possi-
bly terminate in obtaining real proof. But for this purpose, as is justly
remarked by M. Comte, it is indispensable that the cause suggested by the
hypothesis should be in its own nature susceptible of being proved by other
evidence. This seems to be the philosophical import of Newton's maxim,
(so often cited with approbation by subsequent writers), that the cause as-
signed for any phenomenon must 'not only be such as if admitted would
explain the phenomenon, but must also be a vera causa. What he meant
by a vera causa Newton did not indeed very explicitly define ; and Dr.
Whewell, who dissents from the propriety of any such restriction upon the
latitude of framing hypotheses, has had little difficulty in showing* that his
conception of it was neither precise nor consistent with itself; according-
ly his optical theory was a signal instance of the violation of his own rule.
It is certainly not necessary that the cause assigned should be a cause al-
ready known ; otherwise we should sacrifice our best opportunities of be-
coming acquainted with new causes. But what is true in the maxim is,
that the cause, though not known previously, should be capable of being
known thereafter ; that its existence should be capable of being detected,
and its connection with the effect ascribed to it should be susceptible of
being proved, by independent evidence. The hypothesis, by suggesting
observations and experiments, puts us on the road to that independent ev-
idence, if it be really attainable ; and till it be attained, the hypothesis
ought only to count for a more or less plausible conjecture.
§ 5. This function, however, of hypotheses, is one which must be reckon-
ed absolutely indispensable in science. "When Newton said, " Hypotheses
non fingo," he did not mean that he deprived himself of the facilities of
investigation afforded by assuming in the first instance what he hoped ul-
timately to be able to prove. Without such assumptions, science could
never have attained its present state ; they are necessary steps in thQ prog-
ress to something more certain ; and nearly every thing which is now theo-
ry was once hypothesis. Even in purely experimental science, some in-
ducement is necessai-y for trying one experiment rather than another ; and
though it is abstractedly possible that all the experiments which have been
tried, might have been produced by the mere desire to ascertain what
would happen in certain circumstances, without any previous conjecture
as to the result ; yet, in point of fact, those unobvious, delicate, and often
cumbrous and tedious processes of experiment, which have thrown most
light upon the general constitution of nature, would hardly ever have been
undertaken by the persons or at the time they wore, unless it had seemed
to depend on them whether some general doctrine or theory which had
been suggested, but not yet proved, should be admitted or not. If this be
* Philosophy 0/ Discovery, p. 185 et aeq.
23
354 INDUCTION.
true even of merely experimental inquiry, the conversion of experimental
into deductive truths could still less have been effected without large
temporary assistance from hypotheses. The process of tracing regularity
in any complicated, and at first sight confused, set of appearances, is neces-
sarily tentative; we begin by making any supposition, even a false one, to
[?ee what consequences will follow from it ; and by observing how these
differ from the real phenomena, we learn what corrections to make in our
assumption. The simplest supposition which accords with the more obvi-
ous facts is the best to begin with ; because its consequences are the most
easily traced. This rude hypothesis is then rudely corrected, and the op-
eration repeated ; and the comparison of the consequences deducible from
-the corrected hypothesis, with the observed facts, suggests still further
correction, until the deductive results are at last made to tally with the phe-
nomena. " Some fact is as yet little understood, or some law is unknown ;
we frame on the subject an hypothesis as accordant as possible with the
whole of the data already possessed ; arid the science, being thus enabled
to move forward freely, always ends by leading to new consequences ca-
pable of observation, which either confirm or refute, unequivocally, the
first supposition." Neither induction nor deduction would enable us to
understand even the simplest phenomena, " if we did not often commence
by anticipating on the results ; by making a provisional supposition, at first
essentially conjectural, as to some of the very notions which constitute the
final object of the inquiry."* Let any one watch the manner in which he
himself unravels a complicated mass of evidence ; let him observe how, for
instance, he elicits the true history of any occurrence from the involved
statements of one or of many witnesses ; he will find that he does not take
all the items of evidence into his mind at once, and attempt to weave them
together ; he extemporizes, from a few of the particulars, a first rude the-
ory of the mode in which the facts took place, and then looks at the other
statements one by one, to try whether they can be reconciled with that
provisional theory, or what alterations or additions it requires to make it
square with them. In this way, which has been justly compared to the
Methods of Approximation of mathematicians, we arrive, by means of hy-
potheses, at conclusions not hypothetical.!
* Comte, Philosophie Positive, ii., 434-437.
t As an example of legitimate hypothesis according to the test here laid down, has been
justly cited. that of Broussais, who, proceeding on the very rational principle that every dis-
ease must ori^nate in some definite part or other of the organism, boldly assumed that cer-
tain fevers, which not being known to be local were called constitutional, had their origin in
the mucous membrane of the alimentary canal. The supposition was, indeed, as is now gen-
erally admitted, erroneous ; but he was justified in making it, since by deducing the conse-
quences of the supposition, and comparing them with the facts of those maladies, he might be
certain of disproving his hypothesis if it was ill founded, and might expect that the compari-
son would materially aid him in framing another more conformable to the phenomena.
The doctrine now universally received that the earth is a natural magnet, was originally an
hypothesis of the celebrated Gilbert.
Another hypothesis, to the legitimacy of which no objection can lie, and which is well cal-
culated to light the path of scientific inquiry, is that suggested T)y several recent writers, that
the brain is a voltaic pile, and that each of its pulsations is a discharge of electricity through
the system. It has been remarked that the sensation felt by the hand from the beating of a
brain, bears a strong resemblance to a voltaic shock. And the hypothesis, if followed to its
consequences, might afford a plausible explanation of many physiological facts, while there is.
nothing to discourage the hope that we may in time sufficiently understand the conditions of
voltaic phenomena to render the truth of the hypothesis amenable to observation and experi-
ment.
The attempt to localize, in different regions of the brain, the physical organs of our different
HYPOTHESES. 355
§ 6. It is perfectly consistent with the spirit of the method, to assume in
this provisional manner not only an hypothesis respecting the law of what
we already know to be the cause, but an hypothesis respecting the cause
itself. It is allowable, useful, and often even necessary, to begin by asking
•ourselves what cause may have produced the effect, in order that we may
know in what direction to look out for evidence to determine whether it
actually did. The vortices of Descartes would have been a perfectly legit-
imate hypothesis, if it had been possible, by any mode of exploration which
we could entertain the hope of ever possessing, to bring the reality of the
vortices, as a fact in nature, conclusively to the test of observation. The
vice of the hypothesis was that it could not lead to any course of inves-
tigation capable of converting it from an hypothesis into a proved fact.
It might chance to be cKsproved, either by some want of correspondence
with the phenomena it purported to explain, or (as actually happened) by
isome extraneous fact. " The free passage of comets thi-ough the spaces in
which these vortices should have been, convinced men that these vortices
did not exist."* But the hypothesis would have been false, though no such
•direct evidence of its falsity had been procurable. Direct evidence of its
truth there could not be.
The prevailing hypothesis of a luminiferous ether, in other respects not
without analogy to that of Descartes, is not in its own nature entirely cut
■off from the possibility of direct evidence in its favor. It is well known
that the difference between the calculated and the observed times of the
periodical return of Encke's comet, has led to a conjecture that a medium
capable of opposing resistance to motion is diffused through space. If
this surmise should be confirmed, in the course of ages, by the gradual ac-
■cumulation of a similar variance in the case of the other bodies of the solar ;
system, the luminiferous ether would have made a considerable advance
toward the character of a vera causa, since the existence would have been
ascertained of a great cosmical agent, possessing some of the attributes
which the hypothesis assumes ; though there would still remain many dif-
ficulties, and the identification of the ether with the resisting medium
would even, I imagine, give rise to new ones. At present, however, this
mental faculties and propensities, was, on the part of its original author, a legitimate example
of a scientific hypothesis ; and we ought not, therefore, to blame him for the extremely slight
grounds on which he often proceeded, in an operation which could only be tentative, though we
may regret that materials barely sufiBcient for a first rude hypothesis should have been hastily
worked up into the vain semblance of a science. If there be really a connection between the
scale of mental endowments and the various degrees of complication in the cerebral system, the
nature of that connectioi. was in no other way so likely to be brought to light as by framing,
in the first instance, an hypothesis similar to that of Gall. But the verification of any such
hypothesis is attended, from the peculiar nature of the phenomena, with difiiculties which
phrenologists have not shown themselves even competent to appreciate, much less to overcome.
Mr. Darwin's remarkable speculation on the Origin of Species is another unimpeachable
example of a legitimate hypothesis. What he terms "natural selection" is not only a vera
causa, but one proved to be capable of producing efiects of the same kind with those which
the hypothesis ascribes to it ; the question of possibility is entirely one of degree. It is un-
reasonable to accuse Mr. Darwin (as has been done) of violating the rules of Induction. The
rules of Induction are concerned with the conditions of Proof. Mr. Darwin has never pre-
tended that his doctrine was proved. He was not bound by the rules of Induction, but by
those of Hypothesis. And these last have seldom been more completely fulfilled. He has
•opened a path of inquiry full of promise, the results of which none can foresee. And is it
not a wonderful feat of scientific knowledge and ingenuity to have rendered so bold a sugges-
tion, which the first impulse of every one was to reject at once, admissible and discussible,
even as a conjecture ?
* Whewell's Phil, of Discovery, pp. 275, 276.
356 INDUCTION.
supposition can not be looked upon as more than a conjecture; the exist-
ence of the ether still rests on the possibility of deducing from its as-
sumed laws a considerable number of actual phenomena ; and this evidence
I can not regard as conclusive, because we can not have, in the case of such
an hypothesis, the assurance that if the hypothesis be false it must lead to
results at variance with the true facts.
Accordingly, most thinkers of any degree of sobriety allow that an hy-
pothesis of this kind is not to be received as probably true because it ac-
counts for all the known phenomena; since this is a condition sometimes
fulfilled tolerably well by two- conflicting hypotheses ; while there are prob-
ably many others which are equally possible, but which, for want of any
thing analogous in our experience, our minds are unfitted to conceive. But
it seems to be thought that an hypothesis of the sort in question is entitled
to a more favorable reception, if, besides accounting for all the facts previ-
ously known, it has led to the anticipation and prediction of others which
experience afterward verified; as the undulatory theory of light led to the
prediction, subsequently realized by experiment, that two luminous rays
might meet each other in such a manner as to produce darkness. Such
predictions and their fulfillment are, indeed, well calculated to impress the
uninformed, whose faith in science rests solely on similar coincidences be-
tween its prophecies and what comes to pass. But it is strange that any
considerable stress should be laid upon such a coincidence by persons of
scientific attainments. If the laws of the propagation of light accord with
those of the vibrations of an elastic fluid in as many respects as is necessa-
ry to make the hypothesis afford a correct expression of all or most of the
phenomena known at the time, it is nothing strange that they should ac-
cord with each other in one respect more. Though twenty such coinci-
dences should occur, they would not prove the reality of the undulatory
ether ; it would not follow that the phenomena of light were results of the
laws of elastic fluids, but at most that they are governed by laws partially
identical with these ; which, we may observe, is already certain, from the
fact that the hypothesis in question could be for a moment tenable.*
Cases may be cited, even in our imperfect acquaintance with nature, where
agencies that we have good reason to consider as radically distinct produce
their effects, or some of their effects, according to laws which are identical.
The law, for example, of the invei'se square of the distance, is the measure
of the intensity not only of gravitation, but (it is believed) of illumination,
and of heat diffused fi-om a centre. Yet no one looks upon this identity
as proving similarity in the mechanism by which the three kinds of phe-
nomena are produced.
According to Dr. Whewell, the coincidence of results predicted from an
hypothesis with facts afterward observed, amounts to a conclusive proof
of the truth of the theory. " If I copy a long series of letters, of which
the last half-dozen are concealed, and if I guess these aright, as is found
to be the case when they are afterward uncovered, this must be because I
have made out the import of the inscription. To say that because I have
* What has most contributed to accredit the hypothesis of a physical medium for the con-
veyance of light, is the certain fact that light travels (which can not be proved of gravita-
tion) ; that its communication is not instantaneous, but requires time ; and that it is intercepted
(which gravitation is not) by intervening objects. These are analogies between its phenome-
na and those of the mechanical motion of a solid or fluid substance. But we are not entitled
to assume that mechanical motion is the only power in nature capable of exhibiting those at-
tributes.
HYPOTHESES. 357
copied all that I could see, it is nothing strange that I should guess those
which I can not see, would be absurd, without supposing such a ground for
guessing."* If any one, from examining the greater part of a long inscrip-
tion, can interpret the characters so that the inscription gives a rational
meaning in a known language, there is a strong presumption that his inter-
pretation is correct; but I do not think the presumption much increased
by his being able to guess the few remaining letters without seeing them ;
for we should naturally expect (when the nature of the case excludes
chance) that even an erroneous interpretation which accorded with all the
visible parts of .the inscription would accord also with the small remain-
der ; as would be the case, for example, if the inscription had been design-
edly so contrived as to admit of a double sense. I assume that the uncov-
ered characters afford an amount of coincidence too great to be merely
casaal; otherwise the illustration is not a fair one. No one supposes
the agreement of the phenomena of light with the theory of undulations
to be merely fortuitous. It must arise from the actual identity of some
of the laws of undulations with some of those of light; and if thei'e be
that identity, it is reasonable to suppose that its consequences would not
€nd with the phenomena which first suggested the identification, nor be
«ven confined to such phenomena as were known at the time. But it does
not follow, because some of the laws agree with those of undulations, that
there are any actual undulations ; no more than it followed because some
(though not so many) of the same laws agreed with those of the projection
of particles, that there was actual emission of particles. Even the undula-
tory hypothesis does not account for all the phenomena of light. The nat-
ural colors of objects, the compound nature of the solar ray, the absorption
of light, and its chemical and vital action, the hypothesis leaves as myste-
rious as it found them ; and some of these facts are, at least apparently,
more reconcilable with the emission theory than with that of Young and
Fresnel. Who knows but that some third hypothesis, including all these
phenomena, may in time leave the undulatory theory as far behind as that
has left the theory of Newton and his successors ?
To the statement, that the condition of accounting for all the known
phenomena is often fulfilled equally well by two conflicting hypotheses.
Dr. Whewell makes answer that he knows "of no such case in the history
of science, where the phenomena are at all numerous and complicated."!
Such an affirmation, by a writer of Dr. Whewell's minute acquaintance with
the history of science, would carry great authority, if he had not, a few
pages before, taken pains to refute it,J by maintaining that even the ex-
ploded scientific hypotheses might always, or almost always, have been so
modified as to make them correct i-epresentations of the phenomena. The
hypothesis of vortices, he tells us, was, by successive modifications, brought
to coincide in its results with the Newtonian theory and with the facts.
The vortices did not, indeed, explain all the phenomena which the Newto-
nian theory was ultimately found to account for, such as the precession of
the equinoxes ; but this phenomenon was not, at the time, in the contem-
plation of either party, as one of the facts to be accounted for. All the
facts which they did contemplate, we may believe on Dr. Whewell's au-
thority to have accorded as accurately with the Cartesian hypothesis, in its
finally improved state, as with Newton's.
But it is not, I conceive, a valid reason for accepting any given hypothe-
* Phil, of Discovery, p. 27i. t P. 271. t P. 251 and the whole of Appendix G.
358 INDUCTION.
sis, that we are unable to imagine any other which will account for the
facts. Thei'e is no necessity for supposing that the true explanation must
be one which, with only our present experience, we could imagine. Among
the natural agents with which we are acquainted, the vibrations of an elas-
tic fluid may be the only one whose laws bear a close resemblance to those
of light; but we can not tell that there does not exist an unknown cause,
other than an elastic ether diffused through space, yet producing effects,
identical in some respects with those which would result from the undula-
tions of such an ether. To assume that no such cause can exist, appears to-
me an extreme case of assumption without evidence. And at the risk of
being charged with want of modesty, I can not help expressing astonish-
ment that a philosopher of Dr. Whewell's abilities and attainments should
have written an elaborate treatise on the philosophy of induction, in whichi
he recognizes absolutely no mode of induction except that of trying hy-
pothesis after hypothesis until one is found which fits the phenomena;,
which one, when found, is to be assumed as true, with no other reservation
than that if, on re-examination, it should appear to assume more than is-
needful for explaining the phenomena, the superfluous part of the assump-
tion should be cut off. And this without the slightest distinction between
the cases in which it may be known beforehand that two different hypoth-
eses can not lead to the same result, and those in which, for aught we can
ever know, the range of suppositions, all equally consistent with the phe-
nomena, may be infinite.*
Nevertheless, I do not agree with M. Comte in condemning those who
employ themselves in working out into detail the application of these hy-
potheses to the explanation of ascertained facts, provided they bear in
mind that the utmost they can prove is, not that the hypothesis is, but that
it may be true. The ether hypothesis has a very strong claim to be so fol-
lowed out, a claim greatly strengthened since it has been shown to afford
a mechanism which would explain the mode of production, not of light
only, but also of heat. Indeed, the speculation has a smaller element of
hypothesis in its application to heat, than in the case for which it was-
originally framed. We have proof by our senses of the existence of molec-
ular movement among the particles of all heated bodies ; while we have no
similar experience in the case of light. When, therefore, heat is communi-
cated from the sun to the earth across apparently empty space, the chaia
* In Dr. Whewell's latest version of his theory (Philosophy of Discovery, p. 331) he makes-
a concession respecting the medium of the transmission of light, which, taken in conjunction
with the rest of his doctrine on the subject, is not, I confess, Very intelligible to me, but which
goes far toward removing, if it does not actually remove, the whole of the difference between
us. He is contending, against Sir William Hamilton, that all matter has weight. Sir Wil-
liam, in proof of the contrary, cited the luminiferous ether, and the calorific and electric fluids,
"which," he said, "we can neither denude of their character of substance, nor clothe with
the attribute of weight." " To which," continues Dr. Whewell, " my reply is, that precisely
because I can not clothe these agents with the attribute of Weight, I do denude them of the
character of Substance. They are not substances, but agencies. These Imponderable Agent*
are not properly called Imponderable Fluids. This I conceive that I have proved." Noth-
ing can be more philosophical. But if the luminiferous ether is not matter, and fluid matter,
too, what is the meaning of its undulations ? Can an agency undulate ? Can there be al-
ternate motion forward and backward of the particles of an agency ? And does not the whole-
mathematical theory of the undulations imply them to be material ? Is it not a series of de-
ductions from the known properties of elastic fluids? This opinion of Dr. Whewell reduces-
the undulations to a figure of speech, and the undulatory theory to the proposition which all
must admit, that the transmission of light takes place according to laws which present a very
striking and remarkable agreement with those of undulations. If Dr. Whewell is prepared
to stand by this doctrine, I have no difference with him on the subject.
HYPOTHESES. 359
of causation has molecular motion both at the beginning and end. The
hypothesis only makes the motion continuous by extending it to the mid-
dle. Now, motion in a body is known to be capable of being imparted ta
another body contiguous to it ; and the intervention of a hypothetical elas-
tic fluid occupying the space between the sun and the earth, supplies the
contiguity which is the only condition wanting, and which can be supplied
by no supposition but that of an intervening medium. The supposition,
notwithstanding, is at best a probable conjecture, not a proved truth. For
there is no proof that contiguity is absolutely required for the communica-
tion of motion from one body to another. Contiguity does not always ex-
ist, to our senses at least, in the cases in which motion produces motion..
The forces which go under the name of attraction, especially the greatest
of all, gravitation, are examples of motion producing motion without ap-
parent contiguity. When a planet moves, its distant satellites accompany
its motion. The sun carries the whole solar system along with it in the-
progress which it is ascertained to be executing through space. And even
if we were to accept as conclusive the geometrical reasonings (strikingly-
similar to those by which the Cartesians defended their vortices) by which,
it has been attempted to show that the motions of the ether may account
for gravitation itself, even then it would only have been proved that the.
supposed mode of production may be, but not that no other mode can be,,
the true one.
§ T. It is necessary, before quitting the subject of hypotheses, to guard
against the appearance of reflecting upon the scientific value of several
branches of physical inquiry, which, though only in their infancy, I hold to
be strictly inductive. There is a great difference between inventing agen-
cies to account for classes of phenomena, and endeavoring, in conformity
with known laws, to conjecture what former collocations of known agents
may have given birth to individual facts still in existence. The latter is
the legitimate operation of inferring from an observed effect the existence,.
in time past, of a cause similar to that by which we know it to be produced
in all cases in which we have actual experience of its origin. This, for ex-
ample, is the scope of the inquiries of geology ; and they are no more illogic-
al or visionary than judicial inquiries, which also aim at discovering a past,
event by inference from those of its effects which still subsist. As we can
ascertain whether a man was murdered or died a natural death, from the-
indications exhibited by the corpse, the presence or absence of signs of
struggling on the ground or on the adjacent objects, the marks of blood,,
the footsteps of the supposed murderers, and so on, proceeding throughout
on uniformities ascertained by a perfect induction without any mixture of
hypothesis ; so if we find, on and beneath the surface of our planet, masses
exactly similar to deposits from water, or to results of the cooling of mat-
ter melted by fire, we may justly conclude that such has been their origin ;,
and if the effects, though similar in kind, are on a far larger scale than any
which are now produced, we may rationally, and without hypothesis, con-
clude either that the causes existed formerly with greater intensity, or that
they have operated during an enormous length of time. Further than this
no geologist of authority has, since the rise of the present enlightened,
school of geological speculation, attempted to go.
In many geological inquiries it doubtless happens that though the laws-
to which the phenomena are ascribed are known laws, and the agents
known agents, those agents are not known to have been present in the par-
360 INDUCTION.
ticular case. In the speculation respecting the igneous origin of trap or
granite, the fact does not admit of direct proof that those substances have
been actually subjected to intense heat. But the same thing might be said
of all judicial inquiries which proceed on circumstantial evidence. We can
conclude that a man was murdered, though it is not proved by the testimony
of eye-witnesses that some person who had the intention of murdering him
was present on the spot. It is enough for most purposes, if no other known
cause could have generated the effects shown to have been produced.
The celebrated speculation of Laplace concerning the origin of the earth
and planets, participates essentially in the inductive character of modern
geological theory. The speculation is, that the atmosphere of the sun
originally extended to the present limits of the solar system ; from whicfL
by the process of cooling, it has contracted to its present dimensions ; and
since, by the general principles of mechanics the rotation of the sun and
of its accompanying atmosphere must increase in rapidity as its volume
<Jiminishe8, the increased centrifugal force generated by the more rapid
rotation, overbalancing the action of gravitation, has caused the sun to
abandon successive rings of vaporous matter, which are supposed to have
condensed by cooling, and to have become the planets. There is in this
theory no unknown substance introduced on supposition, nor any unknown
property or law ascribed to a known substance. The known laws of mat-
ter authorize us to suppose that a body which is constantly giving out so
large an amount of heat as the sun is, must be progressively cooling, and
that, by the process of cooling it must contract ; if, therefore, we endeavor,
from the present state of that luminary, to infer its state in a time long
past, we must necessarily suppose that its atmosphere extended much far-
ther than at present, and we are entitled to suppose that it extended as far
as we can trace effects such as it might naturally leave behind it on retir-
ing; and such the planets are. These suppositions being made, it follows
from known laws that successive zones of the solar atmosphere might be
abandoned; that these would continue to revolve round the sun with the
same velocity as when they formed part of its substance ; and that they
would cool down, long before the sun itself, to any given temperature, and
consequently to that at which the greater part of the vaporous matter of
which they consisted would become liquid or solid. The known law of
gravitation would then cause them to agglomerate in masses, which would
assume the shape our planets actually exhibit ; would acquire, each about
its own axis, a rotatory movement ; and would in that state revolve, as the
planets actually do, about the sun, in the same direction with the sun's ro-
tation, but with less velocity, because in the same periodic time which the
sun's rotation occupied when his atmosphere extended to that point. There
is thus, in Laplace's theory, nothing, strictly speaking, hypothetical; it is
an example of legitimate reasoning from a present effect to a possible past
cause, according to the known laws of that cause. The theory, therefore,
is, as I have said, of a similar character to the theories of geologists ; but
considerably inferior to them in point of evidence. Even if it were proved
(which it is not) that the conditions necessary for determining the break-
ing off of successive rings would certainly occur, there would still be a
much greater chance of error in assuming that the existing laws of nature
are the same which existed at the origin of the solar system, than in mere-
ly presuming (with geologists) that those laws have lasted through a few
revolutions and transformations of a single one among the bodies of which
that system is composed.
PROGRESSIVE EFFECTS. 36I
CHAPTER XV.
01" PEOGBESSIVE EFFECTS ; AND OF THE CONTINUED ACTION OF CAUSES.
§ 1. In the last four chapters we have traced the general outlines of the
theory of the generation of derivative Iftws from ultimate ones. In the
present chapter our attention will be directed to a particular case of the
derivation of laws from other laws, butf a case so general, and so important
as not only to repay, but to require, a separate examination. This is the
case of a complex phenomenon resulting from one siniple law, by the con-
tinual addition of an effect to itself.
There are some phenomena, some bodily sensations, for example, which
are essentially instantaneous, and whose existence can only be prolonged
by the prolongation of the existence of the cause by which they are pro-
duced. But most phenomena are in their own nature permanent ; having
begun to exist, they would exist forever unless some cause intervened hav-
ing a tendency to alter or destroy them. Such, for example, are all the
facts of phenomena which we call bodies. Water, once produced, will not
of itself relapse into a state of hydrogen and oxygen ; such a change re-
quires some agent having the power of decomposing the compound. Such,
again, are the positions in space and the movements of bodies. No object
at rest alters its position without the intervention of some conditions ex-
traneous to itself; and when once in motion, no object returns to a state
of rest, or alters either its direction or its velocity, unless some new exter-
nal conditions are superinduced. It, therefore, perpetually happens that a
temporary cause gives rise to a permanent effect. The contact of iron
with moist air for a few hours, produces a rust which may endure for cen-
turies; or a projectile force which launches a cannon-ball into space, pro-
duces a motion which would continue forever unless some other forca
counteracted it.
Between the two examples which we have here given, there is a differ-
ence worth pointing out. In the former (in which the phenomenon pro-
duced is a substance, and not a motion of a substance), since the rust re-
mains forever and unaltered unless some new cause supervenes, we may
speak of the contact of air a hundred years ago as even the proximate
cause of the rust which has existed from that time until now. But when
the effect is motion, which is itself a change, we must use a different lan-
guage. The permanency of the effect is now only the permanency of a
series of changes. The second foot, or inch, or mile of motion is not the
mere prolonged duration of the first foot, or inch, or mile, but another fact
which succeeds, and which may in some respects be very unlike the former,
since it carries the body through a different region of space. Now, the
original projectile force which set the body moving is the remote cause of
all its motion, however long continued, but the proximate cause of no mo-
tion except that which took place at the first instant. The motion at any
subsequent instant is proximately caused by the motion which took place
at the instant preceding. It is on that, and not on the original moving
cause, that the motion at any given moment depends. For, suppose that
the body passes through some resisting medium, which partially counter-
362 INDUCTION.
acts the effect of the original impulse, and retards the motion ; this coun-
teraction (it need scarcely here be repeated) is as strict an example of obe-
dience to the law of the impulse, as if the body had gone on moving with
its original velocity ; but the motion which results is different, being now
a compound of the effects of two causes acting in contrary directions, in-
stead of the single effect of one cause. 'Now, what cause does tlie body
obey in its subsequent motion ? The original cause of motion, or the act-
ual motion at the preceding instant? The latter; for when the object
issues from the resisting medium, it continues moving, not with its orig-
inal, but with its retarded velocitjr. The motion having once been dimin-
ished, all that which follows is diminished. The effect changes, because
the cause which it really obeys, the "proximate cause, the real cause in fact,
has changed. This principle is recognized by mathematicians when they
enumerate among the causes by which the motion of a body is at any in-
stant determined the force generated by the previous motion ; an expres-
sion which would be absurd if taken to imply that this " force " was an in-
termediate link between the cause and the effect, but which really means
only the previous motion itself, considered as a cause of further motion.
We must, therefore, if we would speak with perfect precision, consider
each link in the succession of motions as the effect of the link preceding it.
But if, for the convenience of discourse, we speak of the whole series as
one effect, it must be as an effect produced by the original impelling force ;
a permanent effect produced by an instantaneous cause, and possessing the
property of self-perpetuation.
Let us now suppose that the original agent or cause, instead of being in-
stantaneous, is permanent. Whatever effect has been produced up to a
given time, would (unless prevented by the intervention of some new cause)
subsist permanently, even if the cause were to perish. Since, however, the
•cause does not perish, but continues to exist and to operate, it must go on
producing more and more of the effect; and instead of a unifoi-m effect,
"we have a progressive series of effects, arising from the accumulated influ-
ence of a permanent cause. Thus, the contact of iron with the atmosphere
•causes a portion of it to rust ; and if the cause ceased, the effect already
produced would be permanent, but no further effect would be added. If,
however, the cause, namely, exposure to moist air, continues, more and
more of the iron becomes rusted, until all which is exposed is converted
into a red powder, when one of the conditions of the production of rust,
namely, the presence of unoxidized iron, has ceased, and the effect can not
any longer be produced. Again, the earth causes bodies to fall toward it ;
that is, the existence of the earth at a given instant causes an unsupported
body to move toward it at the succeeding instant ; and if the earth .were
annihilated, as much of the effect as is already produced would continue ;
-the object would go on moving in the same direction, with its acquired
velocity, until intercepted by some body or deflected by some other force.
The earth, however, not being annihilated, goes on producing in the sec-
ond instant an effect similar and of equal amount with the first, which two
■effects being added together, there results an accelerated velocity ; and
this operation being repeated at each successive instant, the mere perma-
nence of the cause, though without increase, gives rise to a constant pro-
gressive increase of the effect, so long as all the conditions, negative and
positive, of the production of that effect continue to be realized.
It is obvious that this state of things is merely a case of the Composi-
tion of Causes. A cause which continues in action must on a strict analy-
PROGRESSIVE EFFECTS. 363
•sis be considered as a number of causes exactly similar, successively intro-
duced, and producing by their combination the sum of the effects which
they would severally produce if they acted singly. The progressive rust-
ing of the iron is in strictness the sum of the effects of many particles of
air acting in succession upon corresponding particles of iron. The con-
tinued action of the earth upon a falling body is equivalent to a series of
forces, applied in successive instants, each tending to produce a certain con-
stant quantity of motion ; and the motion at each instant is the sum of the
■effects of the new force applied at the preceding instant, and the motion
already acquired. In each instant a fresh effect, of which gravity is the
proximate cause, is added to the effect of which it was the remote cause ;
or (to express the same thing in another manner), the effect produced by
the earth's influence at the instant last elapsed is added to the sum of the
effects of which the remote causes were the influences exerted by the earth
at all the previous instants since the motion began. The case, therefore,
comes under the principle of a concurrence of causes producing an effisct
€qnal to the sum of their separate effects. But as the causes come into
play not all at once, but successively, and as the effect at each instant is the
sum of the effects of those causes only which have come into action up to
that instant, the'result assumes the form of an ascending sei'ies ; a succes-
sion of sums, each greater than that which preceded it ; and we have thus
a progressive effect from the continued action of a cause.
Since the continuance of the cause influences the effect only by adding
to its quantity, and since the addition takes place according to a fixed law
(equal quantities in equal times), the result is capable of being computed
on mathematical principles. In fact, this case, being that of infinitesimal
increments, is precisely the case which the differential calculus was invent-
ed to meet. The questions, what effect will result from the continual ad-
dition of a given cause to itself, and what amount of the cause, being con-
tinually added to itself, will produce a given amount of the effect, are evi-
dently mathematical questions, and to be treated, therefore, deductively.
If, as we have seen, cases of the Composition of Causes are seldom adapt-
ed for any other than deductive investigation, this is especially true in the
case now examined, the continual composition of a cause with its own pre-
vious effects; since such a case is peculiarly amenable to the deductive
method, while the undistinguishable manner in which the effects are blend-
ed with one another and with the causes, must make the treatment of such
an instance experimentally still more chimerical than in any other case.
§ 2. We shall next advert to a rather more intricate operation of the
same principle, namely, when .the cause does not merely continue in action,
but undergoes, during the same time, a progressive change in those of its
circumstances which contribute to determine the effect. In this case, as
in the former, the total effect goes on accumulating by the continual addi-
tion of a fresh effect to that already produced, but it is no longer by the
addition of equal quantities in equal times ; the quantities added are un-
equal, and even the quality may now be different. If the change in the
state of the permanent cause be progressive, the effect will go through a
■double series of changes, arising partly from the accumulated action of the
cause, and partly from the changes in its action. The effect is still a pro-
gressive effect, produced, however, not by the mere continuance of a cause,
Sut by its continuance and its progressiveness combined.
A familiar example is afforded by the increase of the temperature as
364 INDUCTION.
summer advances, that is, as the sun draws nearer to a vertical position, and
remains a greater number of hours above the horizon. This instance ex-
emplifies in a very interesting manner the twofold operation on the effect,
arising from the continuance of the cause, and from its progressive change.
When once the sun has come near enough to the zenith, and remains above
the horizon long enough, to give more warmth during one diurnal rotation
than the counteracting cause, the earth's- radiation, can carry off, the mere
continuance of the cause would progressively increase the effect, even if the
Bun came no nearer and the days grew no longer ; but in addition to this»
a change takes place in the accidents of the cause (its series of diurnal po-
sitions), tending to increase the quantity of the effect. When the summer
solstice has passed, the progressive change in the cause begins to take place
the reverse way, but, for some time, the accumulating effect of the mere
continuance of the cause exceeds the effect of the changes in it, and the
temperature continues to increase.
Again, the motion of a planet is a progressive effect, produced by causes
at once permanent and progressive. The orbit of a planet is determined
(omitting perturbations) by two causes : first, the action of the central body,
a permanent cause, which alternately increases and diminishes as the planet
draws nearer to or goes farther from its perihelion, and which acts at every
point in a different direction ; and, secondly, the tendency of the planet to
continue moving in the direction and with the velocity which it has already
acquired. This force also grows greater as the planet draws nearer to its
perihelion, because as it does so its velocity increases, and less, as it recedes,
from its perihelion ; and this force as well as the other acts at each point in
a different direction, because at every point the action of the central force,
by deflecting the planet from its previous direction, alters the line in which
it tends to continue moving. The motion at each instant is determined by
the amount and direction of the motion, and the amount and direction of
the sun's action, at the previous instant; and if we speak of the entire rev-
olution of the planet as one phenomenon (which, as it is periodical and
similar to itself, we often find it convenient to do), that phenomenon is the
progressive effect of two permanent and progressive causes, the central
force and the acquired motion. Those causes happening to be progressive
in the particular way which is called periodical, the effect necessarily is so
too; because the quantities to be added together returning in a regular
order, the same sums must also regularly return.
This example is worthy of consideration also in another respect. Though
the causes themselves are permanent, and independent of all conditions
known to us, the changes which take place in the quantities and relations
of the causes are actually caused by the periodical changes in the effects.
The causes, as they exist at any moment, having produced a certain motion,
that motion, becoming itself a cause, reacts upon the causes, and produces.
a change in them. By altering the distance and direction of the central
body relatively to the planet, and the direction and quantity of the force in
the direction of the tangent, it alters the elements which determine the mo-
tion at the next succeeding instant. This change renders the next motion
somewhat different ; and this difference, by a fresh reaction upon the causes,
renders the next motion again different, and so on. The original state of
the causes might have been such that this series of actions modified by
reactions would not have been periodical. The sun's action, and the origi-
nal impelling force, might have been in such a ratio to one another, that the
reaction of the effect would have been such as to alter the causes more and
PROGRESSIVE EFFECTS. 365
more, without ever bringing them back to what they were at any former
time. The planet would then have moved in a parabola, or an hyperbola,
curves not returning into themselves. The quantities of the two forces were,
however, originally such, that the successive reactions of the effect bring back
the causes, after a certain time, to what they were before ; and from that time
all the variations continued to recur again and again in the same periodical
order, and must so continue while the causes subsist and are not counteracted.
§ 3. In all cases of progressive effects, whether arising from the accumu-
lation of unchanging or. of changing elements, there is a uniformity of suc-
cession not merely between the cause and the effect, but between the first
stages of the effect and its subsequent stages. That a body in vacuo falls
sixteen feet in the first second, forty-eight in the second, and so on in the
ratio of the odd numbers, is as much a uniform sequence as that when the
supports are removed the body falls. The sequence of spring and summer
is as regular and invariable as that of the approach of the sun and spring ;
but we do not consider spring to be the cause of summer ; it is evident
that both are successive effects of the heat received from the sun, and that,
considered merely in itself, spring might continue forever without having the
shghtest tendency to produce summer. As we have so often remarked, not
the conditional, but the unconditional invariable antecedent is termed the
cause. That which would not be followed by the effect unless something
else had preceded, and which if that somethng else had preceded, would
not have been required, is not the cause, however invariable the sequence
may in fact be.
It is in this way that most of those uniformities of succession are gen-
erated, which are not cases of causation. When a phenomenon goes on
increasing, or periodically increases and diminishes, or goes through any
continued and unceasing process of valuation reducible to a uniform rule
or law of succession, we do not on this account presume that any two suc-
cessive terms of the series are cause and effect. We presume the contrary ;
we expect to find that the whole series originates either from the continued
action of fixed causes or from causes which go through a corresponding proc-
ess of continuous change. A tree grows from half an inch high to a hun-
dred feet ; and some trees will generally grow to that height unless pre-
vented by some counteracting cause. Biit we do not call the seedling the
cause of the full-grown tree ; the invariable antecedent it certainly is, and
we know very imperfectly on what other antecedents the sequence is contin-
gent, but we are convinced that it is contingent on something ; because the
homogeneonsness of the antecedent with the consequent, the close resem-
blance of the seedling to the tree in all respects except magnitude, and the
graduality of the growth, so exactly resembling the progressively accumu-
lating effect produced by the long action of some one cause, leave no possi-
bility of doubting that the seedling and the tree are two terms in a series
of that description, the first term of which is yet to seek. The conclusion
is further confirmed by this, that we are able to prove by strict induction
the dependence of the growth of the tree, and even of the continuance of
its existence, upon the continued repetition of certain processes of nutri-
tion, the rise of the sap, the absorptions and exhalations by the leaves, etc. ;
and the same experiments would probably prove to us that the growth of
the tree is the accumulated sum of the effects of these continued processes,
were we not, for want of sufiiciently microscopic eyes, unable to observe
correctly and in detail what those effects are.
366 INDUCTION.
This supposition by no means requires that the effect should not, during
its progress, undergo many modifications besides those of quantity, or that
it should not sometimes appear to undergo a very marked change of char-
acter. This may be either because the unknown cause consists of several
component elements or agents, whose effects, accumulating according to
different laws, are compounded in different proportions at different periods
in the existence of the organized being ; or because, at certain points in its
progress, fresh causes or agencies come in, or are evolved, which intermix
their laws with those of the prime agent.
CHAPTER XVI.
OF BMPIKICAL LAWS.
§ 1. Scientific inquirers give the name of Empirical Laws to those
uniformities which observation or experiment has shown to exist, but on
which they hesitate to rely in cases varying much from those which have
been actually observed, for want of seeing any reason why such a law
should exist. It is implied, therefore, in the notion of an empirical law,
that it is not an ultimate law ; that if true at all, its truth is capable of
being, and requires to be, accounted for. It is a derivative law, the deriva-
tion of which is not yet known. To state the explanation, the why, of the
empirical law, would be to state the laws from which it is derived — the
ultimate causes on which it is contingent. And if we knew these, we
should also know what are its limits ; under what conditions it would cease
to be fulfilled.
The periodical return of eclipses, as originally ascertained by the perse-
vering observation of the early Eastern astronomers, was an empirical law,
until the general laws of the celestial motions had accounted for it. The
following are empirical laws still waiting to be resolved into the simpler
laws from which they are derived: the local laws of the flux and reflux
of the tides in different places ; the succession of certain kinds of weather
to certain appearances of sky ; the apparent exceptions to the almost uni-
versal truth that bodies expand by increase of temperature ; the law that
breeds, both animal and vegetable, are improved by crossing ; that gases
have a strong tendency to permeate animal membranes ; that substances
containing a very high proportion of nitrogen (such as hydi'ocyanic acid
and morphia) are powerful poisons ; that when different metals are fused
together the alloy is harder than the various elements ; that the number of
atoms of acid required to neutralize one atom of any base is equal to the
number of atoms of oxygen in the base ; that the solubility of substances
in one another depends,* at least in some degree, on the similarity of
their elements.
An empirical law, then, is an observed uniformity, presumed to be re-
* Thns water, of which eight-ninths in weight are oxygen, dissolves most bodies whichi
contain a high proportion of oxygen, snch as all the nitrates (which have more oxygen than
any others of the common salts), most of the sulphates, many of the carbonates, etc. Again,
bodies largely composed of combustible elements, like hydrogen and carbon, are soluble in
bodies of similar composition ; resin, for instance, will dissolve in alcohol, tar in oil of turpen-
tine. This empirical generalization is far from being universally true; no doubt because it is-
a remote, and therefore easily defeated, result of general laws too deep for iis at present to
penetrate ; but it will probably in time suggest processes of inquiry, leading to the discovery
of those laws.
EMPIRICAL LAWS. 367'
solvable into simpler laws, but not yet resolved inito them. The ascertain-
iceEt of the empirical laws of phenomena often precedes by a long interval
the explanation of those laws by the Deductive Method ; and the verifica-
tion of a deduction usually consists in the comparison of its results with
empirical laws previously ascertained.
§ 2. From a limited number of ultimate laws of causation, there are
necessarily generated a vast number of derivative uniformities, both of
succession and co-existence. Some are laM's of succession or of co-existence
between different effects of the same cause ; of these we had examples in
the last chapter. Some are laws of succession between effects and their
remote causes, "resolvable into the laws which connect each with the in-
termediate link. Thirdly, when causes act together and compound their
effects, the laws of those causes generate the fundamental law of the effect,
namely, that it depends on the co-existence of those causes. And, finally,
the order of succession or of co-existence which obtains among effects
necessarily depends on their causes. If they are effects of the same cause,
it depends on the laws of that cause; if on different causes, it depends on
the laws of those causes sevei'ally, and on the circumstances which deter-
mine their co-existence. If we inquire further when and how the causes
will co-exist, that, again, depends on their causes; and we may thus trace
back the phenomena higher and higher, until the different series of effects
meet in a point, and the whole is shown to have depended ultimately on
some common cause ; or until, instead of converging to one point, they ter-
minate in different points, and the order of the effects is proved to have
arisen from the collocation of some of the primeval causes, or natural
agents. For example, the order of succession and of co-existence among
the heavenly motions, which is expressed by Kepler's laws, is derived from
the co-existence of two primeval causes, the sun, and the original impulse
or projectile force belonging to each planet.* Kepler's laws are resolved
into the laws of these causes and the fact of their co-existence.
Derivative laws, therefore, do not depend solely on the ultimate laws into
which they are resolvable ; they mostly depend on those ultimate laws, and
an ultimate fact ; namely, the mode of co-existence of some of the component
elements of the universe. The ultimate laws of causation might be the
same as at present, and yet the derivative laws completely different, if the
causes co-existed in different proportions, or with any difference in those
of their relations by which the effects are influenced. If,' for example, the
sun's attraction, and the original projectile force, had existed in some oth-
er ratio to one another than they did (and we know of no reason why this
should not have been the case), the derivative laws of the heavenly motions
might have been quite different from what they are. The proportions
which exist happen to be such as to produce regular elliptical motions ;
any other proportions would have produced different ellipses, or circular,
or parabolic, or hyperbolic motions, but still regular ones ; because the ef-
fects of each of the agents accumulate according to a uniform law ; and two
regular series of quantities, when their corresponding terms are added, must
produce a regular series of some sort, whatever the quantities themselves are.
§ 3. Now this last - mentioned element in the resolution of a derivative
law, the element which is not a law of causation, but a collocation of causes,
* Or, according to Laplace's theoiy, the sun and the snn's rotation.
368 INDUCTION.
can not itself be reduced to any law. There is, as formerly remarked,* no
uniformity, no norma, principle, or rule, perceivable in the distribution of
the primeval natural agents through the universe. The different substances
composing the earth, the powers that pervade the universe, stand in no con-
stant relation to one another. One substance is more abundant than oth-
ers, one power acts through a larger extent of space than others, with-
out any pervading analogy that we can discover. We not only do not
know of any reason why the sun's attraction and the force in the direc-
tion of the tangent co-exist in the exact proportion they do, but we can trace
no cftincidence between it and the proportions in which any other element-
ary powers in the universe are intermingled. The utmost disorder is ap-
parent in the combination of the causes, which is consistent with the most
regular order in their effects ; for when each agent carries on its own op-
erations according to a uniform law, even the most capricious combination
of agencies will generate a regularity of some sort ; as we see in the kalei-
doscope, where any casual arrangement of colored bits of glass produces
by the laws of reflection a beautiful regularity in the effect.
§ 4. In the above considerations lies the justification of the limited degree of
reliance which scientific inquirers are accustomed to place in empirical laws.
A derivative law which results wholly from the operation of some one
cause, will be as universally true as the laws of the cause itself ; that is,
it will always be true except where some one of those effects of the cause,
■on which the derivative law depends, is defeated by a counteracting cause.
But when the derivative law results not from different effects of one cause,
but from effects of several causes, we can not be certain that it will be true
■under any variation in the mode of co-existence of those causes, or of the
primitive natural agents on which the causes ultimately depend. The
proposition that coal-beds rest on certain descriptions of strata exclusively,
though true on the earth, so far as our observation has reached, can not be
extended to the moon or the other planets, supposing coal to exist there ;
because we can not be assured that the original constitution of any other
planet was such as to produce the different depositions in the same order
as in our globe. The derivative law in this case depends not solely on
laws, but on a collocation; and collocations can not be reduced to any law.
Now it is the very nature of a derivative law which has not yet been re-
solved into its elements, in other words, an empirical law, that we do not
know whether it results from the different effects of one cause, or from efr
fects of different causes. We can not tell whether it depends wholly on
laws, or partly on laws and partly on a collocation. If it depends on a
collocation, it will be true in all the cases in which that particular colloca-
tion exists. But, since we are entirely ignorant, in case of its depending
Off a collocation, what the collocation is, we are not safe in extending the
law beyond the limits of time and place in which we have actual experience
of its truth. Since within those limits the law has always been found
true, we have evidence that the collocations, whatever they are, on which
it depends, do really exist within those limits. But, knowing of no rule or
principle to which the collocations themselves conform, we can not con-
clude that because a collocation is proved to exist within certain limits of •
place or time, it will exist beyond those limits. Empirical laws, therefore,
can only be received as true within the limits of time and place in which
* Supra, book iii., chap, v., § 7.
EMPIRICAL LAWS. 369
they have been found true by observation ; and not merely the limits of
time and place, but of time, place, and circumstance ; for, since it is the very
meaning of an empirical law that we do not know the ultimate laws of cau-
sation on which it is dependent, we can not foresee, without actual trial, in
what manner or to what extent the introduction of" any new circumstance
may affect it.
§ 5. But how are we to know that a uniformity ascertained by experi-
ence is only an empirical law ? Since, by the supposition, we have not been
able to resolve it into any other laws, how do we know that it is not an
ultimate law of causation ?
I answer that no generalization amounts to more than an empirical law
when the only proof on which it rests is that of the Method of Agreement.
For it has been seen that by that method alone we never can arrive at
causes. The utmost that the Method of Agreement can do is, to ascertain
the whole of the circumstances common to all cases in which a phenome-
non is produced ; and this aggregate includes not only the cause of the
phenomenon, but all phenomena with which it is connected by any deriva-
tive uniformity, whether as being collateral efEects of the same cause, or
effects of any other cause which, in all the instances we have been able to
observe, co-existed with it. The method affords no means of determining
which of these uniformities are laws of causation, and which are merely
derivative laws, resulting from those laws of causation and from the collo-
cation of the causes. None of them, therefore, can be received in any oth-
er character than that of derivative laws, the derivation of which has not
been traced ; in other words, empirical laws : in which light all results ob-
tained by the Method of Agreement (and therefore almost all truths obtain-
ed by simple observation without experiment) must be considered, until
either confirmed by the Method of Difference, or explained deductively; in
other words, accounted for a priori.
These empirical laws may be of greater or less authority, according as
there is reason to presume that they are resolvable into laws only, or into
laws and collocations together. The sequences which we observe in the
production and subsequent life of an animal or a vegetable, resting on the
Method of Agreement only, are mere empirical laws ; but though the ante-
cedents in those sequences may not be the causes of the consequents, both
the one and the other are doubtless, in the main, successive stages of a pro-
gressive effect originating in a common cause, and therefore independent
of collocations. The uniformities, on the other hand, in the order of super-
position of strata on the earth, are empirical laws of a much weaker kind,
since they not only are not laws of causation, but there is no reason to be-
lieve that they depend on any common cause ; all appearances are in favor
of their depending on the particular collocation of natural agents which at
some time or other existed on our globe, and from which no inference can
be drawn as to the collocation which exists or has existed in any other por-
tion of the universe.
§ 6. Our definition of an empirical law, including not only those uniform-
ities which are not known to be laws of causation, but also those which are,
provided there be reason to presume that they are not ultimate laws; this
is the proper place to consider by what signs we may judge that even if an
observed uniformity be a law of causation, it is not an ultimate, but a deriv.
ative law.
24
3^0 INDUCTION.
The first sign is, if between the antecedent a and the consequent h there'
be evidence of some intermediate link ; some phenomenon of which we can
surmise the existence, though from the imperfection of our senses or of our
instruments we are unable to ascertain its precise nature and laws. If there
be such a phenomenon (which may be denoted by the letter a;), it follows
that even if a be the cause of h, it is but the remote cause, and that the-
law, a causes h, is resolvable into at least two laws, a causes as, and x causes
b. This is a very frequent case, since the operations of nature mostly take
place on so minute a scale, that many of the successive steps are either im-
perceptible, or very indistinctly perceived.
Take, for example, the laws of the chemical composition of substances ;,
as that hydrogen and oxygen being combined, water is produced. All we
see of the process is, that the two gases being mixed in certain proportions,,
and heat or electricity being applied, an explosion takes place, the gases-
disappear, and water remains. There is no doubt about the law, or about
its being a law of causation. But between the antecedent (the gases in a
state of mechanical mixture, heated or electrified), and the consequent (the-
production of water), there must be an intermediate process which we dO'
not see. For if we take any portion whatever of the water, and subject it
to analysis, we find that it always contains hydrogen and oxygen ; nay, the
very same proportions of them, namely, two-thirds, in volume, of hydrogen,
and one-third oxygen. This is true of a single drop ; it is true of the mi-
nutest portion which our instruments are capable of appreciating. Since,
then, the smallest perceptible portion of the water contains both those sub-
stances, portions 01 hydrogen and oxygen smaller than the smallest percep-
tible must have come together in every such minute poi'tion of space; must
have come closer together than when the gases were in a state of mechan-
ical mixture, since (to mention no other reasons) the water occupies far less
space than the gases. Now, as we can not see this contact or close ap-
proach of the minute particles, we can not observe with what circumstances
it is attended, or according to what laws it produces its effects. The pro-
duction of water, that is, of the sensible phenomena which characterize the
compound, may be a very remote effect of those laws. There may be in-
numerable intervening links; and we are sure that there must be some.
Having full proof that corpuscular action of some kind takes place pre-
vious to any of the great transformations in the sensible properties of sub-
stances, we can have no doubt that the laws of chemical action, as at pres-
ent known, are not ultimate, but derivative laws ; however ignorant we may
be, and even though we should forever remain ignorant, of the nature of
the laws of corpuscular action from which they are derived.
In like manner, all the processes of vegetative life, whether in the vege-
table properly so called or in the animal body, are corpuscular processes.
Nutrition is the addition • of particles to one another, sometimes merely
replacing other particles sep^ated and excreted, sometimes occasioning
an increase of bulk or weight so gradual that only after a long contin-
uance does it become perceptible. Various organs, by means of peculiar
vessels, secrete from the blood fluids, the component particles of which
must have been in the blood, but which differ from it most widely both in
mechanical properties and in chemical composition. Here, then, are abun-
dance of unknown links to be filled up ; and there can be no doubt that the
laws of the phenomena of vegetative or organic life are derivative laws, de-
pendent on properties of the corpuscles, and of those elementary tissues
which are comparatively simple combinations of corpuscles.
EMPIRICAL LAWS. '3 71
The first sign, then, from which a law of causation, though hitherto un-
resolved, may be inferred to be a derivative law, is any indication of the
existence of an intermediate link or links between the antecedent and the
consequent. The second is, when the antecedent is an extremely complex
phenomenon, and its effects, therefore, probably in part at least, compound-
ed of the effects of its different elements ; since we know that the case in
which the effect of the whole is not made up of the effects of its parts is
exceptional, the Composition of Causes being by far the more ordinary
case.
We wiU illustrate this by two examples, in one of which the antecedent is
the sum of many homogeneous, in the other of heterogeneous, parts. The
weight of a body is made up of the weights of its minute particles ;" a truth
which astronomers express in its most general terms when they say that
bodies, at equal distances, gravitate to one another in proportion to their
quantity of matter. All true propositions, therefore, which can be made
concerning gravity, are derivative laws ; the ultimate law into which they
are all resolvaUe being, that every particle of matter attracts every other.
As our second ( xample, we may take any of the sequences observed in
meteorology ; for instance, a diminution of the pressure of the atmosphere
(indicated by a fall of the barometer) is followed by rain. The antecedent
is here a complex phenomenon, made up of heterogeneous elements ; the
column of the atmosphere over any particular place consisting of two parts,
a column of air, and a column of aqueous vapor mixed with it ; and the
change in the two together manifested by a fall of the barometer, and fol-
lowed by rain, must be either a change in one of these, or in the other, or
in both. We might, then, even in the absence of any other evidence, form
a reasonable presumption, from the invariable presence of both these ele-
ments in the antecedent, that the sequence is probably not an ultimate law,
but a result of the laws of the two different agents ; a presumption only
to be destroyed when we had made ourselves so well acquainted with the
laws of both, as to be able to affirm that those laws could not by them-
selves produce the observed result.
There are but few known cases of succession from vei-y complex ante-
cedents which have not either been actually accounted for from simpler
laws, or inferred with great probability (from the ascertained existence of
intermediate links of causation not yet understood) to be capable of being
so accounted for. It is, therefore, highly probable that all sequences from
complex antecedents are thus resolvable, and that ultimate laws are in all
cases comparatively simple. If there were not the other reasons already
mentioned for believing that the laws of organized nature are resolvable
into simpler laws, it would be almost a sufficient reason that the ante-
cedents in most of the sequences are so very complex.
§ 1. In the preceding discussion we have recognized two kinds of em-
pirical laws : those known to be laws of causation, but presumed to be re-
solvable into simpler laws ; and those not known to be laws of causation
at all. Both these kinds of laws agree in the demand which they make for
being explained by deduction, and agree in being the appropriate means
of verifying such deduction, since they represent the experience with which
the result of the deduction must be compared. They agree, further, in
this, that until explained, and connected with the ultimate laws from which
they result, they have not attained the highest degree of certainty of which
laws are susceptible. It has been shown on a former occasion that lawa
372 INDUCTION.
of causation which are derivative, and compounded of simpler laws, are
not only, as the nature of the case implies, less general, but even less cer-
tain, than the simpler laws from which they result ; not in the same de-
gree to be relied on as universally true. The inferiority of evidence, how-
ever, which attaches to this class of laws, is trifling, compared with that
which is inherent in uniformities not known to be laws of causation at
all. So long as these are unresolved, we can not teU on how many collo-
cations, as well as laws, their truth may be dependent ; we can never, there-
fore, extend them with any confidence to cases in which we have not as-
sured ourselves, by trial, that the necessary collocation of causes, whatever
it may be, exists. It is to this class of laws alone that the property, which
philosophers usually consider as characteristic of empirical laws, belongs in
all its strictness — the property of being unfit to be relied on beyond the
limits of time, place, and circumstance in which the observations have been
made. These are empirical laws in a more emphatic sense; and when I
employ that term (except where the context manifestly indicates the re-
verse) I shall generally mean to designate those uniformiti^ only, whether
of succession or of co-existence, which are not known to be laws of causa-
tion.
CHAPTER XVII.
OF CHAlirCE AND ITS ELIMINATION.
§ 1. Considering, then, as empirical laws only those observed uniform-
ities respecting which the question whether they are laws of causation
must remain undecided until they can be explained deductively, or until
some means are found of applying the Method of Difference to the case,
it has been shown in the preceding chapter that until a uniformity can,
in one or the other of these modes, be taken out of the class of empirical
laws, and brought either into that of laws of causation or of the demon-
strated results of laws of causation, it can not with any assurance be pro-
nounced true beyond the local and other limits within which it has been
found so by actual observation. It remains to consider how we are to
assure ourselves of its truth even within those limits ; after what quantity
of experience a generalization which rests solely on the Method of Agree-
ment can be considered sufficiently established, even as an empirical law.
In a former chapter, when treating of the Methods of Direct Induction, we
expressly reserved this question,* and the time is now come for endeavor-
ing to solve it.
We found that the Method of Agreement has the defect of not proving
causation, and can, therefore, only be employed for the ascertainment of
empirical laws. But we also found that besides this deficiency, it labors
under a characteristic imperfection, tending to render uncertain even such
conclusions as it is in itself adapted to prove. This imperfection arises
from Plurality of Causes. Although two or more cases in which the phe-
nomenon a has been met with may have no common antecedent except A,
this does not prove that there is any connection between a and A, since a
may have many causes, and may have been produced, in these different
instances, not by any thing which the instances had in common, but by
some of those elements in them which were different. We nevertheless
* Supra, book iii., chap, x., § 2.
CHANCE, AND ITS ELIMINATION. 373
observed, that in proportion to the multiplication of instances pointing to A
as the antecedent, the characteristic uncertainty of the method diminishes,
and the existence of a law of connection between A and a more nearly
approaches to certainty. It is now to be determined after what amount
of experience this certainty may be deemed to be practically attained, and
the connection between. A and a may be received as an empirical law.
This question may be otherwise stated in more familiar terms : After how
many and what sort of instances may it be concluded that an observed
coincidence between two phenomena is not the effect of chance ?
It is of the utmost importance for understanding the logic of induction,
that we should form a distinct conception of what is meant by chance, and
how the phenomena which common language ascribes to that abstraction
are really produced.
§ 2. Chance is usually spoken of in direct antithesis to law ; whatever, it
is supposed, can not be ascribed to any law is attributed to chance. It is,
however, certain that whatever happens is the result of some law; is an
effect of causes, and could have been predicted from a knowledge of the
existence of those causes, and from their laws. If I turn up a particular
card, that is a consequence of its place in the pack. Its place in the pack
was a consequence of the manner in which the cards were shuffled, or of
the order in which they were played in the last game ; which, again, were
effects of prior causes. At every stage, if we had possessed an accurate
knowledge of the causes in existence, it would have been abstractedly pos-
sible to foretell the effect.
An event occurring by chance may be better described as a coincidence
from which we have no ground to infer a uniformity — the occurrence of
a phenomenon in certain circumstances, without our having reason on that
account to infer that it will happen again in those circumstances. This,
however, when looked closely into, implies that the enumeration of the cir-
cumstances is not complete. Whatever the fact be, since it has occurred
once, we may be sure that if all the same circumstances were repeated it
would occur again ; and not only if all, but there is some particular portion
of those circumstances on which the phenomenon is invariably consequent.
With most of them, however, it is not connected in any permanent man-
ner; its conjunction with those is said to be the effect of chance, to be
merely casual. Facts casually conjoined are separately the effects of
causes, and therefore of laws ; but of different causes, and causes not con-
nected by any law.
It is incorrect, then, to say that any phenomenon is produced by chance ;
but we may say that two or more phenomena are conjoined by chance, that
they co-exist or succeed one another only by chance; meaning that they
are in no way related through causation; that they are neither cause and
effect, nor effects of the same cause, nor effects of causes between which
there subsists any law of co-existence, nor even effects of the same coUocar
tion of primeval causes.
If the same casual coincidence never occurred a second time, we should
have an easy test for distinguishing such from the coincidences which are
the results of a law. As long as the phenomena had been found together
only once, so long, unless we knew some more general laws from which the
coincidence might have resulted, we could not distinguish it from a casual
one ; but if it occurred twice, we should know that the phenomena so con-
joined must be in some Way connected through their causes.
374 INDUCTION.
There is, however, no such test. A coincidence may occur again and
again, and yet be only casual. Nay, it would be inconsistent with what we
know of the order of nature to doubt that every casual coincidence will
sooner or later be repeated, as long as the phenomena between which it oc-
curred do not cease to exist, or to be reproduced. The recurrence, there-
fore, of the same coincidence moi-e than once, or even its frequent recur-
rence, does not prove that it is an instance of any law ; does not prove that
it is not casual, or, in common language, the effect of chance.
And yet, when a coincidence can not be deduced fi'oni known laws, nor
proved by experiment to be itself a case of causation, the frequency of its
occurrence is the only evidence from which we can infer that it is the re-
sult of a law. N"ot, however, its absolute frequency. The question is not
whether the coincidence occurs often or seldom, in the ordinary sense of
those terms; but whether it occurs more often than chance will account
for ; more often than might rationally be expected if the coincidence were
casual. We have to decide, therefore, what degree of frequency in a coin-
cidence chance will account for; and to this there can be no general an-
swer. We can only state the principle by which ,the answer must be de-
termined ; the answer itself will be diEEerent in every different case.
Suppose that one of the phenomena, A, exists always, and the other phe-
nomenon, B, only occasionally ; it follows that every instance of B will be
an instance of its coincidence with A, and yet the coincidence will be mere-
ly casual, not the result of any connection between them. The fixed stars
have been constantly in existence since the beginning of human experience,
and all phenomena that have come under human observation have, in every
single instance, co-existed with them ; yet this coincidence, though equally
invariable with that which exists between any of those phenomena and its
own cause, does not prove that the stars are its cause, nor that they are in
anywise connected with it. As strong a case of coincidence, therefore, as
can possibly exist, and a much stronger one in point of mere frequency
than most of those which prove laws, does not here prove a law; why? be-
cause, since the stars exist always, they must co-exist with every other phe-
nomenon, whether connected with them by causation or not. The uniform-
ity, great though it be, is np greater than would occur on the supposition
that no such connection exists.
On the other hand, suppose that we were inquiring whether there be any
connection between rain and any particular wind. Rain, we know, occa-
sionally occurs with every wind ; therefore, the connection, if it exists, can
not be an actual law ; but still rain may be connected with some particular
wind through causation ; that is, though they can not be always effects of
the same cause (for if so they would regularly co-exist), there may be some
causes common to the two, so that in so far as either is produced by those
common causes, they will, from the laws of the causes, be found to co-exist.
How, then, shall we ascertain this? The obvious answer is, by observing
whether rain occurs with one wind more frequently than with any other.
That, however, is not .enough ; for perhaps that one wind blows more fre-
quently than any other; so that its blowing more frequently in rainy
weather is no more than would happen, although it had no connection with
the causes of rain, provided it were not connected with causes adverse to
rain. In England, westerly winds blow during about twice as great a por-
tion of the year as easterly. If, therefore, it rains only twice as often with
a westerly as with an easterly wind, we have no reason to infer that any
law of nature is concerned in the coincidence. If it rains more than twice
CHANCE, AND ITS ELIMINATION. 373
as often, we may be sure that some law is concerned ; either there is some
•cause in nature which, in this climate, tends to produce both rain and a
westerly wind, or a westerly wind has itself some tendency to produce rain.
But if it rains less than twice as often, we may draw a directly opposite in-
ference : the one, instead of being a cause, or connected with causes of the
other, must be connected with causes adverse to it, or with the absence of
some cause which produces it; and though it may still rain much oftener
with a westerly wind than with an easterly, so far would this be from prov-
ing any connection between the phenomena, that the connection proved
would be between rain and an easterly wind, to which, in mere frequency
of coincidence, it is less allied.
Here, then, are two examples : in one, the greatest possible frequency of
coincidence, with no instance whatever to the contrary, does not prove that
there is any law ; in the other, a much less frequency of coincidence, even
when non-coincidence is still more frequent, does prove that there is a law.
In both cases the principle is the same. In both we' consider the positive
frequency of the phenomena themselves, and how great frequency of coin-
cidence that must of itself bring about, without supposing any connection
between them, provided there be no repugnance ; provided neither be con-
oected with any cause tending to frustrate the other. If we find a greater
frequency of coincidence than this, we conclude that there is some connec-
tion ; if a less frequency, that there is some repugnance. In the former
-case, we conclude that one of the phenomena can under some circumstances
cause the other, or that there exists something capable of causing them
both ; in the latter, that one of them, or some cause which produces one of
them, is capable of counteracting the production of the other. "We have
thus to deduct from the observed frequency of coincidence as much as may
be the effect of chance, that is, of the mere frequency of the phenomena
themselves ; and if any thing remains, what does remain is the residual
fact which proves the existence of a law.
The frequency of the phenomena can only be ascertained within definite
•limits of space and time ; depending as it does on the quantity and distri-
bution of the primeval natural agents, of which we can know nothing be-
yond the boundaries of human observation, since no law, no regularity, can
be traced in it, enabling us to infer the unknown from the known. But for
•the present purpose this is no disadvantage, the question being confined
within the same limits as the data. The coincidences occurred in certain
■places and times, and within those we can estimate the frequency with
which such coincidences would be produced by chance. If, then, we find
from observation that A exists in one case out of every two, and B in one
•case out of every three ; then, if there be neither connection nor repugnance
between them, or between any of their causes, the instances in which A
and B will both exist, that is to say will co-exist, will be one case in every
six. For A exists in three cases out of six ; and B, existing in one case
•out of every three without regard to the presence or absence of A, will
exist in one case out of those three. There will therefore be, of the whole
number of cases, two in which A exists without B ; one case of B without
A; two in which neither B nor A exists, and one case out of six in which
they both exist. If, then, in point of fact, they are found to co-exist oftener
tlian in one case out of six ; and, consequently, A does not exist without
B so often as twice in three times, nor B without A so often as once in ev-
•ery twice, there is some cause in existence which tends to produce a con-
junction between A and B.
S'76 INDUCTION.
Generalizing the result, we may say that if A occurs in a larger propor-
tion of the cases where B is than of the cases where B is not, then will
B also occur in a larger proportion of the cases where A is than of the
cases where A is not ; and there is some connection, through causation, be-
tween A and B. If we could ascend to the causes of the two phenomena^
we should find, at some stage, either proximate or remote, some cause or
causes common to both ; and if we could ascertain what these are, we could
frame a generalization which would be true without restriction of place or
time ; but until we can do so, the fact of a connection between the two
phenomena remains an empirical law.
§ 3. Having considered in what manner it may be determined whether
any given conjunction of phenomena is casual, or the result of some law,
to complete the theory of chance it is necessary that we should now con-
sider those effects which are partly the result of chance and partly of law,
or, in other words, in which the effects of casual conjunctions of causes
are habitually blended in one result with the effects of a constant cause.
This is a case of Composition of Causes ; and the peculiarity of it is,
that instead of two or more causes intermixing their effects in a regular
manner with those of one another, we have now one constant cause, pro-
ducing an effect which is successively modified by a series of vai'iable
causes. Thus, as summer advances, the approach of the sun to a vertical
position tends to produce a constant increase of teraperatui-e ; but with
this effect of a constant cause, there are blended the effects of many vari-
able causes, winds, clouds, evaporation, electric agencies and the like, so
that the temperature of any given day depends in part on these fleeting
causes, and only in part on the constant cause. If the effect of the con-
stant cause is always accompanied and disguised by effects of variable
causes, it is impossible to ascertain the law of the constant cause in the or-
dinary manner by separating it from all other causes and observing it apart.
Hence arises the necessity of an additional rule of experimental inquii-y.
When the action of a cause A is liable to be interfered with, not stead-
ily by the same cause or causes, but by different causes at different times,
and when these are so frequent, or so indeterminate, that we can not pos-
sibly exclude all of them from any experiment, though we may vary them ;
our resource is, to endeavor to ascertain what is the effect of all the vari-
able causes taken together. In order to do this, we make as many trials
as possible, preserving A invariable. The results of these different trials
will naturally be different, since the indeterminate modifying causes are
different in each ; if, then, we do not find these results to be progressive,
but, on the contrary, to oscillate about a certain point, one experiment giv-
ing a result a little greater, another a little less, one a result tending a little
more in one direction, another a little more in the contrary direction ; while
the average or middle point does not vary, but different sets of experi-
ments (taken in as great a variety of circumstances as possible) yield the
same mean, provided only they be suflBciently numerous ; then that mean,
or average result, is the part, in each experiment, which is due to the cause
A, and is the effect which would have been obtained if A could have acted
alone ; the variable remainder is the effect of chance, that is, of causes the
co-existence of which with the cause A was merely casual. The test of
the sufficiency of the induction in this case is, when any increase of the
number of trials from which the average is struck does not materially
alter the average.
CHANCE, AND ITS ELIMINATION. 377
This kind of elimination, in which we do not eliminate any one assignable
cause, but the multitude of floating unassignable ones, may be termed the
Elimination of Chance. We afford an example of it when we repeat an ex-
periment, in order, by taking the mean of different results, to get rid of the
effects of the unavoidable errors of each individual experiment. When there
is no permanent cause, such as would produce a tendency to error peculiar-
ly in one direction, we are warranted by experience in assuming that the
errors on one side will, in a certain number of experiments, about balance
the errors on the contrary side. We therefore repeat the experiment, un-
til any change which is produced in the average of the whole by further
repetition, falls within limits of error consistent with the degree of accuracy
required by the purpose we have in view.*
§ 4. In the supposition hitherto made, the effect of the constant cause A
lias been assumed to form so great and conspicuous a part of the general
result, that its existence never could be a matter of uncertainty, and the ob-
ject of the eliminating process was only to ascertain how much is attribu-
table to that cause ; what is its exact law. Cases, howevei', occur iu which
the effect of a constant cause is so small, compared with that of some of the
changeable causes with which it is liable to be casually conjoined, that of it-
self it escapes notice, and the very existence of any effect arising from a
■constant cause is first learned by the process which in general serves only for
ascertaining the quantity of that effect. This case of induction may be char-
acterized as follows : A given effect is known to be chiefly, and not known
not to be wholly, determined by changeable causes. If it be wholly so pro-
duced, then if the aggregate be taken of a sufficient number of instances, the
effects of these different causes will cancel one another. If, therefore, we
do not find this to be the case, but, on the contrary, after such a number of
trials has been made that no further increase alters the average result,
we find that average to be, not zero, but some other quantity, about which,
though small in comparison with the total effect, the effect nevertheless
oscillates, and which is the middle point in its oscillation ; we may conclude
this to be the effect of some constant cause ; which cause, by some of the
methods already treated of, we may hope to detect. This may be called
the discovery of a residual phenomenon iy eliminating the effects of
■chance.
It is in this manner, for example, that loaded dice may be discovered.
Of course no dice are so clumsily loaded that they must always throw cer-
tain numbers ; otherwise the fraud would be instantly detected. The load-
ing, a constant cause, mingles with the changeable causes which determine
what cast will be thrown in each individual instance. If the dice were not
* In the preceding discussion, the mean is spoken of as if it were exactly the same thing
with the average. But the mean, for purposes of inductive inquiry, is not the average, or ar-
ithmetical mean, though in a familiar illustration of the theory the difference may be disre-
garded. If the deviations on one side of the average are much more numerous than those on
the other (these last being fewer but greater), the effect due to the invariable cause, as dis-
tinct from the variable ones, will not coincide with the average, but will be either below or
above the average, the deviation being toward the side on which the greatest number of the
instances are found. This follows from a truth, ascertained both inductively and deductively,
that small deviations from the true central point are greatly more frequent than large ones.
T-he mathematical law is, "that the most probable deteimination of one or more invariable
elements from observation is that in which the sum of the squares of the individual aberra-
tions," or deviations, "shall be the least possible." See this principle stated, and its grounds
popularly explained, by Sir John Herschel, in his review of Quetelet on Probabilities, JEssays,
p. 395 et seq.
^78 INDUCTION.
loaded, and the throw were left to depend entirely on the changeable causes,
these in a sufficient number of instances would balance one another, and
there would be no preponderant number of throws of any one kind. If,,
therefore, after such a number of trials that no further increase of their
number has any material effect upon the average, we find a preponderance-
in favor of a particular throw ; we may conclude with assurance that there-
is some constant cause acting in favor of that throw, or, in other words, that
the dice are not fair ; and the exact amount of the unfairness. In a similar
manner, what is called the diurnal variation of the barometer, which is very
small compared with the variations arising from the irregular changes ia
the state of the atmosphere, was discovered by comparing the average-
height of the barometer at different hours of the day. When this compari-
son was made, it was found that there was a small difference, which on the
average was constant, however the absolute quantities might vary, and which
difference, therefore, must be the effect of a constant cause. This cause-
was afterward ascertained, deductively, to be the rarefaction of the air^
occasioned by the increase of temperature as the day advances.
§ 5. After these general remarks on the nature of chance, we are pre-
pared to consider in what manner assurance may be obtained that a con-
junction between two phenomena, which has been observed a certain num-
ber of times, is not casual, but a result of causation, and to be received^
therefore, as one of the uniformities of nature, though (until accounted for
a priori) only as an empirical law.
We will suppose the strongest case, namely, that the phenomenon B has
never been observed except in conjunction with A. Even then, the proba-
bility that they are connected is not measured by the total number of in-
stances in which they have been found together, but by the excess of that
number above the number due to the absolutely frequency of A. If, for
example, A exists always, and therefore co-exists with every thing, no num-
ber of instances of its co-existence with B would prove a connection ; as in-
cur example of the fixed stars. If A be a fact of such common occurrence
that it may be presumed to be present in half of all the cases that occur,,
and therefore in half the cases in which B occurs, it is only the proportional
excess above half that is to be reckoned as evidence toward proving a con-
nection between A and B.
In addition to the question. What is the number of coincidences which^
on an average of a great multitude of trials, may be expected to arise from
chance alone ? there is also another question, namely. Of what extent of de-
viation from that average is the occurrence credible, from chance alone, in
some number of instances smaller than that required for striking a fair av-
erage? It is not only to be considered what is the general result of the
chances in the long run, but also what are the extreme limits of variatioa
from the general result, which may occasionally be expected as the result
of some smaller number of instances.
The consideration of the latter question, and any consideration of the-
former beyond that already given to it, belong to what mathematician*
term the doctrine of chances, or, in a phrase of greater pretension, the The-
ory of Probabilities.
OF THE CALCULATION OF CHANCES, 379
CHAPTER XVIII.
OP THE CALCULATION OP CHANCES.
§ 1. " Peobabilitt," says Laplace,* " has reference partly to our igno-
rance, partly to our knowledge. We know that among three or more
events, one, and only one, must happen ; but there is nothing leading us to
believe that any one of them will happen rather than the others. In this
state of indecision, it is impossible for us to pronounce with certainty on
their occurrence. It is, however, probable that any one of these events,
selected at pleasure, will not take place ; because we perceive several cases,
all equally possible, which exclude its occurrence, and only one which fa-
vors it.
" The theory of chances consists in reducing all events of the same kind
to a certain number of cases equally possible, that is, such that we are
equally undecided as to their existence ; and in determining the number of
these cases which are favorable to the event of which the probability is
sought. The ratio of that number to the number of all the possible cases
is the measure of the probability ; which is thus a fraction, having for its
numerator the number of cases favorable to the event, and for its denom-
inator the number of all the cases which are possible."
To a calculation of chances, then, according to Laplace, two things are
necessary ; we must know that of several events some one will certainly
happen, and no more than one ; and we must not know, nor have any rea-
son to expect, that it will be one of these events rather than another. It
has been contended that these are not the only requisites, and that Laplace
has overlooked, in the general theoretical statement, a necessary part of the
foundation of the doctrine of chances. To be able (it has been said) to
pronounce two events equally probable, it is not enough that we should
know that one or the other must happen, and should have no grounds for
conjecturing which. Experience must have shown that the two events are
of equally frequent occurrence. Why, in tossing up a half-penny, do we reck-
on it equally probable that we shall throw cross or pile ? Because we know
that in any great number of throws, cross and pile are thrown about equally
often ; and that the more throws we make, the more nearly the equality is
perfect. We may know this if we please by actual experiment, or by the
daily experience which life affords of events of the same general character,
or, deductively, from the effect of mechanical laws on a symmetrical body
acted upon by forces varying indefinitely in quantity and direction. We
may know it, in short, either by specific experience, or on the evidence of
our general knowledge of nature. But, in one way or the other, we must
know it, to justify us in calling the two events equally probable; and if we
knew it not, we should proceed as much at hap-hazard in staking equal sums
on the result, as in laying odds.
This view of the subject was taken in the first edition of the present
work ; but I have since become convinced that the theory of chances, aa
* Eisai Philosophique sur les Probahilitis, fifth Paris edition, p. 7.
380 INDUCTION.
conceived by Laplace and by mathematicians generally, has not the funda-
mental fallacy which I had ascribed to it.
We must remember that the probability of an event is not a quality of
the event itself, but a mere name for the degree of ground which we, or
some one else, have for expecting it. The probability of an event to one
person is a different thing from the probability of the same event to an-
other, or to the same person after he has acquired additional evidence. The
probability to me, that an individual of whom I know nothing but his name
will die within the year, is totally altered by my being told the next minute
that he is in the last stage of a consumption. Yet this makes no difference
in the event itself, nor in any of the causes on which it depends. Every
event is in itself certain, not probable ; if we knew all, we should either
know positively that it will happen, or positively that it will not. But its
i probability to us means the degree of expectation of its occurrence, which
we are warranted in entertaining by our present evidence.
Bearing this in mind, I think it must be admitted, that even when we
have no knowledge whatever to guide our expectations, except the knowl-
edge that what happens must be some one of a certain number of possibili-
ties, we may still reasonably judge, that one supposition is more probable
to us than another supposition ; and if we have any interest at stake, we
shall best provide for it by acting conformably to that judgment.
§ 2. Suppose that we are required to take a ball from a box, of which
we only know that it contains balls both black and white, and none of any
other color. "We know that the ball we select will be either a black or a
white ball ; but we have no ground for expecting black rather than white,
or white rather than black. In that case, if we are obliged to make a choice,
and to stake something on one or the other supposition, it will, as a question
of prudence, be perfectly indifferent which ; and we shall act precisely as
we should have acted if we had known beforehand that the box contained
an equal number of black and white balls. But though our conduct would
be the same, it would not be founded on any surmise that the balls were in
fact thus equally divided ; for we might, on the contrary, know by au-
thentic information that the box contained ninety-nine balls of one color,
and only one of the other ; still, if we are not told which color has only one,
and which has ninety-nine, the drawing of a white and of a black ball will
be equally probable to us. We shall have no reason for staking any thing
on the one event rather than on the other ; the option between the two will
be a matter of indifference ; in other words, it will be an even chance.
But let it now be supposed that instead of two there are three colors —
white, black, and red ; and that we are entirely ignorant of the proportion
in which they are mingled. We should then have no reason for expecting
one more than another, and if obliged to bet, should venture our stake on
red, white, or black with equal indifference. But should we be indifferent
whether we betted for or against some one color, as, for instance, white ?
Surely not. From the very fact that black and red are each of them sep-
arately equally probable to us with white, the two together must be twice
as probable. We should in this case expect not white rather than white,
and so much rather that we would lay two to one upon it. It is true, there
might, for aught we knew, be more white balls than black and red together ;
and if so, our bet would, if we knew more, be seen to be a disadvantageous
one. But so also, for aught we knew, might there be more red balls than
black and white, or more black balls than white and red, and in such case
OF THE CALCULATION OF CHANCES. 381
the effect of additional knowledge would be to prove to ns that our bet
was more advantageous than we had supposed it to be. There is in the
existing state of our knowledge a rational probability of two to one against
white; a probability fit to be made a basis of conduct. No reasonable
person would lay an even wager in favor of white against black and red ;
though against black alone or red alone he might do so without impru-
dence.
The common theory, therefore, of the calculation of chances, appears to
be tenable. Even when we know nothing except the number of the possi-
ble and mutually excluding contingencies, and are entirely ignorant of their
comparative frequency, we may have grounds, and grounds numerically ap-
preciable, for acting on one supposition rather than on another ; and this
is the meaning of Probability.
§ 3. The principle, however, on which the reasoning proceeds, is suffi-
ciently evident. It is the obvious one that when the cases which exist are
shared among several kinds, it is impossible that each of those kinds
should be a majority of the whole : on the contrary, there must be a ma-
jority against each kind, except one at most ; and if any kind has more
than its share in proportion to the total number, the others collectively
must have less. Granting this axiom, and assuming that we have no
ground for selecting any one kind as more likely than the rest to surpass
the average proportion, it follows that we can not rationally presume this
of any, which we should do if we were to bet in favor of it, receiving less-
odds than in the ratio of the number of the other kinds. Even, therefore,
in this extreme case of the calculation of probabilities, which does not rest
on special experience at all, the logical ground of the process is our knowl-
edge— such knowledge as we then have — of the laws governing the fre-
quency of occurrence of the different cases; but in this case the knowledge
is limited to that which, being universal and axiomatic, does not require
reference to specific experience, or to any considerations arising out of the
special nature of the problem under discussion.
Except, however, in such cases as games of chance, where the very pur-
pose in view requires ignorance instead of knowledge, I can conceive no
case in which we ought to be satisfied with such an estimate of chances as
this — an estimate founded on the absolute minimum of knowledge respect-
ing the subject. It is plain that, in the case of the colored balls, a very
slight ground of surmise that the white balls were really more numerous
than either of the other colors, would suffice to vitiate the whole of the cal-
culations made in oar previous state of indifference. It would place us in
that position of more advanced knowledge, in which the probabilities, to us,
would be different from what they were before ; and in estimating these
new probabilities we should have to proceed on a totally different set of
data, furnished no longer by mere counting of possible suppositions, but by
specific knowledge of facts. Such data it should always be our endeavor
to obtain; and in all inquiries, unless on subjects equally beyond the range
of our means of knowledge and our practical uses, they may be obtained,
if not good, at least better than none at all.*
* It even appears to me that the calcnlation of chances, where there are no data grounded
either o^i special experience or on special inference, must, in an immense majority of cases,
break down, from sheer impossibility of assigning any principle by which to be guided in set-
ting out the list of possibilities. In the case of the colored balls we have no difSculty in mak-
ing the enumeration, because we ourselves determine what the possibilities shall be. But
382 INDUCTION.
It is obvious, too, that even when the probabilities are derived from ob-
servation and experiment, a very slight improvement in the data, by better
observations, or by taking into fuller consideration the special circumstances
of the case, is of more use than the most elaborate application of the cal-
culus to probabilities founded on the data in their previous state of inferi-
ority. The neglect of this obvious reflection has given rise to misapplica-
tions of the calculus of probabilities which have made it the real oppro-
brium of mathematics. It is sufficient to refer to the applications made of
it to the credibility of witnesses, and to the correctness of the verdicts of
juries. In regai-d to the first, common sense would dictate that it is im-
possible to strike a general average of the veracity and other qualifications
for true testimony of mankind, or of any class of them ; and even if it were
possible, the employment of it for such a purpose implies a misapprehen-
sion of the use of averages, which serve, indeed, to protect those whose in-
terest is at stake, against mistaking the general result of large masses of
instances, but are of extremely small value as grounds of expectation in any
one individual instance, unless the case be one of those in which the great
majority of individual instances do not differ much from the average. In
the case of a witness, persons of common sense would draw their conclu-
sions from the degree of consistency of his statements, his conduct under
cross-examination, and the relation of the case itself to his interests, his
partialities, and his mental capacity, instead of applying so rude a standard
(even if it were capable of being verified) as the ratio between the num-
ber of true and the number of erroneous statements which he may be sup-
posed to make in the course of his life.
Again, on the subject of juries or other tribunals, some mathematicians
have set out from the proposition that the judgment of any one judge or
juryman is, at least in some small degree, more likely to be right than
wrong, and have concluded that the chance of a number of persons concur-
ring in a wrong verdict is diminished the more the number is increased;
so that if the judges are only made sufficiently numerous, the correctness
of the judgment may be reduced almost to certainty. I say nothing of the
disregard shown to the effect produced on the moral position of the judges
by multiplying their numbers, the virtual destruction of their individual
responsibility, and weakening of the application of their minds to the sub-
ject. I remark only the fallacy of reasoning from a wide average to cases
necessarily differing greatly from any average. It may be true that, taking
all causes one with another, the opinion of any one of the judges would be
oftener right than wrong; but the argument forgets that in all but the
more simple cases, in all cases in which it is really of much consequence
what the tribunal is, the proposition might probably be reversed ; besides
which, the cause of error, whether arising from the intricacy of the case or
from some common prejudice or mental infirmity, if it acted upon one
judge, would be extremely likely to affect all the others in the same man-
suppose a case more analogous to those which occur In nature : instead of three colors, let
there be in the box all possible colors, we being supposed ignorant of the comparative fre-
quency with which different colors occur in nature, or in the productions of art. How is the
list of cases to be made out? Is every distinct shade to count as a color? If so, is the test
to be a common eye, or an educated eye — a painter's, for instance ? On the answer to these
questions would depend whether the chances against some particular color would be esti-
mated at ten, twenty, or perhaps five hundred to one. While if we knew from experience
that the particular color occurs on an average a certain number of times in every hundred or
thousand, we should not require to know any thing either of the frequency or of the number
of the other possibilities.
OF THE CALCULATION OF CHANCES. . 383
ner, or at least a majority, and thus render a wrong instead of a right de-
-cision more probable the more the number was inci-eased.
These are but samples of the errors frequently committed by men who,
having made themselves familiar with the difficult formulae which algebra
affords for the estimation of chances under suppositions of a complex char-
acter, like better to employ those formulae in computing what are the prob-
abilities to a person half informed about a case than to look out for means
of being better informed. Before applying the doctrine of chances to any
scientific purpose, the foundation must be laid for an evaluation of the
chances, by possessing ourselves of the utmost attainable amount of posi-
tive knowledge. The knowledge required is that of the comparative fre-
quency with which the different events in fact occur. For the purposes,
therefore, of the present work, it is allowable to suppose that conclusions
respecting the probability of a fact of a particular kind rest on our knowl-
edge of the proportion between the cases in which facts of that kind occur,
and those in which they do not occur; this knowledge being either de-
rived from specific experiment, or deduced from our knowledge of the
■causes in operation which tend to produce, compared with those which
tend to prevent, the fact in question.
Such calculation of chances is grounded on an induction ; and to render
the calculation legitimate, the induction must be a valid one. It is not
less an induction, though it does not prove that the event occurs in all
cases of a given description, but only that out of a given number of such
cases it occurs in about so many. The fraction which mathematicians use
to designate the probability of an event is the ratio of these two numbers ;
the ascertained proportion between the number of cases in which the event
occurs and the sum of all the cases, those in which it occurs and in which
it does not occur, taken together. In playing at cross and pile, the descrip.
tion of cases concerned are throws, and the probability of cross is one-half,
because if we throw often enough cross is thrown about once in every two
throws. In the cast of a die, the probability of ace is one-sixth; not sim-
ply because there are six possible throws, of which ace is- one, and because
we do not know any reason why one should turn up rather than another —
though I have admitted the validity of this ground in default of a better —
but because we do actually know, either by reasoning or by experience,
that in a hundred or a million of throws ace is thrown in about one-sixth
of that number, or once in six times.
§ 4. I say, " either by reasoning or by experience," meaning specific ex-
perience. But in estimating probabilities, it is not a matter of indifference
from which of these two sources we derive our assurance. The probabili-
ty of events, as calculated from their mere frequency in past experience,
affords a less secure basis for practical guidance than their probability as
deduced from an equally accurate knowledge of the frequency of occur-
rence of their causes.
The generalization that an event occurs in ten out of every hundred cases
•of a given description, is as real an induction as if the generalization were
that it occurs in all cases. But when we arrive at the conclusion by mere-
ly counting instances in actual experience, and comparing the number of
oases in which A has been present with the number in which it has been
absent, the evidence is only that of the Method of Agreement, and the con-
clusion amounts only to an empirical law. We can make a step beyond
this when we can ascend to the causes on which the occurrence of A or its
384 INDUCTION.
non-occurrence ■will depend, and form an estimate of the coniparative fre-
queney of the causes favorable and of those unfavorable to the occurrence.
These are data of a higher order, by which the empirical law derived from
a mere numerical comparison of affirmative and negative instances will be
either corrected or confirmed, and in either case we shall obtain a more
correct measure of probability than is given by that numerical comparison.
It has been well remarked that in the kind of examples by which the doc-
trine of chances is usually illustrated, that of balls in a box, the estimate
of probabilities is supported by reasons of causation, stronger than specific
experience. " What is the reason that in a box where there are nice black
balls and one white, we expect to draw a black ball nine times as much (in
other words, nine times as often, frequency being the gauge of intensity in
expectation) as a white ? Obviously because the local conditions are nine
times as favorable ; because the hand may alight in nine places and get a
black ball, while it can only alight in one place and find a white ball; just
for the same reason that we do not expect to succeed in finding a friend
in a crowd, the conditions in order that we and he should come together
being many and difficult. This of course would not hold to the same ex-
tent were the white balls of smaller size than the black, neither would the
probability remain the same; the larger ball would be much more likely
to meet the hand."*
It is, in fact, evident that when once cansation is admitted as a universal
law, our expectation of events can only be rationally grounded on that law.
To a person who recognizes that every event depends on causes, a thing's
having happened once is a reason for expecting it to happen again, only be-
cause proving that there exists, or is liable to exist, a cause adequate to
produce it.f The frequency of the particular event, apart from all surmise
respecting its cause, can give rise to no other induction than that per erm-
merationem simplicem; and the precarious inferences derived from this are
superseded, and disappear from the field as soon as th.e principle of causa-
tion makes its appearance there.
Notwithstanding, however, the abstract superiority of an estimate of
probability grounded on causes, it is a fact that in almost all cases in
"which chances admit of estimation sufficiently precise to render their
numerical appreciation of any practical value, the numerical data are not
drawn from knowledge of the causes, but from experience of the events
* Prospective Review for Tebraary, 1850.
t "If this be not so, why do we feel so much more probability added by the first instance
than by any single subsequent instance ? Why, except that the first instance gives us its pos-
sibility (a cause adequate to it), while every other only gives us the frequency of its conditions ?
If no reference to a cause be supposed, possibility would have no meaning ; yet it is clear that,
antecedent to its happening, we might have supposed the event impossible, i. e., have believed
that there was no physical energy really existing in the world equal to producing it Af-
ter the first time of happening, which is, then, more important to the whole probability than
any other single instance (because proving the possibility), the number of times becomes im-
portant as an index to the intensity or extent of the cause, and its independence of any par-
ticular time. If we took the case of a tremendous leap, for instance, and wished to form an
estimate of the probability of its succeeding a certain number of times ; the first instance, by
showing its possibihty (before doubtful) is of the most importance ; but every succeeding leap
shows the power to be more perfectly under control, greater and more invaiiable, and so in-
creases the probability ; and no one would think of reasoning in this case straight from one
Instance to the next, without referring to the physical energy which each leap indicated. Is
it not, then, clear that we do not ever" (let us rather say, that we do not in an advanced state
of our knowledge) " conclude directly from the happening of an event to the probability of its
happening again ; but that we refer to the cause, regarding the past cases as an index to the
cause, and the cause as our guide to the future ?" — Jbid.
OF THE CALCULATION OF CHANCES. 385
themsulves. The probabilities of life at different ages or in different cli-
mates ; the probabilities of recovery from a particular disease ; the chances
of the birth of male or female offspring ; the chances of the destruction of
houses or other property by fire ; the chances of the loss of a ship in a
particular voyage, are deduced from bills of mortality, returns from hos-
pitals, registers of births, of shipwrecks, etc., that is, from the observed
frequency not of the causes, but of the effects. The reason is, that in all
these classes of facts the causes are either not amenable to direct observa-
tion at all, or not with the requisite precision, and we have no means of
judging of their frequency except from the empirical law afforded by the
frequency of the effects. The inference does not the less depend on cau-
sation alone. We reason from an effect to a similar effect by passing
through the cause. If the actuary of an insurance office infers from his
tables that among a hundred persons now living of a particular age, five
on the average will attain the age of seventy, his inference is legitimate,
not .for the simple reason that this is the pi-oportion who have lived till
seventy in times past, but because the fact of their having so lived shows
that this is the proportion existing, at that place and time, between the
causes which prolong life to the age of seventy and those tending to bring
it to an earlier close.*
§ 5. From the preceding principles it is easy to deduce the demonstra-
tion of that theorem of the doctrine of probabilities which is the founda-
tion of its application to inquiries for ascertaining the occurrence of a
given event, or the reality of an individual fact. The signs or evidences by
which a fact is usually proved are some of its consequences ; and the in-
quiry hinges upon determining what cause is most likely to have produced
a given effect. The theorem applicable to such investigations is the Sixth
Principle in Laplace's "Essai Philosophique sur les Probabilites" which is
described by him as the " fundamental principle of that branch of the Analy-
sis of Chances which consists in ascending from events to their causes."f
Given an effect to be accounted for, and there being several causes which
might have produced it, but of the presence of which in the particular case
nothing is known ; the probability that the effect was produced by any one
of these causes is as the antecedent probability of the cause, multiplied by
the probability that the cause, if it existed, would have produced the given
effect.
Let M be the effect, and A, B, two causes, by either of which it might
* The writer last quoted says that the valuation of chances by comparing the number of
cases in which the event occurs with the number in which it does not occur, "would gen-
erally be wholly erroneous," and "is not the true theory of probability." It is at least that
which forms the foundation of insurance, and of all those calculations of chances in the busi-
ness of life which experience so abundantly verifies. The reason which the reviewer gives for
rejecting the theory is, that it " would regard an event as certain which had hitherto never
failed; which is exceedingly far from the truth, even for a very large number of constant suc-
cesses." This is not a defect in a particular theory, but in any theory of chances. No prin-
ciple of evaluation can provide for such a case as that which the reviewer supposes. If an
event has never once failed, in a number of trials sufficient to eliminate chance, it really has
all the certainty which can be given by an empirical law ; it is certain during the continuance
of the same collocation of causes which existed during the observations. If it ever fails, it is
in consequence of some change in that collocation. Now, no theory of chances will enable us
to infer^the future probability of an event from the past, if the causes in operation, capable of
influencing the event, have intermediately undergone a change.
t Pp. 18, 19. The theorem is not stated by Laplace in the exact terms in which I have
stated it ; but the identity of import of the two modes of expression is easily demonstrable.
25
386 INDUCTION.
have been produced. To find the probability that it was produced by the
one and not by the other, ascertain which of the two is most likely to have
existed, and which of them, if it did exist, was most likely to produce the
effect M : the probability sought is a compound of these two probabilities.
Case I. Let the causes be both alike in the second respect : either A or
B, when it exists, being supposed equally likely (or equally certain) to pro-
duce M ; but let A be in itself twice as likely as B to exist, that is, twice
as frequent a phenomenon. Then it is twice as likely to have existed in
this case, and to have been the cause which produced M.
For, since A exists in nature twice as often as B, in any 300 cases in
which one or other existed, A has existed 200 times and B 100. But ei-
ther A or B must have existed wherever M is produced ; therefore, in 300
times that M is produced, A was the producing cause 200 times, B only
100, that is, in the ratio of 2 to 1. Thus, then, if the causes are alike in
their capacity of producing the effect, the probability as to which actually
produced it is in the ratio of their antecedent probabilities.
Case II. Reversing the last hypothesis, let us suppose that the causes
are equally frequent, equally likely to have existed, but not equally likely, if
they did exist, to produce M ; that in three times in which A occurs, it
produces that effect twice, while B, in three times, produces it only once.
Since the two causes are equally frequent in their occurrence ; in every six
times that either one or the other exists, A exists three times and B three
times. A, of its three times, produces M in two ; B, of its three times,
produces M in one. Thus, in the whole six times, M is only produced
thrice ; but of that thrice it is produced twice by A, once only by B. Con-
sequently, when the antecedent probabilities of the causes are equal, the
chances that the effect was produced by them are in the ratio of the proba-
bilities that if they did exist they would produce the effect.
Case III. The third case, that in which the causes are unlike in both re-
spects, is solved by what has preceded. For, when a quantity depends on
two other quantities, in such a manner that while either of them remains
constant it is proportional to the other, it must necessarily be proportional
to the product of the two quantities, the product being the only function
of the two which obeys that law of variation. Therefore, the probability
that M was produced by either cause, is as the antecedent probability of
the cause, multiplied by the probability that if it existed it would produce
JM. Which was to be demonstrated.
Or we may prove the third case as we proved the first and second. Let
A be twice as frequent as B, and let them also be unequally likely, when
they exist, to produce M ; let A produce it twice in four times, B thrice in
four times. The antecedent probability of A is to that of B as 2 to 1 ;
the probabilities of their producing M are as 2 to 3 ; the product of these
ratios is the ratio of 4 to 3 ; and this will be the ratio of the probabilities
that A or B was the producing cause in the given instance. For, since A
is twice as frequent as B, out of twelve cases in which one or other exists,
A exists in 8 and B in 4. But of its eight cases, A, by the supposition,
produces M in only 4, while B of its four cases produces M in 3. M, there-
fore, is only produced at all in seven of the twelve cases ; but in four of
these it is produced by A, in three by B ; hence the probabilities of its be-
ing produced by A and by B are as 4 to 3, and are expressed by the frac-
tions ^ and 4- Which was to be demonstrated.
§ 6. It remains to examine the bearing of the doctrine of chances on
OF THE CALCULATION OF CHANCES. 387
<the peculiar problem which occupied us in the preceding chapter, namely,
iow to distinguish coincidences which are casual from those which are the
result of law; from those in which the facts which accompany or follow
■one another are somehow connected through causation.
The doctrine of chances affords means by which, if we knew the average
number of coincidences to be looked for between two phenomena connected
-only casually, we could determine how often any given deviation from that
average will occur by chance. If the probability of any casual coincidence,
considered in itself, be — , the probability that the same coincidence will
be repeated n times in succession is — j. For example, in one throw of a
die the probability of ace being -; the probability of throwing ace twice
in succession will be 1 divided by the square of 6, or — . For ace is thrown
36
at the first throw once in six, or six in thirty-six times, and of those six, the
die being cast again, ace will be thrown but once ; being altogether once in
thirty-six times. The chance of the same cast three times successively is,
by a similar reasoning, -j or — — ; that is, the event will happen, on a large
average, only once in two hundred and sixteen throws.
We have thus a rule by which to estimate the probability that any given
series of coincidences arises from chance, provided we can measure correct-
ly the probability of a single coincidence. If we can obtain an equally
precise expression for the probability that the same series of coincidences
arises from causation, we should only have to compare the numbers. This,
however, can rarely be done. Let us see what degree of approximation
■can practically be made to the necessary precision.
The question falls within Laplace's sixth principle, just demonstrated.
The given fact, that is to say, the series of coincidences, may have origi-
nated either in a casual conjunction of causes or in a law of nature. The
probabilities, therefore, that the fact originated in these two modes, are as
their antecedent probabilities, multiplied by the probabilities that if they
existed they would produce the effect. But the particular combination of
chances, if it occurred, or the law of nature if real, would certainly produce
the series of coincidences. The probabilities, therefore, that the coinci-
dences are produced by the two causes in question are as the antecedent
probabilities of the causes. One of these, the antecedent probability of the
combination of mere chances which would produce the given result, is an
appreciable quantity. The antecedent probability of the other supposition
may be susceptible of a more or less exact estimation, according to the na-
ture of the case.
In some cases, the coincidence, supposing it to be the result of causation
at all, must be the result of a known cause ; as the succession of aces, if not
accidental, must arise from the loading of the die. In such cases we may
be able to form a conjecture as to the antecedent probability of such a cir-
cumstance from the characters of the parties concerned, or other such evi-
dence; but it would be impossible to estimate that probability with any
thing like numerical precision. The counter-probability, however, that of
the accidental origin of the coincidence, dwindling so rapidly as it does at
each new trial, the stage is soon reached at which the chance of unfairness
388 INDUCTION.
in the die, however small in itself, must be greater than that of a casual
coincidence ; and on this ground, a practical decision can generally be come
to without much hesitation, if there be the power of repeating the experi-
ment.
When, however, the coincidence is one which can not be accounted for
by any known cause, and the connection between the two phenomena, if
produced by causation, must be the result of some law of nature hitherto
unknown; which is the case we had in view in the last chapter; then,
though the probability of a casual coincidence may be capable of appreciar-
tion, that of the counter-supposition, the existence of an undiscovered law
of nature, is clearly unsusceptible of even an approximate valuation. In
order to have the data which such a case would require, it would be neces-
sary to know what proportion of all the individual sequences or co-exist-
ences occurring in nature are the result of law, and what proportion are
mere casual coincidences. It being evident that we can not form any
plausible conjecture as to this proportion, much less appreciate it numer
ically, we can not attempt any precise estimation of the comparitive proba-
bilities. But of this we are sure, that the detection of an unknown law of
nature — of some previously unrecognized constancy of conjunction among
phenomena — is no uncommon event. If, therefore, the number of instances
in which a coincidence is observed, over and above that which would arise
on the average from the mere concurrence of chances, be such that so great
an amount of coincidences from accident alone would be an extremely un-
common event ; we have reason to conclude that the coincidence is the ef-
fect of causation, and may be i-eceived (subject to correction from further
experience) as an empirical law. Further than this, in point of precision,
we can not go ; nor, in most cases, is greater precision required, for the
solution of any practical doubt.*
CHAPTER XIX.
OF THE EXTENSION OF DEEITATIVE I.AWS TO ADJACENT CASES.
§ 1. We have had frequent occasion to notice the inferior generality of
derivative laws, compared with the ultimate laws from which they are de-
rived. This inferiority, which affects not only the extent of the proposi-
tions themselves, but their degree of certainty within that extent, is most
conspicuous in the uniformities of co-existence and sequence obtaining be-
tween effects which depend ultimately on different primeval causes. Such
uniformities will only obtain where there exists the same collocation of
those primeval causes. If the collocation varies, though the laws them-
selves remain the same, a totally different set of derivative uniformities
may, and generally will, be the result.
Even where the derivative uniformity is between different effects of the
same cause, it will by no means obtain as universally as the law of the
* Por a fuller treatment of the many interesting questions raised by the theory of probabili-
ties, I may now refer to a recent work by Mr. Venn, Fellow of Cains College, Cambridge,
"The Logic of Chance;" one of the most thoughtful and philosophical treatises on any sub-
ject connected with Logic and Evidence which have been produced, to my knowledge, for
many years. Some criticisms contained in it have been very useful to me in revising the cor-
responding chapters of the present work. In several of Mr. Venn's opinions, however, I do
not agree. What these are will be obvious to any reader of Mr. Venn's work who is also »
reader of this.
EXTENSION OF LAWS TO ADJACENT CASES. 389
■cause itself. If a and h accompany or succeed one another as effects of the
cause A, it by no nieans follows that A is the only cause which can pro-
duce them, or that if there be another cause, as B, capable of producing a,
it must produce b likewise. The conjunction, therefore, of a and b perhaps
■does not hold universally, but only in the instances in which a arises from
A. When it is produced by a cause other than A, a and b may be dissev-
ered. Day (for example) is always in our experience followed by night;
but day is not the cause of night; both are successive effects of a common
<!ause, the periodical passage of the spectator into and out of the earth's
shadow, consequent on the earth's rotation, and on the illuminating prop-
erty of the sun. If, therefore, day is ever produced by a different caus3
or set of causes from this, day will not, or at least may not, be followed by
night. On the sun's own surface, for instance, this may be the case.
Finally, even when the derivative uniformity is itself a law of causation
(resulting from the combination of several causes), it is not altogether in-
■dependent of collocations. If a cause supervenes, capable of wholly or par-
tially counteracting the effect of any one of the conjoined causes, the effect
will no longer conform to the derivative law. While, therefore, each ulti-
mate law is only liable to frustration from one set of counteracting- causes,
the derivative law is liable to it from several. Now, the possibility of the
occurrence of countei'acting causes which do not arise from any of the con-
ditions involved in the law itself depends on the original collocations.
It is true that, as we formerly remarked, laws of causation, whether ulti-
mate or derivative, are, in most cases, fulfilled even when counteracted ;
the cause produces its effect, though that effect is destroyed by something
else. That the effect may be frustrated, is, therefore, no objection to the
universality of laws of causation. But it is fatal to the universality of the
sequences or co-existences of effects, which compose the greater part of the
derivative laws flowing from laws of causation. When, from the law of a
certain combination of causes, there results a certain order in the effects ;
as from the combination of a single sun with the rotation of an opaque
body round its axis, there results, on the whole surface of that opaque
body, an alternation of day and night ; then, if we suppose one of the com-
bined causes counteracted, the rotation stopped, the sun extinguished, or a
second sun superadded, the truth of that particular law of causation is in
no way affected ; it is still true that one sun shining on an opaque revolv-
ing body will alternately produce day and night; but since the sun no
longer does shine on such a body, the derivative uniformity, the succession
of day and night on the given planet, is no longer true. Those derivative
uniformities, therefore, which are not laws of causation, are (except in the
rare case of their depending on one cause alone, not on a combination of
causes) always more or less contingent on collocations ; and are hence sub-
ject to the characteristic infirmity of empirical laws — that of being admis-
sible only where the collocations are known by experience to be such as
are requisite for the truth of the law; that is, only within the conditions
of time and place confirmed by actual observation.
§ 2. This principle, when stated in general terms, seems clear and indis-
putable ; yet many of the ordinary judgments of mankind, the propriety
of which is not questioned, have at least the semblance of being inconsist-
ent with it. On what grounds, it may be asked, do we expect that the
sun will rise to-morrow ? To-morrow is beyond the limits of time compre-
hended in our observations. They have extended over some thousands of
390 INDUCTION.
years past, but they do not include the future. Yet we infer with confix
dence that the sun will rise to-morrow ; and nobody doubts that we are-
entitled to do so. Let us consider what is the warrant for this confidence.
In the example in question, we know the causes on which the derivative-
uniformity depends. They are : the sun giving out light, the earth in a
state of rotation and intercepting light. The induction which shows these
to be the real causes, and not merely prior effects of a common cause, be-
ing complete, the only circumstances which could defeat the derivative law
are such as would destroy or counteract one or other of the combined
causes. While the causes exist and are not counteracted, the effect will
continue. If they exist aqd are not counteracted to-morrow, the sun will
rise to-morrow.
Since the causes, namely, the sun and the earth, the one in the state of
giving out light, the other in a state of rotation, will exist until something
destroys them, all depends on the probabilities of their destruction, or of
their counteraction. We know by observation (omitting the inferential
proofs of an existence for thousands of ages anterior) that these phenomena
have continued for (say) five thousand years. Within that time there has
existed no cause sufiicient to diminish them appreciably, nor which has-
counteracted their effect in any appreciable degree. The chance, therefore,
that the sun may not rise to-morrow amounts to the chance that some
cause, which has not manifested itself in the smallest degree during five
thousand years, will exist to-morrow in such intensity as to destroy the
sun or the earth, the sun's light or the earth's rotation, or to produce an
immense disturbance in the effect resulting from those causes.
Now, if such a cause will exist to-morrow, or at any future time, some
cause, proximate or remote, of that cause must exist now, and must have ex-
isted during the whole of the five thousand years. If, therefore, the sun do
not rise to-morrow, it will be because some cause has existed, the effects of
which, though during five thousand years they have not amounted to a per-
ceptible quantity, will in one day become overwhelming. Since this cause
has not been recognized during such an interval of time by observers sta-
tioned on our earth, it must, if it be a single agent, be either one whose
effects develop themselves gradually and very slowly, or one which existed
in regions beyond our observation, and is now on the point of arriving in
our part of the universe. Now all causes which we have experience of act
according to laws incompatible with the supposition that their effects, af-
ter accumulating so slowly as to be imperceptible for five thousand years,
should start into immensity in a single day. No mathematical law of pro-
portion between an effect and the quantity or relations of its cause could
produce such contradictory results. The sudden development of an effect
of which there was no previous trace always arises from the coming to-
gether of several distinct causes, not previously conjoined ; but if such sud-
den conjunction is destined to take place, the causes, or their causes, must
have existed during the entire five thousand years ; aiid their not having
once come together during that period shows how rare that particular com-
bination is. We have, therefore, the warrant of a rigid induction for con-
sidering it probable, in a degree undistinguishable from certainty, that the
known conditions requisite for the sun's rising will exist to-morrow.
§ 3. But this extension of derivative laws, not causative, beyond the lim-
its of observation can only be to adjacent cases. If, instead of to-morrow,
we had said this day twenty thousand years, the inductions would have
EXTENSION OF LAWS TO ADJACENT CASES. 391
been any thing but conclusive. That a cause which, in opposition to very
powerful causes, produced no perceptible effect during five thousand years,
should produce a very considerable one by the end of twenty thousand, has-
nothing in it which is not in conformity with our experience of causes.
We know many agents, the effect of which in a short period does not
amount to a perceptible quantity, but by accumulating for a much longer
period becomes considerable. Besides, looking at the immense multitude
of the heavenly bodies, their vast distances, and the rapidity of the motion
of such of them as are known to move, it is a supposition not at all contra-
dictory to experience that some body may be in motion toward us, or we
toward it, within the limits of whose influence we have not come dui-ing^
five thousand years, but which in twenty thousand more may. be producing-
effects upon us of the most extraordinary kind. Or the fact which is ca-
pable of preventing sunrise may be, not the cumulative effect of one cause,,
but some new combination of causes ; and the chances favorable to that
combination, though they have not produced it once in five thousand years,.
may produce it once in twenty thousand. So that the inductions which
authorize us to expect future events, grow weaker and weaker the further
we look into the future, and at length become inappreciable.
We have considered the probabilities of the sun's rising to-morrow, as-
derived from the real laws; that is, from the laws of the causes on which,
that uniformity is dependent. Let us now consider how the matter would
have stood if the uniformity had been known only as an empirical law ; if
we had not been aware that the sun's light and the earth's rotation (or the
sun's motion) were the causes on which the periodical occurrence of day-
light depends. We could have extended this empirical law to cases adja-
cent in time, though not to so great a distance of time as we can now..
Having evidence that the effects had remained unaltered and been punctu-
ally conjoined for five thousand years, we could infer that the unknown,
causes on which the conjunction is dependent had existed undiminished and
uncounteracted during the same period. The same conclusions, therefore^
would follow as in the preceding case, except that we should only know-
that during five thousand years nothing had occurred to defeat perceptibly
this particular effect ; while, when we know the causes, we have the addi-
tional assurance that during that interval no such change has been notice-
able in the causes themselves as by any degree of multiplication or length
of continuance could defeat the effect.
To this must be added, that when we know the causes, we may be able
to judge whether there exists any known cause capable of counteracting
them, while as long as they are unknown, we can not be sure but that if we
did know them, we could predict their destruction from causes actually ia
existence. A bed-ridden savage, who had never seen the cataract of Niag-
ara, but who lived within hearing of it, might imagine that the sound he
heard would endure forever ; but if be knew it to be the effect of a rush of
waters over a barrier of rock which is progi-essively wearing away, he would
know that within a number of ages which may be calculated it will be heard
no more. In proportion, therefore, to our ignorance of the causes on which
the empirical law depends, we can be less assured that it will continue tO'
hold good ; and the further we look into futurity, the less improbable is it
that some one of the causes, whose co-existence gives rise to the derivative-
uniformity, may be destroyed or counteracted. With every prolongatioa
of time the chances multiply of such an event ; that is to say, its non-occur-
rence hitherto becomes a less guarantee of its not occurring within the
392 INDUCTION.
given time. If, then, it is only to cases which in point of time are adjacent
(or nearly adjacent) to those which we have actually observed, that any
derivative law, not of causation, can be extended with an assurance equiv-
alent to certainty, much more is this true of a merely empirical law. Hap-
pily, for the purposes of life it is to such cases alone that we can almoet
€ver have occasion to extend them.
In respect of place, it might seem that a merely empirical law could not
be extended even to adjacent cases ; that we could have no assurance of its
being true in any place where it has not been specially observed. The past
duration of a cause is a guarantee for its future existence, unless something
occurs to destroy it; but the existence of a cause in one or any number of
places is no guarantee for its existence in any other place, since there is no
uniformity in the collocations of primeval causes. When, therefore, an em-
pirical law is extended beyond the local limits within which it has been
found true by observation, the cases to which it is thus extended must be
such as are presumably within the influence of the same individual agents.
If we discover a new planet within the known bounds of the solar system
{or even beyond those bounds, but indicating its connection with the system
by revolving round the sun), we may conclude, with great probability, that
it revolves on its axis. For all the known planets do so ; and this uniform-
ity points to some common cause, antecedent to the first records of astro-
nomical observation ; and though the nature of this cause can only be mat-
ter of conjecture, yet if it be, as is not unlikely, and as Laplace's theory
supposes, not merely the same kind of cause, but the same individual cause
(such as an impulse given to all the bodies at once), that cause, acting at
the extreme points of the space occupied by the sun and planets, is likely,
unless defeated by some counteracting cause, to have acted at every inter-
mediate point, and probably somewhat beyond ; and therefore acted, in all
probability, upon the supposed newly-discovered planet.
When, therefore, effects which are always found conjoined can be traced
■with any probability to an identical (and not merely a similar) origin, we
may with the same probability extend the empirical law of their conjunc-
tion to all places within the extreme local boundaries within which the fact
has been observed, subject to the possibility of counteracting causes in some
portion of the field. Still more confidently may we do so when the law is
not merely empirical; when the phenomena which we find conjoined are
effects of ascertained causes, from the laws of which the conjunction of their
effects is deducible. In that case, we may both extend the derivative uni-
formity over a larger space, and with less abatement for the chance of
counteracting causes. The first, because instead of the local boundaries of
our observation of the fact itself, we may include the extreme boundaries
of the ascertained influence of its causes. Thus the succession of day and
night, we know, holds true of all the bodies of the solar system except the
sun itself ; but we know this only because we are acquainted with the
causes. If we were not, we could not extend the proposition beyond the
orbits of the earth and rtioon, at both extremities of which we have the
evidence of observation for its truth. With respect to the probability of
counteracting causes, it has been seen that this calls for a greater abatement
of confidence, in proportion to our ignorance of the causes on which the
phenomena depend. On both accounts, therefore, a derivative law which
we know how to resolve, is susceptible of a greater extension to cases ad-
jacent in place, than a merely empirical law.
ANALOGY. J593
CHAPTER XX.
OP ANALOGY.
§ 1. The word Analogy, as the name of a mode of reasoning, is generally
taken for some kind of argument supposed to be of an inductive nature,,
but not amounting to a complete induction. There is no_^ word, however,,
which is used more loosely, or in a greater variety of sense's, than Analogy.
It sometimes stands for arguments which may be examples of the most
rigorous induction. Archbishop Whately, for instance, following Fergu-
son and other writers, defines Analogy conformably to its primitive accep-
tation, that which was given to it by mathematicians : Resemblance of Re-
lations. In this sense, when a country which has sent out colonies is term-
ed the mother country, the expression is analogical, signifying that the col-
onies of a country stand in the same relation to her in which children
stand to their parents. And if any inference be drawn from this resem-
blance of relations, as, for instance, that obedience or affection is due from
colonies to the mother country, this is called reasoning by analogy. Or, if
it be argued that a nation is most beneficially governed by an assembly
elected by the people, from the admitted fact that other associations for a
common purpose, such as joint-stock companies, are best managed by a
committee chosen by the parties interested ; this, too, is an argument from
analogy in the preceding sense, because its foundation is, not that a nation
is like a joint-stock company, or Parliament like a board of directors, but
that Parliament stands in the same relation to the nation in which a board
of directors stands to a joint-stock company. Now, in an argument of this,
nature, there is no inherent inferiority of conclusiveness. Like other argu-
ments' from resemblance, it may amount to nothing, or it may be a perfect
and conclusive induction. The circumstance in which the two cases re-
semble, may be capable of being shown to be the material circumstance ;;
to be that on which all the consequences, necessary to be taken into ac-
count in the particular discussion, depend. In the example last given, the
resemblance is one of relation; the fundamentum relationis being the-
management, by a few persons, of affairs in which a much greater number
are interested along with them. Now, some may contend that this cir-
cumstance which is common to the two cases, and the various consequences
which follow from it, have the chief share in determining all the effect*
which make up what we term good or bad administration. If they can es-
tablish this, their argument has the force of a rigorous induction ; if they
can not, they are said to have failed in proving the analogy between the
two cases ; a mode of speech which implies that when the analogy can be
proved, the argument founded on it can not be resisted.
§ 2. It is on the whole more usual, however, to extend the name of ana-
logical evidence to arguments from any sort of resemblance, provided they
do not amount to a complete induction; without peculiarly distinguishing
resemblance of relations. Analogical reasoning, in this sense, may be re-
duced to the following formula : Two things resemble each other in one or
394 INDUCTION.
more respects ; a certain proposition is true of the one ; therefore it is true
■of the other. But we have nothing here by which to discriminate analogy
from induction, since this type will serve for all reasoning from experience.
In the strictest induction, equally with the faintest analogy, we conclude
because A resembles B in one or more propertiec, that it does so in a cer-
tain other property. The difference is, that in the case of a complete in-
duction it has been previously shown, by due comparison of instances, that
there is an invariable conjunction between the former property or proper-
ties and the latter property; but in what is called analogical reasoning, no
such conjunction has been made out. There have been no opportunities of
putting in practice the Method of Difference, or even the Method of Agree-
ment ; but we conclude (and that is all which the argument of analogy
amounts to) that a fact m, known to be true of A, is more likely to be true
of B if B agrees with A in some of its properties (even though no connec-
tion is known to exist between m and those properties), than if no resem-
blance at all could be traced between B and any other thing known to pos-
sess the attribute m.
To this argument it is of course requisite that the properties common to
A with B shall be merely not known to be connected with m; they must
Tiot be properties known to be unconnected with it. If, either by processes
■of elimination, or by deduction from previous knowledge of the laws of the
properties in question, it can be concluded that they have nothing to do
-with m, the argument of analogy is put out of court. The supposition
must be that m is an effect really dependent on some property of A, but
we know not on which. We can not point out any of the properties of A,
•which is the cause of m, or united with it by any law. After rejecting all
which we know to have nothing to do with it, there remain several between
•which we are unable to decide ; of which remaining properties, B possesses
one or more. This, accordingly, we consider as affording grounds, of more
■or less strength, for concluding by analogy that B possesses the attribute m.
There can be no doubt that every such resemblance which can be point-
•ed out between B and A, affords some degree of probability, beyond what
would otherwise exist, in favor of the conclusion drawn from it. If 'B re-
sembled A in all its ultimate properties, its possessing the attribute m
would be a certainty, not a probability ; and every resemblance which can be
.-shown to exist between them, places it by so much the nearer to that point.
If the resemblance be in an ultimate property, there will be resemblance in
all the derivative properties dependent on that ultimate property, and of
these m may be one. If the resemblance be in a derivative property, there
is reason to expect resemblance in the ultimate property on which it de-
pends, and in the other derivative properties dependent on the same ultimate
pi'operty. Every resemblance which can be shown to exist, affords ground
for expecting an indefinite number of other resemblances; the particular
resemblance sought will, therefore, be oftener found among things thus
known to resemble, than among things between which we know of no re-
semblance.
For example, I might infer that there are probably inhabitants in the
moon, because there are inhabitants on the earth, in the sea, and in the air :
and this is the evidence of analogy. The circumstance of having inhabit-
ants is here assumed not to be an ultimate property, but (as is reasonable
to suppose) a consequence of other properties ; and depending, therefore,
in the case of the earth, on some of its properties as a portion of the uni-
verse, but on which of those properties we know not. Now the moon re-
ANALOGY. 395
.sembles the earth in being a solid, opaque, nearly spherical substance, ap-
pearing to contain, or to have contained, active volcanoes ; receiving heat
and light from the sun, in about the same quantity as our earth ; revolving
on its axis ; composed of materials which gravitate, and obeying all the va-
rious laws resulting from that property. And I think no one will deny
that if this were all that was known of the moon, the existence of inhabit-
ants in that luminary would derive from these various resemblances to
the earth, a greater degree of probability than it would otherwise have;
though the amount of the augmentation it would be useless to attempt to
estimate.
If, however, every resemblance proved between B and A, in any point
cot known to be immaterial with respect to m, forms some additional rea-
son for presuming that B has the attribute m; it is clear, ^ contra, that ev-
ery dissimilarity which can be proved betweeu them furnishes a counter-
probability of the same nature on the other side. It is not, indeed, unusual
that different ultimate properties should, in some particular instances, pro-
duce the same derivative property ; but on the whole it is certain that
things which differ in their ultimate properties, will differ at least as much
in the aggregate of their derivative properties, and that the differences
which are unknown will, on the average of cases, bear some proportion to
those which are known. There will, therefore, be a competition between
the known points of agreement and the known points of difference in A
and B ; and according as the one or the other may be deemed to prepon-
derate, the probability derived from analogy will be for or against B's hav-
ing the property m. The moon, fcfi* instance, agrees with the earth in the
circumstances already mentioned ; but differs in being smaller, in having
its surface more unequal, and apparently volcanic throughout, in having, at
least on the side next the earth, no atmosphere sufficient to refract light, no
clouds, and (it is therefore concluded) no water. These differences, consid-
ered'merely as such, might perhaps balance the resemblances, so that anal-
ogy would afford no presumption either way. But considering that some
of the circumstances which are wanting on the moon are among those
which, on the earth, are found to be indispensable conditions of animal life,
we may conclude that if that phenomenon does exist in the moon (or at all
events on the nearer side), it must be as an effect of causes totally different
from those on which it depends here ; as a consequence, therefore, of the
moon's differences from the earth, not of the points of agreement. Viewed
in this light, all the resemblances which exist become presumptions against,
not in favor of, the moon's being inhabited. Since life can not exist there
in the manner in which it exists here, the greater the resemblance of the
Innar world to the terrestrial in other respects, the less reason we have to
Relieve that it can contain life.
There are, however, other bodies in our system, between which and the
earth there is a much closer resemblance ; which possess an atmosphere,
clouds, consequently water (or some fluid analogous to it), and even give
strong indications of snow in their polar regions ; while the cold, or heat,
though differing greatly on the average from ours, is, in some parts at least
of those planets, possibly not more extreme than in some regions of our
own which are habitable. To balance these agreements, the ascertained
differences are chiefly in the average light and heat, velocity of rotation,
density of material, intensity of gravity, and similar circumstances of a sec-
ondary kind. With regard to these planets, therefore, the argument of
analogy gives a decided preponderance in favor of their resembling the
396 INDUCTION.
earth in any of its derivative properties, such as that of having inhabitants j
though when we consider how immeasurably multitudinous are those of
their properties which we are entirely ignorant of, compared with the few
which we know, we can attach but trifling weight to any considerations of
resemblance in which the known elements bear so inconsiderable a propor-
tion to the unknown.
Besides the competition between analogy and diversity,^ there may be a
competition of conflicting analogies. The new case may be similar in some
of its circumstances to cases in which the fact m exists, but in others to-
cases in which it is known not to exist. Amber has some properties in
common with vegetable, others with mineral products. A painting of un-
known origin may resemble, in certain of its characters, known works of a
particular master, but in others it may as strikingly resemble those of some
other painter. A vase may bear some analogy to works of Grecian, and
some to those of Etruscan, or Egyptian art. We are of course supposing
that it does not possess any quality which has been ascertained, by a suffi-
cient induction, to be a conclusive mark either of the one or of the other.
§ 3. Since the value of an analogical argument inferring one resemblance
from other resemblances without any antecedent evidence of a connection
between them, depends on the extent of ascertained resemblance, compared
first with the amount of ascertained difference, and next with the extent of
the unexplored region of unascertained properties ; it follows that where
the resemblance is very great, the ascertained difference very small, and our
knowledge of the subject-matter tolerably extensive, the argument from
analogy may approach in strength very near to a valid induction. If, afte"
much observation of B, we find that it agrees with A in nine out of ten of
its known properties, we may conclude with a probability of nine to one,
that it will possess any given derivative property of A. If we discover,
for example, an unknown animal or plant, resembling closely some known
one in the greater number of the properties we observe in it, but differing
in some few, we may reasonably expect to find in the unobserved remain-
der of its properties, a general agreement with those of the former ; but
also a difference corresponding proportionately to the amount 'of observed
diversity.
It thus appears that the conclusions derived from analogy are only of
any considerable value, when the case to which we reason is an adjacent
case ; adjacent, not as before, in place or time, but in circumstances. In
the case of effects of which the causes are imperfectly or not at all known,
wrhen consequently the observed order of their occui-rence amounts only to
an empirical law, it often happens that the conditions which have co-exist-
ed whenever the effect was observed, have been very numerous. "Now if
a new case presents itself, in which all these conditions do not exist, but
the far greater part of them do, some one or a few only being wanting, the
inference that the effect will occur, notwithstanding this deficiency of com-
plete resemblance to the cases in which it has been observed, may, though
of the nature of analogy, possess a high degree of probability. It is hard-
ly necessary to add that, however considerable this probability may be, no
competent inquirer into nature will rest satisfied with it when a complete
induction is attainable; but will consider the analogy as a mere guide-
post, pointing out the direction in which more rigorous investigations
should be prosecuted.
It is in this last respect that considerations of analogy have the highest
EVIDENCE OF UNIVERSAL CAUSATION. 397
scientific value. The cases in which analogical evidence affords in itself
any very high degree of probability, are, as we have observed, only those
in which the resemblance is very close and extensive ; but there is no anal-
■ogy, however faint, which may not be of the utmost value in suggesting
experiments or observations that may lead to more positive conclusions.
When the agents and their effects are out of the reach of further observa-
tion and experiment, as in the speculations already alluded to respecting
the moon and planets, such slight probabilities are no more than an inter-
esting theme for the pleasant exercise of imagination ; but any suspicion,
however slight, that sets an ingenious person at work to contrive an ex-
periment, or affords a reason for trying one experiment rather than anoth-
er, may be of the greatest benefit to science.
On this ground, though I can not accept as positive truths any of those
scientific hypotheses which are unsusceptible of being ultimately brought
to the test of actual induction, such, for instance, as the two theories of
Jight, the emission theory of the last century, and the undulatory theory
which predominates in the present, I am yet unable to agree with those
who consider such hypotheses to be worthy of entire disregard. As is well
said by Hartley (and concurred in by a thinker in general so diametrically
opposed to Hartley's opinions as Dugald Stewart), " any hypothesis which
has so much plausibility as to explain a considerable number of facts, helps
us to digest these facts in proper order, to bring new ones to light, and
make expenmenta crucis for the sake of future inquirers."* If an hypoth-
esis both explains known facts, and has led to the prediction of others
previously unknown, and since verified by experience, the laws of the phe-
nomenon which is the subject of inquiry must bear at least a great similar-
ity to those of the class of phenomena to which the hypothesis assimi-
lates it ; and since the analogy which extends so far may probably extend
further, nothing is more likely to suggest experiments tending to throw
light upon the real properties of the phenomenon, than the following out
such an hypothesis. But to this end it is by no means necessary that the
hypothesis be mistaken for a scientific truth. On the contrary, that illu-
sion is in this respect, as in every other, an impediment to the progress of
real knowledge, by leading inquirers to restrict themselves arbitrarily to
the particular hypothesis which is most accredited at the time, instead of
looking out for every class of phenomena between the laws of which and
those of the given phenomenon any analogy exists, and trying all such ex-
periments as may tend to the discovery of ulterior analogies pointing in
the same direction.
CHAPTER XXI.
OF THE EVIDENCE OF THE LAW OP tTNTVEESAL CAUSATION.
§ 1. We have now completed our review of the logical processes by
which the laws, or uniformities, of the sequence of phenomena, and those
uniformities in their co-existence which depend on the laws of their se-
quence, are ascertained or tested. As we recognized in the commence-
ment, and have been enabled to see more clearly in the progress of the in
vestigation, the basis of all these logical operations is the law of causation.
• Hartley's Observations on Man, vol. i., p. 16. The passage is not in Priestley's curtailed
edition.
398 INDUCTION.
The validity of all the Inductive Methods depends on the assumption that
every event, or the beginning of every phenomenon, must have some cause ;
some antecedent, on the existence of which it is invariably and uncondi-
tionally consequent. In the Method of Agreement this is obvious; that
method avowedly proceeding on the supposition that we have found the
true cause as soon as we have negatived every other. The assertion is
equally true of the Method of Difference. That method authorizes us to
infer a general law from two instances ; one, in which A exists together
with a multitude of other circumstances, and B follows ; another, in which,
A being removed, and all other circumstances remaining the same, B is ■
prevented. What, however, does this prove? It proves that B, in the
particular instance, can not have had any other cause than A ; but to con-
clude from this that A was the cause, or that A will on other occasions be
followed by B, is only allowable on the assumption that B must have some
cause; that among its antecedents in any single instance in which it oc-
curs, there must be one which has the capacity of producing it at other
times. This being admitted, it is seen that in the case in question that
antecedent can be no other than A ; but that if it be no other than A it
must be A, is not proved, by these instances at least, but taken for granted.
There is no need to spend time in proving that the same thing is true of
the other Inductive Methods. The universality of the law of causation is
assumed in them all.
But is this assumption warranted? Doubtless (it may be said) most
phenomena are connected as effects with some antecedent or cause, that is,
are never produced unless some assignable fact has preceded them ; but the
very circumstance that complicated processes of induction are sometimes
necessary, shows that cases exist in which this regular order of succession
is not apparent to our unaided apprehension. If, then, the processes which,
bring these cases within the same category with the rest, require that we
should assume the universality of the very law which they do not at iirst
sight appear to exemplify, is not this a petitio principii ? Can we prove a
. proposition, by an argument which takes it for granted ? And if not so
proved, on what evidence does it rest ?
For this difficulty, which I have purposely stated in the strongest terms
it will admit of, the school of metaphysicians who have long predominated
in this country find a ready salvo. They affirm, that the universality of
causation is a truth which we can not help believing ; that the belief in it
is an instinct, one of the laws of our believing faculty. As the proof of
this, they say, and they have nothing else to say, that every body does be-
lieve it ; and they number it among the propositions, rather numerous in
their catalogue, which may be logically argued against, and perhaps can
not be logically proved, but which are of higher authority than logic, and
so essentially inherent in the human mind, that even he who denies them
in speculation, shows by his habitual practice that his arguments make no
impression upon himself.
Into the merits of this question, considered as one of psychology, it
would be foreign to my purpose to enter here ; but I must protest against
adducing, as evidence of the truth of a fact in external nature, the disposi-
tion, however strong or however general, of the human mind to believe it.
Belief is not proof, and does not dispense with the necessity 'of proof. I
am aware, that to ask for evidence of a proposition which we are supposed
to believe instinctively, is to expose one's self to the charge of rejecting the
authority of the human faculties ; which of course no one can consistently
EVIDENCE OF UNIVERSAL CAUSATION. 39a
do, since the human faculties are all which any one has to judge by; and
inasmuch as the meaning of the word evidence is supposed to be, something
which when laid before the mind, induces it to believe ; to demand evidence
when the belief is insured by the mind's own laws, is supposed to be ap-
pealing to the intellect against the intellect. But this, I apprehend, is a
misunderstanding of the nature of evidence. By evidence is not meant
any thing and every thing which produces belief. There are many things
which generate belief besides evidence. A mere strong association of ideas
often causes a belief so intense as to be unshakable by experience or argu-
ment. Evidence is not that which the mind does or must yield to, but
that which it ought to yield to, namely, that, by yielding to which its belief
is kept conformable to fact. There is no appeal from the human faculties
generally, but there is an appeal from one human faculty to another; from
the judging faculty, to those which take cognizance of fact, the faculties of
sense and consciousness. The legitimacy of this appeal is admitted when-
ever it is allowed that our judgments ought to be conformable to fact.
To say that belief suffices for its own justification is making opinion the
test of opinion ; it is denying the existence of any outward standard, the
conformity of an opinion to which constitutes its truth. We call one mode
of forming opinions right and another wrong, because the one does, and the
other does not, tend to make the opinion agree with the fact — to make
people believe what really is, and expect what really will be. Now a mere
disposition to believe, even if supposed instinctive, is no guarantee for the
truth of the thing believed. If, indeed, the belief ever amounted to an ir-
resistible necessity, there would then be no use in appealing from it, be-
cause there would be no possibility of altering it. But even then the truth
of the belief would not follow ; it would only follow that mankind were
under a permanent necessity of believing what might possibly not be true ;
in other words, that a case might occur in which our senses or conscious-
ness, if they could be appealed to, might testify one thing, and our reason
believe another. But in fact there is no such permanent necessity. There
is no proposition of which it can be asserted that every human mind must
eternally and irrevocably believe it. Many of the propositions of which
this is most confidently stated, great numbers of human beings have disbe-
lieved. The things which it has been supposed that nobody could possibly
help believing, are innumerable ; but no two generations would make out
the same catalogue of them. One age or nation believes implicitly what
to another seems incredible and inconceivable; one individual has not a
vestige of a belief which another deems to be absolutely inherent in hu-
manity. There is not one of these supposed instinctive beliefs which is
really inevitable. It is in the power of every one to cultivate habits of
thought which make him independent of them. The habit of philosoph-
ical analysis (of which it is the surest efEect to enable the mind to command,
instead of being commanded by, the laws of the merely passive part of its
own nature), by showing to us that things are not necessarily connected in
fact because their ideas are connected in our minds, is able to loosen innu-
merable associations which reign despotically over the undisciplined or
early -prejudiced mind. And this habit is not without power even over
those associations which the school of which I have been speaking regard
as connate and instinctive. I am convinced that any one accustomed to
abstraction and analysis, who will fairly exert his faculties for the purpose,
will, when his imagination has once learned to entertain the notion, find
no difficulty in conceiving that in some one, for instance, of the many fir-
400 INDUCTION.
maments into which sidereal astronomy now divides the universe, events
may succeed one another at random, without any fixed law ; nor can any
thing in our experience, or in our mental nature, constitute a sufficient, or
indeed any, reason for believing that this is nowhere the case.
Were we to suppose (what it is perfectly possible to imagine) that the
present order of the universe were brought to an end, and that a chaos sue
needed in which there was no fixed succession of events, and the past gave
no assurance of the future ; if a human being were miraculously kept alive
to witness this change, he surely would soon cease to believe in any uni-
formity, the uniformity itself no longer existing. If this be admitted, the
belief in uniformity either is not an instinct, or it is an instinct conquera-
ble, like all other instincts, by acquired knowledge.
But there is no need to speculate on what might be, when we have posi-
tive and certain knowledge of what has been. It is not true, as a matter
of fact, that mankind have always believed that all the successions of events
were uniform and according to fixed laws. The Greek philosophers, not
«ven excepting Aristotle, recognized Chance and Spontaneity {rixn and to
<tiro/imroi') as among the agents in nature ; in other words, they believed
that to that extent there was no guarantee that the past had been similar
to itself, or that the future would resemble the past. Even now a full half
of the philosophical world, including the very same inetaphysicians who
oontend most for the instinctive character of the belief in uniformity, con-
sider one important class of phenomena, volitions, to be an exception to
the uniformity, and not governed by a fixed law.*
§ 2. As was observed in a former place,f the belief we entertain in the
universality, throughout nature, of the law of cause and efBect, is itself an
instance of induction ; and by no means one of the earliest which any of
* I am happy to be able to quote the following excellent passage from Mr. Baden Powell's
Essay on the Inductive Philosophy, in confirmation, both in regard to history and to doctrine,
of the statement made in the text. Speaking of the " conviction of the universal and perma-
nent uniformity of nature," Mr. Powell says (pp. 98-100) :
' ' We may remark that this idea, in its proper extent, is by no means one of popular ac-
ceptance or natural growth. Just so far as the daily experience of every one goes, so far in-
deed he comes to embrace a certain persuasion of this kind, but merely to this limited extent,
that what is going on around him at present, in his own narrow sphere of observation, will
go on in like manner in future. The peasant believes that the sun which rose to-day will rise
again to-morrow ; that the seed put into the ground will be followed in due time by the har-
vest this year as it was last year, and the like ; but has no notion of such inferences in sub-
jects beyond his immediate observation. And it should be observed that each class of per-
sons, in admitting this belief within the limited range of his own experience, though he
doubt or deny it in every thing beyond, is, in fact, bearing unconscious testimony to its uni-
versal truth. Nor, again, is it only among the most ignorant that this limitation is put upon
the truth. There is a very general propensity to believe that every thing beyond common ex-
perience, or especially ascertained laws of nature, is left to the dominion of chance or fate or
arbitrary intervention ; and even to object to any attempted explanation by physical causes,
if conjecturally thrown out for an apparently unaccountable phenomenon.
" The precise doctrine of the generalization of this idea of the uniformity of nature, so far
from being obvious, natural, or intuitive, is utterly beyond the attainment of the many. In
all the extent of its universality it is characteristic of the philosopher. It is clearly the re-
sult of philosophic cultivation and training, and by no means the spontaneous offspring of any
primary principle naturally inherent in the mind, as some seem to believe. It is no mere
vague persuasion taken up without examination, as a common prepossession to which we are
always accustomed ; on the contrary, all common prejudices and associations are against it. It
is pre-eminently an acquired idea. It is not attained without deep study and reflection. The
best informed philosopher is the man who most firmly believes it, even in opposition to receivad
notions ; its acceptance depends on the extent and profoundness of his inductive studies."
t Supra, book iii., chap, ili., § 1.
EVIDENCE OF UNIVERSAL CAUSATION. 401
■us, ov which mankind in general, can have made. "We arrive at this uni-
versal law, by generalization from many laws of inferior generality. We
ehould never ha^ve had the notion of causation (in the philosophical meaning
of the term) as a condition of all phenomena, unless many cases of causation,
«r in other words, many partial uniformities of sequence, had previously be-
come familiar. The more obvious of the particular uniformities suggest,
and give evidence of, the general uniformity, and the general uniformity, once
established, enables us to prove the remainder of th" narticular uniformities
of which it is made up. As, however, all rigorous processes of induction
presuppose the general uniformity, our knowledge of the particular uniform-
ities from which it was first inferred was not, of course, derived from rigor-
ous induction, but from the loose and uncertain mode of induction per enu-
merationem simplicem; and the law of universal causation, being collected
from results so obtained, can not itself rest on any better foundation.
It would seem, therefore, that induction per enumcrationem simplicem
not only is not necessarily an illicit logical process, but is in reality the only
kind of induction possible ; since the more elaborate process depends for
its validity on a law, itself obtained in that inartificial mode. Is there not
then an inconsistency in contrasting the looseness of one method with the
rigidity of another, when that other is indebted to the looser method for
its own foundation ?
The inconsistency, however, is only apparent. Assuredly, if induction
by simple enumeration were an invalid process, no process grounded on
it could be valid ; just as no reliance could be placed on telescopes, if we
could not trust our eyes. But though a valid process, it is a fallible one,
and fallible in very different degrees : if, therefore, we can substitute for
the more fallible forms of the process, an operation grounded on the same
process in a less fallible form, we shall have effected a very material im-
provement. And this is what scientific induction does.
A mode of concluding from experience must be pronounced untrust-
worthy when subsequent experience refuses to confirm it. According to
this criterion, induction by simple enumeration — in other words, generaliza-
tion of an observed fact from the mere absence of any known instance to
the contrary — affords in general a precarious and unsafe ground of assur-
ance ; for such generalizations are incessantly discovered, on further expe-
rience, to be false. Still, however, it affords some assurance, suflBcient, in
many cases, for the ordinary guidance of conduct. It would be absurd to
say, that the generalizations arrived s,t by mankind in the outset of their
experience, such as these — food nourishes, fire burns, water drowns — were
unworthy of reliance.* There is a scale of trustworthiness in the results
* It deserves remark, that these early generalizations did not, likt scientific inductions, pre-
snppose causation. What they did presuppose, was uniformity in physical facts. But the ob-
servers were as ready to presume uniformity in the co-existence of facts as in the sequences.
On the other hand, they never thought of assuming that this uniformity was a principle per-
vading all nature : their generalizations did not imply that there was uniformity in every thing,
but only that as much uniformity as existed within their observation, existed also beyond it.
The induction, fire bums, does not require for its validity that all nature should observe uni-
form laws, but only that there should be uniformity in one particular class of natural phe-
nomena ; the effects of fire on the senses and on combustible substances. And uniformity to
this extent was not assumed, anterior to the experience, but proved by the experience. The
same observed instances which proved the narrower truth, proved as much of the wider one as
corresponded to it. It is from losing sight of this fact, and considering the law of causation
in its full extent as necessarily presupposed in the very earliest generalizations, that persons
have been led into the belief that the law of causation is known a priori, and is not itself a
conclusion from experience.
26
402 INDUCTION.
of the original unscientific induction ; and on this diversity (as observed im
the fourth chapter of the present book) depend the rules for the improve-
ment of the process. The improvement consists in correcting one of these
inartificial generalizations by means of another. As has been already point-
ed out, this is all that art can do. To test a generalization, by showing
that it either follows from, or conflicts with, some stronger induction, some
generalization resting on a broader foundation of experience, is the begin-
ning and end of the logic of induction.
§ 3. "Now the precariousness of the method of simple enumeration is in
an inverse ratio to the largeness of the generalization. The process is
delusive and insufficient, exactly in proportion as the subject-matter of the-
observation is special and limited in extent. As the sphere widens, this
unscientific method becomes less and less liable to mislead ; and the most
universal class of truths, the law of causation, for instance, and the princi-
ples of number and of geometry, are duly and satisfactorily proved by that
method alone, nor are they susceptible of any other proof.
With respect to the whole class of generalizations of which we have re-
cently treated, the uniformities which depend on causation, the truth of
the remark just made follows by obvious inference from the principles laid
down in the preceding chapters. When a fact has been observed a cer-
tain number of times to be true, and is not in any instance known to be
false, if we at once affirm that fact as a universal truth or law of nature,
without either testing it by any of the four methods of induction, or de-
ducing it from other known laws, we shall in general err grossly; but wa
are perfectly justified in affirming it as an empirical law, true within cer-
tain limits of time, place, and circumstance, provided the number of coin-
cidences be greater than can with any probability be ascribed to chance.
The reason for not extending it beyond those limits is, that the fact of its
holding true within them may be a consequence of collocations, which can
not be concluded to exist in one place because they exist in another; or
may be dependent on the accidental absence of counteracting agencies,
which any variation of time, or the smallest change of circumstances, may
possibly bring into play. If we suppose, then, the subject-matter of any
generalization to be so widely diffused that there is no time, no place, and
no combination of circumstances, but must afford an example either of its
truth or of its falsity, and if it be never found otherwise than true, its
truth can not be contingent on any collocations, unless such as exist at all
times and places ; nor can it be frustrated by any counteracting agencies,
unless by such as never actually occur. It is, therefore, an empirical law
co-extensive with all human experience ; at which point the distinction be-
tween empirical laws and laws of nature vanishes, and the proposition
takes its place among the most firmly established as well as largest truths
accessible to science.
'Now, the most extensive in its subject-matter of all generalizations
which experience warrants, respecting the sequences and co-existences of
phenomena, is the law of causation. It stands at the head of all observed
uniformities, in point of universality, and therefore (if the preceding ob-
servations are correct) in point of certainty. And if we consider, not what
mankind would have been justified in believing in the infancy of their
knowledge, but what may rationally be believed in its present more ad-
vanced state, we shall find ourselves warranted in considering this funda-
mental law, though itself obtained by induction from particular laws of causa
EVIDENCE OF UNIVERSAL CAUSATION. 403
tion, as not less certain, but on the contrary, more so, than any of those from
■which it was drawn. It adds to them as much proof as it receives from
them. For there is probably no one even of the best established laws of
causation which is not sometimes counteracted, and to which, therefore,
apparent exceptions do not present themselves, which would have neces-
sarily and justly shaken the confidence of mankind in the universality of
those laws, if inductive processes founded on the universal law had not
enabled us to refer those exceptions to the agency of counteracting causes,
and thereby reconcile them with the law with which they apparently con-
flict. Errors, moreover, may have slipped into the statement of any one
of the speeial laws, thi'ough inattention to some material circumstance : and
instead of the true proposition, another may have been enunciated, false as
a universal law, though leading, in all cases hitherto observed, to the same
result. To the law of causation, on the contrary, we not only do not know
of any exception, but the exceptions which limit or apparently invalidate
the special laws, are so far from contradicting the universal one, that they
confirm it ; since in all cases which are sufiiciently open to our observation,
we are able to trace the difference of result, either to the absence of a cause
which had been present in ordinary cases, or to the presence of one which
had been absent.
The law of cause and effect, being thus certain, is capable of imparting
its certainty to all other inductive propositions which can be deduced from
it; and the narrower inductions may be regarded as receiving their ulti-
mate sanction from that law, since there is no one of them which is not
rendered more certain than it was before, when we are able to connect it
with that larger induction, and to show that it can not be denied, consist-
ently with the law that every thing which begins to exist has a cause.
And hence we are justified in the seeming inconsistency, of holding induc-
tion by simple enumeration to be good for proving this general truth, the
foundation of scientific induction, and yet refusing to rely on it for any of
the narrower inductions. I fully admit that if the law of causation were
unknown, generalization in the more obvious cases of uniformity in phe-
nomena would nevertheless be possible, and though in all cases more or
less precarious, and in some extremely so, would sufiice to constitute a cer-
tain measure of probabilitj' ; but what the amount of this probability might
be, we are dispensed from estimating, since it never could amount to the
degree of assurance which the proposition acquires, when, by the applica-
tion to it of the Four Methods, the supposition of its falsity is shown to
be inconsistent with the Law of Causation. We are therefore logically
entitled, and, by the necessities of scientific induction, required, to disre-
gard the probabilities derived from the early rude method of generalizing,
and to consider no minor generalization as proved except so far as the law
of causation confirms it, nor probable except so far as it may reasonably
be expected to be so confirmed.
§ 4. The assertion, that our inductive processes assume the law of causa-
tion, while the law of causation is itself a case of induction, is a paradox,
only on the old theory of reasoning, which supposes the universal truth, or
major premise, in a ratiocination, to be the real proof of the particular
truths which are ostensibly inferred from it. According to the doctrine
maintained in the present treatise,* the major premise is not the proof of
* Book ii., chap. iii.
404 INDUCTION.
the conclusion, but is itself proved, along with the conclusion from the
same evidence. "All men are mortal" is not the proof that Lord Palmer-
ston is mortal ; but our past experience of mortality authorizes us to infer
both the general truth and the particular fact, and the one with exactly the
same degree of assurance as the other. The mortality of Lord Palmerston
is not an inference from the mortality of all men, but from the experience
which proves the mortality of all men ; and is a correct inference from ex-
perience, if that general truth is so too. This relation between our general
beliefs and their particular applications holds equally true in the more com-
prehensive case which we are now discussing. Any new fact of causation
inferred by induction, is rightly inferred, if no other objection cap be made
to the inference than can be made to the general truth that every event has
a cause. The utmost certainty which can be given to a conclusion arrived
at in the way of inference, stops at this point. When we have ascertained
that the particular conclusion must stand or fall with the general uniform-
ity of the laws of nature — that it is liable to no doubt except the doubt
whether every event has a cause — we have done all that can be done for it.
The strongest assurance we can obtain of any theory respecting the cause
of a given phenomenon, is that the phenomenon has either that cause or
none.
The latter supposition might have been an admissible one in a very early
period of our study of nature. But we have been able to perceive that in
the stage which mankind have now reached, the generalization which gives
the Law of Universal Causation has grown into a stronger and better in-
duction, one deserving of greater reliance, than any of the subordinate gen-
eralizations. We may even, I think, go a step further than this, and regard
the certainty of that great induction as not merely comparative, but, for all
practical purposes, complete.
The considerations, which, as I apprehend, give, at the present day, to the
proof of the law of uniformity of succession as true of all phenomena with-
out exception, this character of completeness and conclusiveness, are the
following : First, that we now know it directly to be true of far the great-
est number of phenomena; that there are none of which we know it not to
be true, the utmost that can be said being, that of some we can not positive-
ly from direct evidence affirm its truth ; while phenomenon after phenome-
non, as they become better known to us, are constantly passing from the
latter class into the former; and in all cases in which that transition has
not yet taken place, the absence of direct proof is accounted for by the rar-
ity or the obscurity of the phenomena, our deficient means of observing
them, or the logical difficulties arising from the complication of the circum-
stances in which they occur; insomuch that, notwithstanding as rigid a
dependence on given conditions as exists in the case of any other phenome-
non, it was not likely that we should be better acquainted with those con-
ditions than we are. Besides this first class of considerations, there is a
second, which still further corroborates the conclusion. Although there are
phenomena the production and changes of which elude all our attempts to
reduce them universally to any ascertained law ; yet in every such case, the
phenomenon, or the objects concerned in it, are found in some instances to
obey the known laws of nature. The wind, for example, is the type of un-
certainty and caprice, yet we find it in some cases obeying with as much
constancy as any phenomenon in nature the law of the tendency of fluids
to distribute themselves so as to equalize the pressure on every side of each
of their particles ; as in the case of the trade-winds and the monsoon&
EVIDENCE OF UNIVERSAL CAUSATION. 405
Lightning might once have been supposed to obey no laws ; but since it
has been ascertained to be identical with electricity, we know that the very
same phenomenon in some of its manifestations is implicitly obedient to the
action of fixed causes. I do not believe that there is now one object or
event in all our experience of nature, within the bounds of the solar system
at least, which has not either been ascertained by direct observation to fol-
low laws of its own, or been proved to be closely similar to objects and
events which, in more familiar manifestations, or on a more limited scale,
follow strict laws ; our inability to trace the same laws on a larger scale and
in the more recondite instances, being accounted for by the number and
complication of the modifying causes, or by their inaccessibility to observa-
tion.
The progress of experience, therefore, has dissipated the doubt which
must have rested on the universality of the law of causation while there
were phenomena which seemed to be sui generis, not subject to the same
laws with any other class ofphenomena, and not as yet ascertained to have
peculiar laws of their own. This great generalization, however, might rea-
sonably have been, as it in fact was, acted on as a probability of the high-
est order, before there were sufficient grounds for receiving it as a certainty.
In matters of evidence, as in all other human things, we neither require, nor
can attain, the absolute. We must hold even our strongest convictions
with an opening left in our minds for the reception of facts which contra-
dict them ; and only when we have taken this precaution, have we earned
the right to act upon our convictions with complete confidence when no
such contradiction appears. Whatever has been found true in innumerable
instances, and never found to be false after due examination in any, we are
safe in acting on as universal provisionally, until an undoubted exception
appears ; provided the nature of the case be such that a real exception
could scarcely have escaped notice. When every phenomenon that we ever
knew sufficiently well to be able to answer the question, had a cause on
which it was invariably consequent, it was more rational to suppose that
our inability to assign the causes of other phenomena arose from our igno-
rance, than that there were phenomena which were uncaused, and which
happened to be exactly those which we had hitherto had no sufficient op-
portunity of studying.
It must, at the same time, be remarked, that the reasons for this reliance
do not hold in circumstances unknown to us, and beyond the possible range
of our experience. In distant parts of the stellar regions, where the phe-
nomena may be entirely unlike those with which we are acquainted, it
would be folly to affirm confidently that this general law prevails, any more
than those special ones which we have found to hold universally on our
own planet. The uniformity in the succession of events, otherwise called
the law of causation, must be received not as a law of the universe, but of
that portion of it only which is within the range of our means of sure ob-
servation, with a reasonable degree of extension to adjacent cases. To ex-
tend it further is to make a supposition without evidence, and to which, in
the absence of any ground from experience for estimating its degree of
probability, it would be idle to attempt to assign any.*
* One of the most rising thinkers of the new generation in France, M. Taine (who has
given, in the Revue des Denx Mondes, the most masterly analysis, at least in one point of
view, ever made of the present work), though he rejects, on this and similar points of psy-
chology, the intuition theory in its ordinary form, nevertheless assigns to the law of causation,
and to some other of the most universal laws, that certainty beyond the bounds of human ex-
406 INDUCTION.
CHAPTER XXII.
OP UNEFOEMITIES OF CO-EXISTBNCE NOT DEPENDENT ON CAUSATION.
§ 1. The order of the occurrence of phenomena in time, is either succes-
sive or simultaneous ; the uniformities, therefore, which obtain in their oc-
perience, which I have not been able to accord to them. He does this on the faith of our
ikcnlty of abstraction, in which he seems to recognize an independent som-ce of evidence, not
indeed disclosing truths not contained in our experience, but affording an assurance which
experience can not give, of the universality of those which it does contain. By abstraction
M. Taine seems to think that we are able, not merely to analyxe that part of nature which we
see, and exhibit apart the elements which pervade it, but'to distinguish such of them as are
elements of the system of nature considered as a whole, not incidents belonging to our limited
terrestrial experience. I am not sure that I fully enter into M. Taine's meaning ; but I con-
fess I do not see how any mere abstract conception, elicited by our minds from our experi-
ence, can be evidence of an objective fact in universal Nature, beyond what the experience it-
self bears witness of; or how, in the process of interpreting in general language the testimony
of experience, the limitations of the testimony itself can be cast off.
Dr. Ward, in an able article in the Dublin Review for October, 1871, contends that the uni-
formity of nature can not be proved from experience, but fiom "transcendental considera-
tions " only, and that, consequently, all physical science would be deprived of its basis, if such
transcendental proof were impossible.
When physical science is said to depend on the assumption that the course of nature is in-
variable, all that is meant is that the conclusions of physical science are not known as absolute
truths : the truth of them is conditional on the uniformity of the course of nature ; and all
that the most conclusive observations and experiments can prove, is that the result arrived at
will be true if, and as long as, the present laws of nature are valid. But this is all the as-
surance we require for the guidance of our conduct. Dr. Ward himself does not think that
his transcendental proofs make it practically greater ; for he believes, as a Catholic, that the
course of nature not only has been, but frequently and even daily is, suspended by supernatu-
ral inteiTention.
But though this conditional conclusiveness of the evidence of experience, which is sufficient
for the purposes of life, is all that I was necessarily concerned to prove, I have given reasons
for thinking that the uniformity, as itself a part of experience, is sufficiently proved to justify
undoubting reliance on it. This Dr. Ward contests, for the following reasons ;
rirst (p. 31.5), supposing it true that there has hitherto been no well authenticated case of
a breach in the uniformity of natui-e; "the number of natural agents constantly at work is
incalculably large ; and the observed cases of uniformity in their action must be immeasur-
ably fewer than one thousandth of the whole. Scientific men, we assume for the moment,
have discovered that in a certain proportion of instances — immeasurably fewer than one
thousandth of the whole — a certain fact has prevailed ; the fact of uniformity ; and they have
not found a single instance in which that fact does not prevail. Are they justified, we ask,
in inferring from these premises that the fact is universal ? Surely the question answers it-
self. Let us make a very grotesque supposition, in which, however, the conclusion would
really be tried according to the arguments adduced. In some desert of Africa there is an
enormous connected edifice, surrounding some vast space, in which dwell certain reasonable
beings, who are unable to leave the inclosure. In this edifice are more than a thousand
chambers, which some years ago were entirely locked up, and the keys no one knew where.
By constatit diligence twenty-five keys have been found, out of the whole number ; and the
corresponding chambers, situated promiscuously throughout the edifice, have been opened.
Each chamber, when examined, is found to be in the precise shape of a dodecahedron. Are
the inhabitants justified on that account in holding with certitude that the remaining 975
chambers are built on the same plan ?"
Not with perfect certitude, but (if the chambers to which the keys have been found are
really " situated promiscuously ") with so high a degree of probability that they would be justi-
fied in acting upon the presumption until an exception appeared.
Dr. Ward's argument, however, does not touch mine as it stands in the text. My argu-
ment is grounded on the fact that the unifoi-mity of the course of nature as a whole, is con-
CO-EXISTENCES INDEPENDENT OF CAUSATION. 407
«currence, are either uniformities of succession or of co-existence. Unifoi'iu-
ities of succession are all comprehended under the law of causation and
its consequences. Every phenomenon has a cause, which it invariably fol-
lows ; and from this are derived other invariable sequences among the suc-
cessive stages of the same efBect, as well as between the effects resulting
from causes which invariably succeed one another.
In the same manner with these derivative uniformities of succession, a
great variety of uniformities of co-existence also take their rise. Co-ordi-
nate effects of the same cause naturally co-exist with one another. High
water at any point on the earth's surface, and high water at the point dia-
.metrically opposite to it, are effects uniformly simultaneous, resulting from
the direction in which the combined attractions of the sun and moon act
upon the waters of the ocean. An eclipse of the sun to us, and an eclipse
-of the earth to a spectator situated in the moon, are in like manner phe-
stituted by the uniform sequences of special effects from special natural agencies ; that the
number of these natural agencies in the part of the universe known to us is not incalculable,
nor even extremely great ; that we have now reason to think that at least the far greater
-number of them, if not separately, at least in some of the combinations into which they en-
ter, have been made sufficiently amenable to observation, to have enabled us actually to as-
certain some of their fixed laws ; and that this amount of experience justifies the same de-
gree of assurance that the course of nature is uniform throughout, which we previpusly had
-of the uniformity of sequence among the phenomena best known to us. This view of the
subject, if correct, destroys the force of Dr. Ward's first argument.
His second argument is, that many or most persons, both scientific and unscientific, believe
that there are well authenticated cases of breach in the uniformity of nature, namely, mira-
cles. Neither does this consideration touch what I have said in the text. I admit no other
uniformity in the events of nature than the law of Causation ; and (as I have explained in
the chapter of this volume which treats of the Grounds of Disbelief) a miracle is no excep-
tion to that law. In every case of alleged miracle, a new antecedent is affirmed to exist ; a
counteracting cause, namely, the volition of a supernatural being. To all, therefore, to whom
beings with superhuman power over nature are a vera causa, a miracle is a case of the Law
of Universal Causation, not a deviation from it.
Dr. Ward's last, and as he says, strongest argument, is the familiar one of Reid, Stewart, and
their followers — that whatever knowledge experience gives us of the past and present, it gives
us none of the future. I confess that I see no force whatever in this argument. Wherein
-does a future fact diffisr from a present or a past fact, except in their merely momentary re-
lation to the human beings at present in existence ? The answer made by Priestley, in his
Examination of Reid, seems to me sufficient, viz., that though we have had no experience of
what is future, we have had abundant experience of what was future. The "leap in the
dark " (as Professor Bain calls it) from the past to the future, is exactly as much in the
dark and no more, as the leap from a past which we have personally observed, to a past
which we have not. I agree with Mr. Bain in the opinion that the resemblance of what we
have not experienced to what we have, is, by a law of our nature, presumed through the
mere energy of the idea, before experience has proved it. This psychological truth, however,
is not, as Dr. Ward when criticising Mr. Bain appears to think, inconsistent with the logical
truth that experience does prove it. The proof comes after the presumption, and consists in
its invariable verification by experience when the experience anives. The fact which while
it was future could not be observed, having as yet no existence, is always, when it becomes
present and can be observed, found conformable to the past.
Dr. M'Cosh maintains (^Examination of Mr. J. S. Milt's Philosophy, p. 257) that the uni-
formitv of the course of nature is a diflFerent thing from the law of causation ; and while he
allows" that the former is only proved by a long continuance of experience, and that it is not
inconceivable nor necessarily incredible that there may be worlds in which it does not pre-
vail, he considers the law of causation to be known intuitively. There is, however, no other
uniformity in the events of nature than that which arises from the law of causation : so long
therefore as there remained any doubt that the course of nature was uniform throughout, at
^least when not modified by the intercention of a new (supernatural) cause, a doubt was nec-
essarily implied, not indeed of the reality of causation, but of its universality. If the uni-
formity of the course of nature has any exceptions — if any events succeed one another without
fixed laws— to that extent the law of causation fails ; there are events which do not depend
•on causes.
408 INDUCTION.
nomena invariably co-existent; and their co-existence can equally be de-
duced from the laws of their production.
It is an obvious question, therefore, vehether all the uniformities of co-ex-
istence among phenomena may not be accounted for in this manner. And
it can not be doubted that between phenomena which are themselves ef.
fects, the co-existences must necessarily depend on the causes of those phe-
nomena. If they are effects immediately or remotely of the same cause^
they can not co-exist except by virtue of some laws or properties of that
cause ; if they are effects of different causes, they can not co-exist unless it
be because their causes co-exist ; and the uniformity of co-existence, if such
there be, between the effects, proves that those particular causes, within the
limits of our observation, have uniformly been co-existent.
§ 2. But these same considerations compel us to recognize that there
must be one class of co-existences which can not depend on causation : the
co-existences between the ultimate properties of things — those properties
which are the causes of all phenomena, but are not themselves caused by
any phenomenon, and a cause for which could only be sought by ascending
to the origin of all things. Yet among these ultimate properties there are
not only co-existences, but uniformities of co-existence. General proposi-
tions nftiy be, and are, formed, which assert that whenever certain proper-
ties are found, certain others are found along with 'them. We perceive an
object ; say, for instance, water. We recognize it to be water, of course by
certain of its properties. Having recognized it, we are able to affirm of it
innumerable other properties ; which we could not do unless it were a gen-
eral truth, a law or uniformity in nature, that the set of properties by
which we identify the substance as water always have those other proper-
ties conjoined with them.
In a former place* it has been explained, in some detail, what is meant
by the Kinds of objects ; those classes which differ from one another not
by a limited and definite, but by an indefinite and unknown, number of dis-
tinctions. To this we have now to add, that every proposition by which
any thing is asserted of a Kind, affirms a uniformity of co-existence.
Since we know nothing of Kinds but their properties, the Kind, to us, is
the set of properties by which it is identified, and which must of course be
sufficient to distinguish it from every other kind.f In affirming any thing,
therefore, of a Kind, we are affirming something to be uniformly co-exist-
ent with the pi-operties by which the kind is recognized ; and that is the
sole meaning of the assei'tion.
Among the uniformities of co-existence which exist in nature, may hence
be numbered all the properties of Kinds. The whole of these, however^
are not independent of causation, but- only a portion of them. Some are
ultimate properties, others derivative : of some, no cause can be assigned,
but others are manifestly dependent on causes. Thus, pure oxygen gas is
a Kind, and one of its most unequivocal properties is its gaseous formj
* Book i. , chap. vii.
t In some cases, a Kind is sufficiently identified by some one remarkable property : but
most commonly several are required ; each property considered singly, being a joint property
of that and of other Kinds. The color and brightness of the diamond are common to it with
the paste from which false diamonds are made ; its octohedral form is common to it with
alum, and magnetic iron ore ; but the color and brightness and the form together, identify its
Kind ; that is, are a mark to us that it is combustible ; that when burned it produces carbon-
ic acid ; that it can not be cut with any known substance ; together with many other ascer-
tained properties, and the fact that there exist an indefinite number still unascertained.
CO-EXISTENCES INDEPENDENT OF CAUSATION. 409
this property, however, has for its cause the presence of a certain quantity
of latent heat ; and if that heat could be taken away (as has been done from
80 many gases in Faraday's experiments), the gaseous form would doubt-
less disappear, together with numerous other properties which depend on,
or are caused by, thaf property.
In regard to all substances which are chemical compounds, and which
therefore may be regarded as products of the juxtaposition of substances
different in Kind from themselves, there is considerable reason to presume
that the specific properties of the compound are consequent, as effects, on
some of the properties of the elements, though little progress has yet been
made in tracing any invariable relation between the latter and the former.
Still more strongly will a similar presumption exist, when the object itself,
as in the case of organized beings, is no primeval agent, but an effect, which
depends on a cause or causes for its very existence. The Kinds, thei-efore,
which are called in chemistry simple substances, or elementary natural
agents, are the only ones, any of whose properties can with certainty be
considered ultimate; and of these the ultimate properties are probably
much more numerous than we at present recognize, since every successful
instance of the resolution of the properties of their compounds into simpler
laws, generally leads to the recognition of properties in the elements dis-
tinct from any previously known. The resolution of the laws o^the heav-
enly motions established the previously unknown ultimate property of a
mutual attraction between all bodies ; the resolution, so far as it has yet
proceeded, of the laws of crystallization, of chemical composition, electricity,
magnetism, etc., points to various polarities, ultimately inherent in the par-
ticles of which bodies are composed; the comparative atomic weights of
different kinds of bodies were ascertained by resolving into more general
laws the uniformities observed in the proportions in which substances com-
bine with one another, and so forth. Thus, although every resolution of a
complex uniformity into simpler and more elementary laws has an appar-
ent tendency to diminish the number of the ultimate properties, and really
does remove many properties from the list; yet (since the result of tliis
•simplifying process is to trace up an ever greater variety of different ef-
fects to the same agents) the further we advance in this direction, the
greater number of distinct properties we are forced to recognize in one
and the same object; the co-existences of which properties must accord-
ingly be ranked among the ultimate generalities of nature.
§ 3. There are, therefore, only two kinds of propositions which assert
nniformity of co-existence between properties. Either the properties de-
pend on causes or they do not. If they do, the proposition which affirms
them to be co-existent is a derivative law of co-existence between effects,
and, until resolved into the laws of causation on which it depends, is an
empirical law, and to be tried by the principles of induction to which such
laws are amenable. If, on the other hand, the properties do not depend
on causes, but are ultimate properties, then, if it be true that they invaria.
bly co-exist, they must all be ultimate properties of one and the same
Kind; and it is of these only that the co- existences can be classed as a
peculiar sort of laws of nature.
When we affirm that all crows are black, or that all negroes have woolly
hair, we assert a uniformity of co-existence. We assert that the property
of blackness or of having woolly hair invariably co-exists with the proper-
ties which, in common language, or in the scientific classification that we
410 rNDUCTIOK
adopt, are taken to constitute the class crow, or the class negro. Now,
supposing blackness to be an ultimate property of black objects, or woolly-
hair an ultimate property of the animals which possess it; supposing that
these properties are not results of causation, are not connected with ante-
cedent phenomena by any law ; then if all crows are black, and all negroes,
have woolly hair, these must be ultimate properties of the kind crow, or
negro, or of some kind which includes them. If, on the contrary, black-
ness or woolly hair be an effect depending on causes, these general propo-
sitions are manifestly empirical laws ; and all that has already been said
respecting that class of generalizations may be applied without modifica-
tion to these.
N^ow, we have seen that in the case of all compounds — of all things, ia
short, except the elementary substances and primary powers of nature —
the presumption is, that the properties do really depend upon causes; and
it is impossible in any case whatever to be certain that they do not. We-
therefore should not be safe in claiming for any generalization respecting
the co-existence of properties, a degree of certainty to which, if the prop,
erties should happen to be the result of causes, it would have no claim.:
A generalization respecting co-existence, or, in other words, respecting the-
properties of kinds, may be an ultimate truth, but it may also be merely a
derivative one ; and since, if so, it is one of those derivative laws which
are neither laws of causation nor have been resolved into the laws of cau-
sation on which they depend, it can possess no higher degree of evidence-
than belongs to an empirical law.
§ 4. This conclusion will be confirmed by the consideration of one great
deficiency, which precludes the application to the ultimate uniformities of
co-existence, of a system of rigorous scientific induction, such as the uni-
formities in the succession of phenomena have been found to admit of.
The basis of such a system is wanting ; there is no general axiom standing-
in the same relation to the uniformities of co-existence as the law of causa-
tion does to those of succession. The Methods of Induction applicable to-
the ascertainment of causes and effects are grounded on the principle that
every thing which has a beginning must have some cause or other ; that
among the circumstances which actually existed at the time of its com-
mencement, there is certainly some one combination, on which the effect
in question is unconditionally consequent, and on the repetition of which
it would certainly again recur. But in an inquiry whether some kind (as
crow) universally possesses a certain property (as blackness), there is no
room for any assumption analogous to this. We have no previous certain-
ty that the property must have something which constantly co-exists with,
it ; must have an invariable co-existent, in the same manner as an event
must have an invariable antecedent. When we feel pain, we must be in
some circumstances under which, if exactly repeated, we should always feel
pain. But when we are conscious of blackness, it does not follow that
there is something else present of which blackness is a constant accompani-
ment. There is, therefore, no room for elimination ; no method of Agree-
ment or Difference, or of Concomitant Variations (which is but a modifi-
cation either of the Method of Agreement or of the Method of Difference).
We can not conclude that the blackness we see in crows must be an in-
variable property of crows merely because there is nothing else present of-
which it can be an invariable property. We therefore inquire into the-
truth of a pi-oposition like "All crows are black," under the same disad-
CO-EXISTENCES INDEPENDENT OF CAUSATION. 4n
vantage as if, in our inquiries into causation, we were compelled to let in, as
one of the possibilities, that the effect may in that particular instance have
arisen without any cause at all.
To overlook this grand distinction was, as it seems to me, the capital
error in Bacon's view of inductive philosophy. The principle of elimina-
tion, that great logical instrument which he had the immense merit of first
bringing into general use, he deemed applicable in the same sense, and in
as unqualified a manner, to the investigation of the co-existences, as to that
of the successions of phenomena. He seems to have thought that as every
event has a cause, or invariable antecedent, so every property of an object
has an invariable co-existent, which he called its form ; and the examples
he chiefly selected for the application and illustration of his method, were
inquiries into such forms ; attempts to determine in what else all those
objects resembled, which agreed in some one general property, as hardness
or softness, dryness or moistness, heat or coldness. Such inquiries could
lead to no result. The objects seldom have any such circumstances in
common. They usually agree in the one point inquired into, and in noth-
ing else. A great proportion of the properties which, so far as we can
conjecture, are the likeliest Vo be really ultimate, would seem to be inher-
ently properties of many different kinds of things not allied in any other
respect. And as for the properties which, being effects of causes, we are
able to give some account of, they have generally nothing to do with the
ultimate resemblances or diversities in the objects themselves, but depend
on some outward circumstances, under the influence of which any objects
whatever are capable of manifesting those properties ; as is emphatically
the case with those favorite subjects of Bacon's scientific inquiries, hotness
and coldness, as well as with hardness and softness, solidity and fluidity,
and many other conspicuous qualities.
In the absence, then, of any universal law of co-existence similar to the
universal law of causation which regulates sequence, we are thrown back
upon the unscientific induction of the ancients, ^e?" enumerationem simpli-
cem, icbi non reperitur instantia contradictoria. The reason we have for
believing that all crows are black, is simply that we have seen and heard of
many black crows, and never one of any other color. It remains to be
considered how far this evidence can reach, and how we are to measure its
8ti"ength in any given case.
§ 5. It sometimes happens that a mere change in the mode of verbally
enunciating a question, though nothing is really added to the meaning ex-
pressed, is of itself a considerable step toward its solution. This, I think,
happens in the present instance. The degree of certainty of any generaliza-
tion which rests on no other evidence than the agreement, so far as it goes,
of all past observation, is but another phrase for the degree of improbability
that an exception, if any existed, could have hitherto remained unobserved.
The reason for believing that all crows are black, is measured by the im-
probability that crows of any other color should have existed to the pres-
ent time without our being aware of it. Let us state the question in this
last mode, and consider what is implied in the supposition that there may
be crows which are not black, and under what conditions we can be justi-
fied in regarding this as incredible.
If there I'eally exist crows which are not black, one of two things must
be the fact. Either the circumstance of blackness, in all crows hitherto
observed, must be, as it were, an accident, not connected with any distinc-
412 INDUCTION.
tion of Kind ; or if it be a property of Kind, the crows which are not
black must be a new Kind, a Kind' hitherto overlooked, though coming
under the same general description by which crows have hitherto been
characterized. The first supposition would be proved true if we were to
discover casually a white crow among black ones, or if it were found that
black crows sometimes turn white. The second would be shown to be the
fact if in Australia or Central Africa a species or a race of white or gray
crows were found to exist.
§ 6. The former of these suppositions necessarily implies that the color
is an effect of causation. If blackness, in the crows in which it has been
observed, be not a property of Kind, but can be present or absent without
any difference generally in the jjroperties of the object, then it is not an
ultimate fact in the individuals themselves, but is certainly dependent on a
cause. There are, no doubt, many properties which vary from individual
to individual of the same Kind, even the same infima species, or lowest
Kind. Some flowers may be either white or red, without differing in any
other respect. But these properties are not ultimate; they depend on
causes. So far as the properties of a thing belong to its own nature, and
do not arise from some cause extrinsic to it, they are always the same in
the same Kind. Take, for instance, all simple substances and elementary
powers ; the only things of which we are certain that some at least of their
properties are really ultimate. Color is generally esteemed the most varia-
ble of all properties : yet we do not find that sulphur is sometimes yellow
and sometimes white, or that it varies in color at all, except so far as color
is the effect of some extrinsic cause, as of the sort of light thrown upon it,
the mechanical arrangement of the particles (as after fusion), etc. We do
not find that iron is sometimes fluid and sometimes solid at the same tem-
perature; gold sometimes malleable and sometimes brittle; that hydrogen
will sometimes combine with oxygen and sometimes not; or the like. If
from simple substances we pass to any of their definite compounds, as
water, lime, or sulphuric acid, there is the same constancy in their proper-
ties. When properties vary from individual to individual, it is either in
the case of miscellaneous aggregations, such as atmospheric air or rock,
composed of heterogeneous substances, and not constituting or belonging
to any real Kind,* or it is in the case of organic beings. In them, indeed,
there is variability in a high degree. Animals of the same species and
race, human beings of the same age, sex, and country, will be most differ-
ent, for example, in face and figure. But organized beings (from the ex-
treme complication of the laws by which they are regulated) being more
eminently modifiable, that is, liable to be influenced by a greater number
and variety of causes, than any other phenomena whatever ; having also
themselves had a beginning, and therefore a cause ; there is reason to be-
lieve that none of their properties are ultimate, but all of them deriva-
tive, and produced by causation. And the presumption is confirmed, by
the fact that the properties which vary from one individual to another, also
generally vary more or less at different times in the same individual; which
variation, like any other event, supposes a cause, and implies, consequently,
that the properties are not independent of causation.
If, therefore, blackness be mei-ely accidental in crows, and capable of
* This doctrine of course assumes that the allotropic forms of what is chemically the same
substance are so many different Kinds ; and such, in the sense in which the. word Kind is
used in this treatise, they really are.
CO-EXISTENCES INDEPENDENT OF CAUisATION. 413
varying while the Kind remains the same, its presence or absence is doubt-
less no ultimate fact, but the effect of some unknown cause : and in that
case the universality of the experience that all crows are black is sufficient
proof of a common cause, and establishes the generalization as an empirical
law. Since there are innumerable instances in the affirmative, and hitherto
none at all in the negative, the causes on which the property depends must
exist everywhere in the limits of the observations which have been made ;
and the proposition may be received as universal within those limits, and
with the allowable degree of extension to adjacent cases.
§ 1. If, in the second place, the property, in the instances in which it has
been observed, is not an effect of causation, it is a property of Kind ; and
in that case the generalization can only be set aside by the discovery of a
new Kind of crow. That, however, a peculiar Kind not hitherto discover-
ed should exist in nature, is a supposition so often realized that it can not
be considered at all improbable. We have nothing to authorize us in at-
tempting to limit the Kinds of things which exist in nature. The only
unlikelihood would be that a new Kind should be discovered in localities
which there was previously reason to believe had been thoroughly ex-
plored ; and even this improbability depends on the degree of conspicuous-
ness of the difference between the newly-discovered Kind and all others,
since new kinds of minerals, plants, and even animals, previously overlooked
or confounded with known species, are still continually detected in the
most frequented situations. On this second ground, therefore, as well as
on the first, the observed uniformity of co-existence can only hold good as
an empirical law, within the limits not only of actual observation, but of an
observation as accurate as the nature of the case required. And hence it
is that (as remarked in an early chapter of the present book) we so often
give up generalizations of this class at the first summons, if any credible
witness stated that he had seen a white crow, uncler circumstances which
made it not incredible that it should have escaped notice previously, we
should give full credence to the statement.
It appears, then, that the uniformities which obtain in the co-existence of
phenomena — those which we have reason to consider as ultimate, no less
than those which arise from the laws of causes yet undetected — are entitled
to reception only as empirical laws ; are not to be presumed true except
within the limits of time, place, and circumstance, in which the observa-
tions were made, or except in cases strictly adjacent.
§ 8. We have seen in the last chapter that there is a point of generality
at which empirical laws become as certain as laws of nature, or, rather, at
which there is no longer any distinction between empirical laws and laws
of nature. As empirical laws approach this point, in other words, as they
rise in their degree of generality, they become more certain ; their univer-
sality may be more strongly relied on. For, in the first place, if they are
results of causation (which, even in the class of uniformities treated of in
the present chapter, we never can be certain that they are not) the more
general they are, the greater is proved to be the space over which the
necessary collocations prevail, and within which no causes exist capable of
counteracting the unknown causes on which the empirical law depends.
To say that any thing is an invariable property of some very limited class
of objects, is to say that it invariably accompanies some very numerous
and complex group of distinguishing properties ; which, if causation be at
414 INDUCTIOIT.
all concerned in the matter, argues a combination of many causes, and
therefore a great liability to counteraction ; while the comparatively nar-
row range of the observations renders it impossible to predict to what ex-
tent unknown counteracting causes may be distributed throughout nature.
But when a generalization has been found to hold good of a very large
proportion of all things whatever, it is already proved that nearly all the
causes which exist in nature have no power over it ; that very few changes
in the combination of causes can affect it; since the greater number of
possible combinations must have already existed in some one or other of
the instances in which it has been found true. If, therefore, any empirical
law is a result of causation, the more general it is, the more it may be de-
pended on. And even if it be no result of causation, but an ultimate co-
existence, the more general it is, the greater amount of experience it is de-
rived from, and the greater therefore is the probability that if exceptions
had existed, some would already have presented themselves.
For these reasons, it requires much more evidence to establish an excep-
tion to one of the more general empirical laws than to the more special
ones. We should not have any difficulty in believing that there might be
a new Kind of crow ; or a new kind of bird resembling a crow in the
properties hitherto considered distinctive of that Kind. But it would re-
quire stronger proof to convince us of the existence of a Kind of crow hav-
ing properties at variance with any generally recognized universal property
of birds ; and a still higher degree if the properties conflict with any rec-
ognized universal property of animals. And this is conformable to the
mode of judgment recommended by the common sense and general prac-
tice of mankind, who are more incredulous as to any novelties in nature,
according to the degree of generality of the experience which these novel-
ties seem to contradict.
§ 9. It is conceivable that the alleged propei-ties might conflict with
some recognized universal property of all matter. In that case their im-
probability would be at the highest, but would not even then amount to
incredibility. There are only two known properties common to all mat-
ter ; in other words, there is but one known uniformity of co-existence of
properties co-extensive with all physical nature, namely, that whatever op-
poses resistance to movement gravitates, or, as Professor Bain expresses it,
Inertia and Gravity are co-existent through all matter, and proportionate
in their amount. These properties, as he truly says, are not mutually im-
plicated ; from neither of them could we, on grounds of causation, presume
the other. But, for this very reason, we are never certain that a Kind may
not be discovered possessing one of the properties without the other. The
hypothetical ether, if it exists, may be such a Kind. Our senses can not
recognize in it either resistance or gravity ; but if the reality of a resisting
medium should eventually be proved (by alteration, for example, in the
times of revolution of periodic comets, combined with the evidences afford-
ed by the phenomena of light and heat), it would be rash to conclude from
this alone, without other proofs, that it must gravitate.
For even the greater generalizations, which embrace comprehensive Kinds
containing under them a great number and variety of infimoe species, are
only empirical laws, resting on induction by simple enumeration merely, and
not on any process of elimination — a process wholly inapplicable to this
sort of case. Such generalizations, therefore, ought to be grounded on an
examination of all the infimoB species comprehended in them, and not of a
CO-EXISTENCES INDEPENDENT OF CAUSATION. 415
portion ' only. "We can not conclude (where causation is not concerned),
because a proposition is true of a number of things resembling one another
•only in being animals, that it is therefore true of all animals. If, indeed,
any thing be true of species which differ more from one another than either
differs from a third, especially if that third species occupies in most of its
known properties a position between the two former, there is some proba-
bility that the same thing will also be true of that intermediate species ; for
it is often, though by no means universally, found, that there is a sort of
parallelism in the properties of different Kinds, and that their degree of
unlikeness in one respect bears some proportion to their unlikeness in oth-
ers. We see this parallelism in the properties of the different metals ; in
those of sulphur, phosphorus, and carbon ; of chlorine, iodine, and bromine ;
in the natural orders of plants and animals, etc. But there are innumera-
ble anomalies and exceptions to this sort of conformity ; if indeed the con-
formity itself be any thing but an anomaly and an exception in nature.
Universal propositions, therefore, respecting the properties of superior
Kinds, unless grounded on proved or presumed connection by causation,
ought not to be hazarded except after separately examining every known
aub-kind included in the larger Kind. And even then such generalizations
must be held in readiness to be given up on the occurrence of some new
anomaly, which, when the uniformity is not derived from causation, can
never, even in the case of the most general of these empirical laws, be con-
sidered very improbable. Thus, all the universal propositions which it has
been attempted to lay down respecting simple substances, or concerning
any of the classes which have been formed among simple substances (and
the attempt has been often made), have, with the progress of experience,
either faded into inanity, or been proved to be erroneous ; and each Kind
of simple substance remains, with its own collection of properties apart
from the rest, saving a certain parallelism with a few other Kinds, the most
similar to itself. In organized beings, indeed, there are abundance of
propositions ascertained to be universally true of superior genera, to many
of which the discovery hereafter of any exceptions must be regarded as
€xtreraely improbable. But these, as already observed, are, we have every
reason to believe, properties dependent on causation.*
* Professor Bain (Logic, ii. , 13) mentions two empirical laws, which he considers to be, with
the exception of the law connecting Gravity with Resistance to motion, " the two most wide-
ly operating laws as yet discovered whereby two distinct properties are conjoined throughout
substances generally." The first is, "a law connecting Atomic Weight and Specific Heat by
an inverse proportion. For equal weights of the simple bodies, the atomic weight multiplied
by a number expressing the specific heat, gives a nearly uniform product. The products, for
all the elements, are near the constant number 6." The other is a law which obtains "be-
tween the specific gravity of substances in the gaseous state, and the atomic weights. The
relationship of the two numbera is in some instances equality ; in other instances the one is a
multiple of the other."
Neither of these generalizations has the smallest appearance of being an ultimate law.
They point unmistakably to higher laws. Since the heat necessary to raise to a given tem-
perature the same weight of different substances (called their specific heat) is inversely as
their atomic weight, that is, directly as the number of atoms in a given weight of the sub-
stance, it follows that a single atom of every substance requires the same amount of heat to
Taise it to a given temperature ; a most interesting and important law, but a law of causation.
The other law mentioned by Mr. Bain points to the conclusion, that in the gaseous state all
substances contain, in the same space, the same number of atoms ; which, as the gaseous
state suspends all cohesive force, might naturally be expected, though it could not have been
positively assumed. This law may also be a result of the mode of action of causes, namely,
of molecular motions. The cases in which one of the numbers is not identical with the oth-
er, but a multiple of it, may be explained on the nowise unlikely supposition, that in our pres-
ent estimate of the atomic weights of some substances, we mistake two, or three, atoms for
one, or one for several.
416 INDUCTION.
Uniformities of co-existence, then, not only when they are consequences
of laws of succession, but also when they are ultimate truths, must be
ranked, for the purpose of logic, among empirical laws ; and are amenable
in every respect to the same rules with those unresolved uniformities which
are known to be dependent on causation.*
CHAPTER XXIII.
OF APPROXIMATE GENERALIZATIONS, AND PEOBABLB EVIDENCE.
§ 1. In our inquiries into the nature of the inductive process, we must
not confine our notice to such generalizations from experience as profess to
be universally true. There is a class of inductive truths avowedly not uni-
versal ; in which it is not pretended that the predicate is always true of.
the subject; but the value of which, as generalizations, is nevertheless ex-
tremely great. An important portion of the field of inductive knowledge
does not consist of universal truths, but of approximations to such truths ;
and when a conclusion is said to rest on probable evidence, the premises it
is drawn from are usually generalizations of this sort.
As every certain inference respecting a particular case implies that there
is ground for a general proposition of the form, every A is B ; so does ev-
ery probable inference suppose that there is ground for a proposition of the
form. Most A are B ; and the degree of probability of the inference in an av-
erage case will depend on the proportion between the number of instances
existing in nature which accord with the generalization, and the number of
those which conflict with it.
§ 2. Propositions in the form. Most A are B, are of a very different de-
gree of importance in science, and in the practice of life. To the scientific
inquirer they are valuable chiefly as materials for, and steps toward uni-
versal truths. The discovery of these is the proper end of science ; its work
is not done if it stops at the proposition that a majority of A are B, with-
out circumscribing that majority by some common character, fitted to dis-
tinguish them from the minority. Independently of the inferior precision
of such imperfect generalizations, and the inferior assurance with which
they can be applied to individual cases, it is plain that, compared with ex-
act generalizations, they are almost useless as means of discovering ulterior
* Dr. M'Cosh (p. 324 of his book) considers the laws of the chemical composition of bodies
as not coming under the principle of Causation ; and thinks it an omission in this work not
to have provided special canons for their investigation and proof. But every case of chem-
ical composition is, as I have explained, a case of causation. When It is said that water is
composed of hydrogen and oxygen, the affirmation is that hydrogen and oxygen, by the ac-
tion on one another which they exert under certain conditions, generate the properties of wa-
ter. The Canons of Induction, therefore, as laid down in this treatise, are applicable to the
case. Such special adaptations as the Inductive methods may require in their application to
chemistry, or any other science, are a proper subject for any one who treats of the logic of
the special sciences, as Professor Bain has done in the latter part of his work ; but they do
not appertain to General Logic.
Dr. M'Cosh also complains Cp. 325) that I have given no canons for those sciences in which
"the end sought is not the discovery of Causes or of Composition, but of Classes; that is,
Natural Classes." Such canons could be no other than the principles and rules of Natur.al
Classification, which I certainly thought that I had expounded at considerable length. But
this is far from the only instance in which Dr. M'Cosh does not appear to be aware of thft
contents of the books he is criticising.
APPROXIMATE GENERALIZATIONS. 411?
truths by way of deduction. We may, it is true, by combining the prop-
osition Most A are B, with a universal proposition. Every B is C, arrive
at the conclusion that Most A are C. But when a second proposition of
the api^roximate kind is introduced — or even when there is but one, if that
one be the major premise — nothing can, in general, be positively concluded.
When the major is Most B are D, then, even if the minor be Every A is B,
we can not infer that most A are D, or with any certainty that even some
A are D. Though the majority of the class B have the attribute signified
by D, the whole of the sub-class A may belong to the minority.*
Though so little use can be made, in science, of approximate generaliza-
tions, except as a stage on the road to something better, for practical guid-
ance they are often all we have to rely on. Even when science has really
determined the universal laws of any phenomenon, not only are those laws
generally too much encumbered with conditions to be adapted for every-
day use, but the cases which present themselves in life are too complicated,
and our decisions require to be taken too rapidly, to admit of waiting till
the existence of a- phenomenon can be proved by what have been scientific-
ally ascertained to be universal marks of it. To be indecisive and reluc-
tant to act, because we have not evidence of a perfectly conclusive character
to act on, is a defect sometimes incident to scientific minds, but which,
wherever it exists, renders them unfit for practical emergencies. If we
would succeed in action, we must judge by indications which, though they
do not generally mislead us, sometimes do, and must make up, as far as
possible, for the incomplete conclusiveness of any one indication, by ob-
taining others to corroborate it. The principles of induction applicable to
approximate generalization are therefore a not less important subject of in-
quiry than the rules for the investigation of universal truths ; and might
reasonably be expected to detain us almost as long, were it not that these
principles are mere corollaries from those which have been already treat-
ed of.
§ 3. There are two sorts of cases in which we are forced to guide our-
selves by generalizations of the imperfect form. Most A are B. The first
is, when we have no others; when we have not been able to carry our in-
vestigation of the laws of the phenomena any further ; as in the following
propositions — Most dark-eyed persons have dark hair; Most springs con-
tain mineral substances; Most stratified formations contain fossils. The
importance of this class of generalizations is not very great ; for, though it
frequently happens that we see no reason why that which is true of most
iadividuale of a class is not true of the remainder, nor are able to bring the
former under any general description which can distinguish them from the
latter, yet if we are willing to be satisfied with propositions of a less de-
gree of generality, and to break down the class A into sub-classes, we may
generally obtain a collection of propositions exactly true. We do not know
why most wood is lighter than water, nor can we point out any general
property which discriminates wood that is lighter than water from that
which is heavier. But we know exactly what species are the one and
what the other. And if we meet with a specimen not conformable to any
* Mr. De Morgan, in his Formal Logic, makes the just remark, that from two such prem-
ises as Most A are B, and Most A are C, we may infer with certainty that some B are C.
But this is the utmost limit of the conclusions which can be drawn from two approximate
generalizations, when the precise degree of their approximation to universality is unknown or
undefined.
27
418 INDUCTION.
known species (the only case in which our previous knowledge affords no
other guidance than the approximate generalization), we can generally
make a specific experiment, which is a surer resource.
It often happens, however, that the proposition. Most A are B, is not
the ultimatum of our scientific attainments, though the knowledge we pos-
sess beyond it can not conveniently be brought to bear upon the particular
instance. We may know well enough what circumstances distinguish the
portion of A which has the attribute B from the portion which has it not,
but may have no means, or may not have time, to examine whether those
characteristic circumstances exist or not in the individual case. This is
the situation we are generally in when the inquiry is of the kind called
moral, that is, of the kind which has in view to predict human actions.
To enable us to affirm any thing universally concerning the actions of
classes of human beings, the classification must be grounded on the circum-
stances of their mental culture and habits, which in an individual case are
seldom exactly known ; and classes grounded on these distinctions would
never precisely accord with those into which mankind ai<e divided for so-
cial purposes. All propositions which can be framed respecting the actions
of human beings as ordinarily classified, or as classified according to any
kind of outward indications, are merely approximate. We can only say,
Most persons of a particular age, profession, country, or rank in society,
have such and such qualities ; or, Most persons, when placed in certain
circumstances, act in such and such a way. Not that we do not often
know well enough on what causes the qualities depend, or what sort of
persons they are who act in that particular way; but we have seldom the
means of knowing whether any individual person has been under the influ-
ence of those causes, or is a person of that particular sort. We could re-
place the approximate generalizations by propositions universally true;
but these would hardly ever be capable of being applied to practice. We
should be sure of our majors, but we should not be able to get minors to
fit ; we are forced, therefore, to draw our conclusions from coarser and
more fallible indications.
§ 4. Proceeding now to consider what is to be regarded as sufficient evi-
dence of an approximate generalization, we can have no difiiculty in at
once recognizing that, when admissible at all, it is admissible only as an
empirical law. Propositions of the form, Every A is B, are not necessarily
laws of causation, or ultimate uniformities of co - existence ; propositions
like Most A are B, can not be so. Propositions hitherto found true in ev-
ery observed instance may yet be no necessary consequence of laws of cau-
sation, or of ultimate uniformities, and unless they are so, may, for aught
we know, be false beyond the limits of actual observation ; still more evi-
dently must this be the case with propositions which are only true in a
mere majority of the observed instances.
There is some difference, however, in the degree of certainty of the
proposition. Most A are B, according as that approximate generalization
composes the whole of our knowledge of the subject, or not. Suppose,
first, that the former is the case. We know only that most A are B, not
why they are so, nor in what respect those which are differ from those
which are not. How, then, did we learn that most A are B ? Precisely
in the manner in which we should have learned, had such happened to be
the fact that all A are B. We collected a number of instances sufficient
to eliminate chance, and, having done so, compared the number of instances
APPROXIMATE GENERALIZATIONS. 419
in the aflii-mative with the number in the negative. The result, like other
unresolved dei-ivative laws, can be relied on solely within the limits not
■only of place and time, but also of circumstance, under which its truth has
been actually observed; for, as we are supposed to be ignorant of the
causes which make the proposition true, we can not tell in what manner
any new circumstance might perhaps affect it. The proposition. Most
judges are inaccessible to bribes, would probably be found true of English-
men, Frenchmen, Germans, North Americans, and so forth ; but if on this
■evidence alone we extended the assertion to Orientals, we should step be-
yond the limits, not only of place but of circumstance, within which the
fact had been observed, and should let in possibilities of the absence of the
■determining causes, or the presence of counteracting ones, which might be
fatal to the approximate generalization.
In the case where the approximate proposition is not the ultimatum of
•our scientific knowledge, but only the most available form of it for practi-
•cal guidance ; where we know, not only that most A have the attribute B,
but also the causes of B, or some properties by which the poition of A
which has that attribute is distinguished from the portion which has it
not, we are rather more favorably situated than in the preceding case.
For we have now a double mode of ascertaining whether it be true that
most A are B ; the direct mode, as before, and an indirect one, that of ex-
.amining whether the proposition admits of being deduced from the known
cause, or from any known criterion, of B. Let the question, for example,
be whether most Scotchmen can read? We may not have observed, or
received the testimony of others respecting, a sufficient mrmber and variety
■of Scotchmen to ascertain this fact; but when we consider that the cause,
of being able to read is the having been taught it, another mode of deter-
mining the question presents itself, namely, by inquiring whether most
Scotchmen have been sent to schools where I'eading is effectually taught.
Of these two modes, sometimes one and sometimes the other is the more
available. In some cases, the frequency of the effect is the more accessi-
ble to that extensive and varied observation which is indispensable to the
establishment of an empirical law ; at other times, the frequency of the
causes, or of some collateral indications. It commonly happens that nei-
ther is susceptible of so satisfactory an induction as could be desired, and
that the grounds on "which the conclusion is received are compounded of
both. Thus a person may believe that most Scotchmen can read, because,
so far as his information extends, most Scotchmen have been sent to school,
and most Scotch schools teach reading effectually ; and also because most
of the Scotchmen whom he has known or heard of could read ; though nei-
ther of these two sets of observations may by itself fulfill the necessary
conditions of extent and variety.
Although the approximate generalization may in most cases be indis-
pensable for our guidance, even when we know the cause, or some certain
mark,Xf the attribute predicated, it needs hardly be observed that we may
always replace the uncertain indication by a certain one, in any case in
which we can actually recognize the existence of the cause or mark. For
example, an assertion is made by a witness, and the question is whether to
believe it. If we do not look to any of the individual circumstances of the
case, ve have nothing to direct us but the approximate generalization,
that truth is more common than falsehood, or, in other words, that most
persons, on most occasions, speak truth. But if we consider in what cir-
cumstances the cases where truth is spoken differ from those in which it is
420 INDUCTION.
not, we find, for instance, the following: the witness's being an honest per.
son or not ; his being an accurate observer or not ; his having an interest
to serve in the matter or not. Now, not only may we be able to obtain
other approximate generalizations respecting the degree of fi-equehcy of
these various possibilities, bat we may know which of them is positively
realized in the individual case. That the witness has or has not an inter-
est to serve, we perhaps know directly ; and the other two points indirect-
ly, by means of marks ; as, for example, from his conduct on some former
occasion ; or from his reputation, which, though a very uncertain mark, af-
fords an approximate generalization (as, for instance. Most persons who
are believed to be honest by those with whom they have had frequent deal-
ings, are really so), which approaches nearer to a universal truth than the
approximate general proposition with which we set out, viz., Most persons
on most occasions speak truth.
As it seems unnecessary to dwell further on the question of the evidence
of approximate generalizations, we shall proceed to a not less important
topic, that of the cautions to be observed in arguing from these incomplete-
ly universal propositions to particular cases.
§ 5. So far as regards the direct application of an approximate generali-
zation to an individual instance, this question presents no difficulty. If the
proposition, Most A are B, has been established, by a sufficient induction,
as an empirical law, we may conclude that any particular A is B with a
probability proportioned to the preponderance of the number of affirmative
instances over the number of exceptions. If it has been found practicable
to attain numerical precision in the data, a corresponding degree of precis-
ion may be given to the evaluation of the chances of error in the conclu-
sion. If it can be established as an empirical law that nine out of every ten
A are B, there will be one chance in ten of error in assuming that any A,
not individually known to us, is a B : but this of course holds only within
the limits of time, place, and circumstance, embraced in the observations,
and therefore can not be counted on for any sub-class or variety of A (or
for A in any set of external circumstances) which were not included in the
average. It must be added, that we can guide ourselves by the proposition.
Nine out of every ten A are B, only in cases of which we know nothing ex-
cept that they fall within the class A. For if we know, of any particular
instances i, not only that it falls under A, but to what species or variety of
A it belongs, we shall generally err in applying to i the average struck for
the whole genus, from which the average corresponding to that species
alone would, in all probability, materially differ. And so if i, instead of be-
ing a particular sort of instance, is an instance known to be under the in-
fluence of a particular set of circumstances, the presumption drawn from
the numerical proportions in the whole genus would probably, in such a
case, only mislead. A general average should only be applied to cases which
are neither known, nor can be presumed, to be other than average cases.
Such averages, therefore, are commonly of little use for the practical guid-
ance of any affairs but those which concern large numbers. Tables of the
chances of life are useful to insurance offices, but they go a very little way
toward informing any one of the chances of his own life, or any other life
in which he is interested, since almost every life is either better or worse
than the average. Such averages can only be considered as supplying the
first term in a series of approximations ; the subsequent terras proceeding
on an appreciation of the circumstances belonging to the particular case.
APPROXIMATE GENERALIZATIONS. 421
§ 6. From the application of a single approximate generalization to in.
dividual cases, we proceed to the application of two or more of them to-
gether to the same case.
When a judgment applied to an individual instance is grounded on two
approximate generalizations taken in conjunction, the propositions may co-
operate toward the result in two different ways. In the one, each proposi-
tion is separately applicable to the case in hand, and our object in combin-
ing them is to give to the conclusion in that particular case the double
probability arising from the two propositions separately. This may be
called joining two probabilities by way of Addition ; and the result is a
probability greater than either. The other mode is, when only one of the
propositions is directly applicable to the case, the second being only appli-
cable to it by virtue of the application of the first. This is joining two
probabilities by way of Ratiocination or Deduction ; the result of which is
a less probability than either. The type of the first argument is, Most A
are B ; most C are B ; this thing is both an A and a C ; therefore it is
probably a B. The type of the second is. Most A are B ; most C are A ;
this is a C ; therefore it is probably an A, therefore it is probably a B.
The first is exemplified when we prove a fact by the testimony of two un-
connected witnesses ; the second, when we adduce only the testimony of one
witness that he has heard the thing asserted by another. Or again, in the
first mode it may be argued that the accused committed the crime, because
he concealed himself, and because his clothes were stained with blood ; in
the second, that he committed it because he washed or destroyed his clothes,
which is supposed to render it probable that they were stained with blood.
Instead of only two links, as in these instances, we may suppose chains of
any length. A chain of the former kind was termed by Bentham* a self-
corroborative chain of evidence ; the second, a self-infirmative chain.
When approximate generalizations are joined by way of addition, we may
deduce from the theary of probabilities laid down in a former chapter, in
what manner each of them adds to the probability of a conclusion which
has the warrant of them all.
If, on an average, two of every three As are Bs, and three of every four
Cs are Bs, the probability that something which is both an A and a C is a
B, will be more than two in three, or than three, in four. Of every twelve
things which are As, all except four are Bs by the supposition ; and if the
whole twelve, and consequently those foiy, have the characters of C like-
wise, three of these will be Bs on that ground. Therefore, out of twelve
which are both As and Cs, eleven are Bs. To state the argument in anoth-
er way ; a thing which is both an A and a C, but which is not a B, is found
in only one of three sections of the class A, and in only one of four sections
of the class C ; but this fourth of C being spread over the whole of A in-
discriminately, only one-third part of it (or one-twelfth of the whole num-
ber) belongs to the third section of A; therefore a thing which is not a B
occurs only once, among twelve things which are both As and Cs. The
argument would, in the language of the doctrine of chances, be thus ex-
pressed : the chance that an A is not a B is ^, the chance that a C is not a
B is :^; hence if the thing be both an A and a C, the chance is i oii=-^.\
* Rationale of Judicial Evidence, vol. iii., p. 224.
t The evaluation of the chances in this statement has been objected to by a mathematical
friend. The correct mode, in his opinion, of setting out the possibilities is as follows. If
the thing (let us call it T) which is both an A and a C, is a B, something is true which is
only true twice in every thrice, and something else which is only true thrice in every font
422 INDUCTION.
In this computation it is of course supposed that the probabilities arising;
from A and C are independent of each other. There must not be any such
connection between A and C, that when a thing belongs to the one class it
will therefore belong to the other, or even have a greater chance of doing
so. Otherwise the not-Bs which are Cs may be, most or even all of them,
identical with the not-Bs which are As ; in which last case the probability
arising from A and C together will be no greater than that arising from A
alone.
When approximate generalizations are joined together in the other mode,,
that of deduction, the degree of probability of the inference, instead of in-
creasing, diminishes at each step. From two such premises as Most A are
B, Most B are C, we can not with certainty conclude that even a single A
is C ; for the whole of the portion of A which in any way falls under B,
may perhaps be comprised in the exceptional part of it. Still, the two
propositions in question afford an appreciable probability that any given A
is C, provided the average on which the second proposition is grounded
was taken fairly with reference to the first ; provided the proposition, Most
times. The first fact being true eight times in twelve, and the second being true six times ii»
every eight, and consequently six times in those eight ; both facts will be true only six times
in twelve. On the other hand, if T, although it is both an A and a C, is not a B, something
is true which is only true once in eveiy thrice, and something else which is only true once in
every four times. The former being true four times out of twelve, and the latter once in
every four, and therefore once in those four ; both are only true in one case out of twelve. So
that T is a B six times in twelve, and T is not a B, only once : making the compaiative prob-
abilities, not eleven to one, as I had previously made them, but six to one.
In the last edition I accepted this reasoning as conclusive. More attentive consideration,
however, has convinced me that it contains a fallacy.
The objector argues, that the fact of A's being a B is true eight times in twelve, and th»
fact of C's being a B six times in eight, and consequently six times in those eight ; both facts,
therefore, are true only six times in every twelve. That is, he concludes that because among As
taken indiscriminately only eight out of twelve are Bs and the remaining four are not, it must
equally hold that four out of twelve are not Bs when the twelve are taken from the select por-
tion of As which are also Cs. And by this assumption he arrives at the strange result, that
there are fewer Bs among things which are both As and Cs than there are among either As
or Cs taken indiscriminately ; so that a thing which has both chances of being a B, is less
likely to be so than if it had only the one chance or only the other.
The objector (as has been acutely remarked by another correspondent) applies to the prob-
lem under consideration, a mode of calculation only suited to the reverse problem. Had
the question been — If two of every three Bs are As and three out of every four Bs are Cs,
how many Bs will be both As and Cs, his reasoning would have been correct. For the B»
that are both As and Cs must be fewer tifan either the Bs that are As or the Bs that are Cs,
and to find their number we must abate either of these numbers in the ratio due to the other.
But when the problem is to find, not how many Bs are both As and Cs, but how many things
that are both As and Cs are Bs, it is evident that among these the proportion of Bs must be
not less, but greater, than among things which are only A, or among things which are only B.
The true theory of the chances is best found by going back to the scientific grounds on.
which the proportions rest. The degree of frequency of a coincidence depends on, and is a
measure of, the frequency, combined with the efficacy, of the causes in operation that are fa-
vorable to it. If out of every twelve As taken indiscriminately eight are Bs and four are not,
it is implied that there are causes operating on A which tend to make it a B, and that these'
causes are sufficiently constant and sufficiently powerful to succeed in eight out of twelve-
cases, but tail in the remaining four. So if of twelve Cs, nine are Bs and three are not, there
must be causes of the same tendency operating on C, which succeed in nine cases and fail in
three,- Now suppose twelve cases which are both As and Cs. The whole twelve are now
under the operation of both sets of causes. One set is sufficient to prevail in eight of the
twelve cases, the other in nine. The analysis of the cases shows that six of the twelve will be
Bs through the operation of both sets of causes ; two more in virtue of the causes operating,
on A ; and three more through those operating on C, and that there will be only one case in
which all the causes will be inoperative. The total number, therefore, which are Bs will be
eleven in twelve, and the evaluation in the text is correct.
APPROXIMATE GENEEALIZATIONS. 42a
B are C, was arrived at in a manner leaving no suspicion that the probabili-
ty arising from it is otherwise than fairly distributed over the section of B
which belongs to A. For though the instances which are A may. be all ia
the minority, they may, also, be all in the majority ; and the one possibility
is to be set against the other. On the whole, the probability arising from
the two propositions taken together, will be cori-ectly measured by the prob-
ability arising from the one, abeted in the ratio of that arising from the
other. If nine out of ten Swedes have light hair, and eight out of nine in-
habitants of Stockholm are Swedes, the probability arising from these two-
propositions, that any given inhabitant of Stockholm is light-haired, will
amount to eight in ten ; though it is rigorously possible that the whole
Swedish population of Stockholm might belong to that tenth section of the
people of Sweden who are an exception to the rest.
If the premises are known to be true not of a bare majority, but of near-
ly the whole, of their respective subjects, we may go on joining one such
proposition to another for several steps, before we reach a conclusion not
presumably true even of a majority. The error of the conclusion will
amount to the aggregate of the errors of all the premises. Let the prop-
osition, most A are B, be true of nine in ten; Most B are C, of eight in
nine ; then not only will one A in ten not be C, because not B, but even of
the nine-tenths which are B, only eight-ninths will be C ; that is, the cases
of A which are C will be only f of -^j or four-fifths. Let us now add
Most C are D, and suppose this to be true of seven cases out of eight;,
the proportion of A which is D will be only -J of -f of -j^, or -}^. Thus the
probability progressively dwindles. The experience, however, on which our
approximate generalizations are grounded, has so rarely been subjected to,,
or admits of, accurate numerical estimation, that we can not in general ap-
ply any measurement to the diminution of probability which takes place at
each illation ; but must be content with remembering that it does diminish
at every step, and that unless the premises approach very nearly indeed to
being universally true, the conclusion after a very few steps is worth noth-
ing. A hearsay of a hearsay, or an argument from presumptive evidence
depending not on immediate mai-ks but on marks of marks, is worthless at
a very few removes from the first stage.
§ 7. There are, however, two cases in which reasonings depending on ap-
proximate generalizations may be carried to any length we please with as
much assurance, and are as strictly scientific, as if they were composed of
universal laws of nature. But these cases are exceptions of the sort which .
are currently said to prove the rule. The approximate generalizations are
as suitable, in the cases in question, for purposes of ratiocination, as if they
were complete generalizations, because they are capable of being transform-^
ed into complete generalizations exactly equivalent.
First : If the approximate generalization is of the class in which our rea-
son for stopping at the approximation is not the impossibility, but only the
inconvenience, of going further ; if we are cognizant of the character which,
distinguishes the cases that accord with the generalization from those
which are exceptions to it; we may then substitute for the approximate
proposition, a universal proposition with a proviso. The proposition,.
Most persons who have uncontrolled power employ it ill, is a generalizatioa
of this class, and may be transformed into the following : All persons wha
have uncontrolled power employ it ill, provided they are not persons of un-
usual strength of judgment and rectitude of purpose. The proposition.
424 INDUCTION.
carrying the hypothesis or proviso with it, may then be dealt with no longer
as an approximate, but as a universal proposition; and to whatever num-
ber of steps the reasoning may reach, the hypothesis, being carried forward
to the conclusion, will exactly indicate how far that conclusion is from be-
ing applicable universally. If in the course of the argument other approx-
imate generalizations are introduced, each of them being in like manner
expressed as a universal proposition with a condition annexed, the sum of
all the conditions will appear at the end as the sum of all the errors which
affect the conclusion. Thus, to the proposition last cited, let us add the
following : All absolute monarchs have uncontrolled power, unless their po-
sition is such that they need the active support of their subjects (as was
the case with Queen Elizabeth, Frederick of Prussia, and others). Com-
bining these two propositions, we can deduce from them a universal con-
clusion, which will be subject to both the hypotheses in the premises; All
absolute monarchs employ their power ill, unless their position makes them
need the active support of their subjects, or unless they are persons of un-
usual strength of judgment and rectitude of purpose. It is of no conse-
quence how rapidly the errors in our premises accumulate, if we are able
in this manner to record each error, and keep an account of the aggregate
as it swells up.
Secondly : there is a case in which approximate propositions, even with-
out our taking note of the conditions under which they are not true of indi-
vidual cases, are yet, for the purposes of science, universal ones ; namely, in
the inquiries which relate to the properties not of individuals, but of multi-
tudes. The principal of these is the science of politics, or of human soci-
■ety. This science is principally concerned with the actions not of solitary
individuals, but of masses; with the fortunes not of single persons, but
of communities. For the statesman, therefore, it is generally enough to
know that most persons act or are acted upon in a particular way; since
his speculations and his practical arrangements refer almost exclusively
to cases in which the whole community, or some large portion of it, is
acted upon at once, and in which, therefore, what is done or felt by most
persons determines the result produced by or upon the body at large. He
can get on well enough with approximate generalizations on human nature,
since what is true approximately of all individuals is true absolutely of all
masses. And even when the operations of individual men have a part to
play in his deductions, as when he is reasoning of kings, or other single
rulers, still, as he is providing for indefinite duration, involving an indefinite
■ succession of such individuals, he must in general both reason and act as
if what is true of most persons were true of all.
The two kinds of considerations above adduced are a sufficient refuta-
tion of the popular error, that speculations on society and government, as
Testing on merely probable evidence, must be inferior in certainty and
scientific accuracy to the conclusions of w-hat are called the exact sciences,
and less to be relied on in practice. There are reasons enough why the
moral sciences must remain inferior to at least the more perfect of the phys-
ical; why the laws of their more complicated phenomena can not be so
-completely deciphered, nor the phenomena predicted with the same degree
of assurance. But though we can not attain to so many truths, there is no
reason that those we can attain should deserve less reliance, or have less
of a scientific character. Of this topic, however, I shall treat more system-
atically in the concluding Book, to which place any further consideration
of it must be deferred.
BEMAINING LAWS OF NATUEE. 425
CHAPTER XXIV.
OP THE KEMAINING LAWS OF NATUEE.
§ 1. In the First Book we found that all the assertions which can be
conveyed by language, express some one or more of five different things :
Existence; Order in Place ; Order in Time; Causation; and Resemblance.*
Of these, Causation, in our view of the subject, not being fundamentally
different from Order in Time, the five species of possible assertions are
reduced to four. The propositions which aflSrm Order in Time in either
of its two modes, Co-existence and Succession, have formed, thus far, the
subject of the present Book. And we have now concluded the exposition,
so far as it falls within the limits assigned to this work, of the nature of
the evidence on which these propositions rest, and the processes of investi-
gation by which they are ascertained and proved. There remain three-
classes of facts : Existence, Order in Place, and Resemblance ; in regard to
which the same questions are now to be resolved.
Regarding the first of these, very little needs be said. Existence in
general, is a subject not for our science, but for metaphysics. To deter-
mine what things can be recognized as really existing, independently of oui'
own sensible or other impressions, and in what meaning the term is, in that
case, predicated of them, belongs to the consider'ation of " Things in them-
selves," from which, throughout this work, we have as much as possible
kept aloof. Existence, so far as Logic is concerned about it, has reference
only to phenomena; to actual, or possible, states of external or internal
consciousness, in ourselves or others. Feelings of sensitive beings, or pos-
sibilities of having such feelings, are the only things the existence of which
can be a subject of logical induction, because the only things of which the
existence in individual cases can be a subject of experience.
It is true that a thing is said by us to exist, even when it is absent, and
therefore is not and can not be perceived. But even then, its existence is-
to us only another word for our conviction that we should perceive it on a
certain supposition ; namely, if we were in the needful circumstances of
time and place, and endowed with the needful perfection of organs. My
belief that the Emperor of China exists,. is simply my belief that if I were
transported to the imperial palace or some other locality in Pekin, I should
see him. My belief that Julius Caesar existed, is my belief that I should
have seen him if I had been present in the field of Pharsalia, or in the-
senate-house at Rome. When I believe that stars exist beyond the utmost
range of my vision, though assisted by the most powerful telescopes yet
invented, my belief, philosophically expressed, is, that with still bettei- tele-
scopes, if such existed, I could see them, or that they may be perceived by
beings less remote from them in space, or whose capacities of perception
are superior to mine.
The existence, therefore, of a phenomenon, is but another word for its
being perceived, or for the inferred possibility of perceiving it. When the
phenomenon is within the range of present observation, by present obser-
* Supra, book i. , chap. v.
426 INDUCTION.
vation we assure ourselves of its existence ; when it is beyond that range,
and is therefore said to be absent, we infer its existence from marks or evi-
dences. But what can these evidences be? Other phenomena; ascertain-
ed by induction to be connected with the given phenomenon, either in the
way of succession or of co-existence. The simple existence, therefore, of an
individual phenomenon, when not directly perceived, is inferred from some
inductive law of succession or co-existence ; and is consequently not amen-
able to any peculiar inductive principles. We prove the existence of a
thing, by proving that it is connected by succession or co-existence with
some known thing.
With respect to general propositions of this class, that is, which aifirm the
bare fact of existence, they have a peculiarity which renders the logical
treatment of them a very easy matter ; they are generalizations which are
sufficiently proved by a single instance. That ghosts, or unicorns, or sea-
serpents exist, would be fully established if it could be ascertained posi-
tively that such things had been even once seen. Whatever has once hap-
pened, is capable of happening again ; the only question relates to the con-
ditions under which it happens.
So far, therefore, as relates to simple existence, the Inductive Logic has
no knots to untie. And we may proceed to the remaining two of the great
classes into which facts have been divided ; Resemblance, and Order in
Place.
§ 2. Resemblance and its opposite, except in the case in which they as-
sume the names of Equality and Inequality, are seldom regarded as sub-
jects of science; they are supposed to be perceived by simple apprehen-
sion ; by merely applying our senses or directing our attention to the two
objects at once, or in immediate succession. And this simultaneous, or
virtually simultaneous, application of our faculties to the two things which
are to be compared, does necessarily constitute the ultimate appeal, wher-
ever such application is practicable. But, in most cases, it is not practica-
ble : the objects can not be brought so close together that the feeling of
their resemblance (at least a complete feeling of it) directly arises in the
inind. We can only compare each of them with some third object, capa-
ble of being transported from one to the other. And besides, even when
the objects can be brought into immediate juxtaposition, their resemblance
■or difference is but imperfectly known to us, unless we have compared
them minutely, part by part. Until this has been done, things in reality
very dissimilar often appear tindistinguishably alike. Two .lines of very
unequal length will appear about equal when lying in different directions ;
but place them parallel with their farther extremities even, and if we look
&% the nearer extremities, their inequality becomes a matter of direct per-
■ception.
To ascertain whether, and in what, two phenomena resemble or differ, is
not always, therefore, so easy a thing as it might at first appear. When
the two can not be brought into juxtaposition, or not so that the observer
is able to compare their several parts in detail, he must employ the indi-
rect means of reasoning and general propositions. When we can not bring
two straight lines together, to determine whether they are equal, we do it
by the physical aid of a foot-rule applied first to one and then to the other,
and the logical aid of the general proposition or formula, "Things which
are equal to the same thing are equal to one another." The comparison
■of two things through the intervention, of a third thing, when their direct
REMAINING LAWS OF NATURE.
427
comparison is impossible, is the appropriate scientific process for ascertain-
ing resemblances and dissimilarities, and is the sum total of what Logic
has to teach on the subject.
An undue extension of this remark induced Locke to consider reasoning
itself as nothing but the comparison of two ideas through the medium of
a third, and knowledge as the perception of the agreement or disagreement
of two ideas ; doctrines which the Condillac school blindly adopted, with-
out the qualifications and distinctions with which they were studiously-
guarded by their illustrious author. Where, indeed, the agreement or dis-
agreement (otherwise called resemblance or dissimilarity) of any two things
is the very matter to be determined, as is the case particularly in the sci-
ences of quantity and extension ; there, the process by which a solution, if
not attainable by direct perception, must be indirectly sought, consists in
■comparing these two things through the medium of a third. But this is
far from_ being true of all inquiries. • The knowledge that bodies fall to the
ground is not a perception of agreement or disagreement, but of a series
■of physical occurrences, a succession of sensations. Locke's definitions of
knowledge and of reasoning required to be limited to our knowledge of,
and reasoning about, resemblances. Nor, even when thus restricted, are the
propositions strictly correct; since the comparison is not made, as he rep-
resents, between the ideas of the two phenomena, but between the phenome-
na themselves. This mistake has been pointed out in an earlier part of our
inquiry,* and we traced it to an imperfect conception of wliat takes place in
mathematics, where very often the comparison is really made between the
ideas, without any appeal to the outward senses ; only, however, because
in mathematics a comparison of the ideas is strictly equivalent to a com-
parison of the phenomena themselves. Where, as in the case of numbers,
lines, and figures, our idea of an object is a complete picture of the object,
so far as respects the matter in hand ; we can, of course, learn from the
picture, whatever could be learned from the object itself by mei'e contem-
plation of it as it exists at the particular instant when the picture is taken.
No mere contemplation of gunpowder would ever teach us that a spark
would make it explode, nor, consequently, would the contemplation of the
idea of gunpowder do so; but the mere contemplation of a straight line
shows that it can not inclose a space; accordingly the contemplation of the
idea of it will show the same. What takes place in mathematics is thus
no argument that the comparison is between the ideas only. It is always,
either indirectly or directly, a comparison of the phenomena.
In cases in which we can not bring the phenomena to the test of direct
inspection at all, or not in a manner sufficiently precise, but must judge of
their resemblance by inference from other resemblances or dissimilarities
more accessible to observation, we of course require, as in all cases of ra-
tiocination, generalizations or formulae applicable to the subject. We must
reason from laws of nature ; from the uniformities which are observable in
the fact of likeness or unlikeness.
§ 3. Of these laws or uniformities, the most comprehensive are those sup-
plied by mathematics ; the axioms relating to equality, inequality, and pro-
portionality, and the various theorems thereon founded. And these are the
only Laws of Resemblance which require to be, or which can be, treated apart.
It is true there are innumerable other theorems which affirm resemblances .
• Sapra, book i., chap, v., § 1, and book ii., chap, v., § 5.
428 INDUCTION.
among phenomena ; as that the angle of the reflection of light is equal
to its angle of incidence (equality being merely exact resemblance in mag-
nitude). Again, that the heavenly bodies describe equal areas in. equal
times ; and that their periods of revolution are proportional (another spe-
cies of resemblance) to the sesquiplicate powers of their distances from the-
centre of force. These and similar propositions affirm resemblances, of the
same nature with those asserted in the theorems of mathematics ; but the-
distinction is, that the propositions of mathematics ai-e true of all phe-
nomena whatever, or at least without distinction of origin ; while the truths-'
in question are affirmed only of special phenomena, which originate in a
certain way ; and the equalities, proportionalities, or other resemblances,,
which exist between such phenomena, must necessarily be either derived
from, or identical with, the law of their origin — the law of causation on
•which they depend. The equality of the areas described in equal times by
the planets, is derived from the laws of the causes ; and, until its derivation
■was shown, it was an empirical law. The equality of the angles of reflec-
tion and incidence is identical with the law of the cause ; for the cause is
the incidence of a ray of light upon a reflecting surface, and the equality
in question is the very law according to which that cause produces its ef-
fects. This class, therefore, of the uniformities of resemblance between
phenomena, are inseparable, in fact and in thought, from the laws of the
production of those phenomena; and the principles of induction applicable
to them are no other than those of which we have treated in the preceding
chapters of this Book.
It is otherwise with the truths of mathematics. The laws of equality
and inequality between spaces, or between numbers, have no connection
with laws of cauBation. That the angle of reflection is equal to the angle
of incidence, is a statement of the mode of action of a particular cause ; but
that when two straight lines intersect each other the opposite angles are
equal, is true of all such lines and angles, by whatever cause produced.
That the squares of the periodic times of the planets are proportional to
the cubes of their distances from the sun, is a uniformity derived from
the laws of the causes (or forces) which produce the planetary motions j
but that the square of any number is four times the square of half the
number, is true independently of any cause. The only laws of resemblance,,
therefore, which we are called upon to consider independently of causation,
belong to the province of mathematics.
§ 4. The same thing is evident with respect to the only one remaining
of our five categories. Order in Place. The order in place, of the effects
of a cause, is (like every thing else belonging to the effects) a consequence
of the laws of that cause. The order in place, or, as we have termed it,
the collocation, of the primeval causes, is (as well as their resemblance) in
each instance an ultimate fact, in which no laws or uniformities are trace-
able. The only remaining general propositions respecting order in place,
and the only ones which have nothing to do with causation, are some of
the truths of geometry ; laws through which we are able, from the order
in place of certain points, lines, or spaces, to infer the order in place of
others which are connected with the former in some known mode ; quite
independently of the particular nature of those points, lines, or spaces, in
.^ny other respect than position or magnitude, as well as independently of
the physical cause from which in any particular case they happen to de-
rive their origin.
EEMAINING LAWS OF NATURE. 429
It thus appears that mathematics is the only department of science into
the methods of which it still remains to inquire. And there is the less ne-
cessity that this inquiry should occupy us long, as we have already, in the
Second Book, made considerable pi-ogress in it. We there remarked, that
the directly inductive truths of mathematics are few in number ; consist
ing of the axioms, together with certain propositions concerning existence,
tacitly involved in most of the so-called definitions. And we gave what
appeared conclusive reasons for affirming that these original premises, from
which the remaining truths of the science are deduced, are, notwithstand-
ing all appearances to the contrary, results of observation and experience ;
iounded, in «hort, on the evidence of the senses. That things equal to the
same thing are equal to one another, and that two straight lines which
have once intersected one another continue to diverge, are inductive truths ;
resting, indeed, like the law of universal causation, only on induction per
^numerationem simpUcem; on the fact that they have been perpetually
perceived to be true, and never once found to be false. But, as we have
seen in a recent chapter that this evidence, in the case of a law so complete-
ly universal as the law of causation, amounts to the fullest proof, so is this
even moi-e evidently true of the general propositions to which we are now
adverting; because, as a perception of their truth in any individual case
whatever, requires only the simple act of looking at the objects in a proper
position, there never could have been in their case (what, for a long period,
there were in the case of the law of causation) instances which were appar-
ently, though not really, exceptions to them. Their infallible truth was
recognized from the very dawn of speculation ; and as their .extreme famil-
iarity made it impossible for the mind to conceive the objects under any
other law, they were, and still are, generally considered as truths recog-
nized by their own evidence, or by instinct.
§ 5. There is something which seems to require explanation, in the fact
that the immense multitude of truths (a multitude still as far from being
exhausted as ever) comprised in the mathematical sciences, can be elicited
from so small a number of elementary laws. One sees not, at first, how it
is that there can be room for such an infinite variety of true propositions,
on subjects apparently so limited.
To begin with the science of number. The elementary or ultimate truths
of this science are the common axioms concerning equality, namely, " Things
which are equal to the same thing are equal to one another," and " Equals
added to equals make equal sums " (no other axioms are required),* to-
gether with the definitions of the various numbers. Like other so-called
definitions, these are composed of two things, the explanation of a name,
and the assertion of a fact ; of which the latter alone can form a first prin-
* The axiom, " Equals subtracted from equals leave equal differences," may be demon-
strated from the two axioms in the text. If A=a and B=6, A— B=o— i. For if not, let A
—B=a—b+c. ThensinceB=6, adding equals to equals, A=a+c. ButA=a. Therefore
a=a+c, which is impossible.
This proposition having been demonstrated, we may, by means of it, demonstrate the fol-
lowing: "If equals be added to unequals, the sums are unequal." If A=a and B not =6,
A-l-B is not=o-f-6. For suppose it to be so. Then, since A=a and A-t-B=a-|-6, sub-
tracting equals from equals, B=6 ; which is contrary to the hypothesis.
So again, it may be proved that two things, one of which is equal and the other unequal to
» third thing, are unequal to one another. If A=a and A not=B, neither is a=B. For
suppose it to be equal. Then since A=a and a=B, and since things equal to the same
thing are equal to one another A=B ; which is contrary to the hypothesis.
430 INDUCTION.
ciple or premise of a science. The fact asserted in the definition of a num.
ber is a pliysical fact. Each of the numbers two, three, four, etc., denotes
physical phenomena, and connotes a physical property of those phenomena.
Two, for instance, denotes all pairs of things, and twelve all dozens of
things, connoting what makes them pairs, or dozens ; and that which
makes them so is something physical ; since it can not be denied that two
apples are physically distinguishable from three apples, two horses from
one horse, and so forth ; that they are a different visible and tangible phe-
nomenon. I am not undertaking to say what the difference is ; it is
enough that there is a difference of which the senses can take cognizance.
And although a hundred and two horses are not so easily distinguished
from a hundred and three, as two horses are from three — though in most
positions the senses do not perceive any difference — yet they may be so
placed that a difference will be perceptible, or else we should never have
distinguished them, and given them different names. Weight is confess-
edly a physical property of things ; yet small differences between great
weights are as imperceptible to the senses in most situations, as small dif-
ferences between great numbers; and are only put in evidence by placing
the two objects in a peculiar position — namely, in the opposite scales of a
delicate balance.
What, then, is that which is connoted by a name of number? Of
course, some property belonging to the agglomeration of things which we
call by the name; and that property is, the characteristic manner in which
the agglomeration is made up of, and may be separated into, parts. I wiU
endeavor to make this more intelligible by a few explanations.
When we call a collection of objects two, three, or four, they are not
two, three, or four in the abstract ; they are two, three, or four things of
some particular kind ; pebbles, horses, inches, pounds' weight. What the
name of number connotes is, the manner in which single objects of the
given kind must be put together, in order to produce that particular aggre-
gate. If the aggregate be of pebbles, and we call it two, the name implies
that, to compose the aggregate, one pebble must be joined to one pebble.
If we call it three, one and one and one pebble must be brought together
to produce it, or else one pebble must be joined to an aggregate of the
kind called two, already existing. The aggregate which we call four, has
a still greater number of characteristic modes of formation. One and one
and one and one pebble may be brought togethei" or two aggregates of the
kind called two may be united ; or one pebble may be added to an aggre-
gate of the kind called three. Every succeeding number in the ascending
series, may be formed by the junction of smaller numbers in a progressive-
ly greater variety of ways. Even limiting the parts to two, the number
may be formed, and consequently may be divided, in as many different
ways as there are numbers smaller than itself; and, if we admit of threes,
fours, etc., in a still greater variety. Other modes of arriving at the same
aggregate present themselves, not by the union of smaller, but by the dis-
memberment of larger aggregates. Thus, three pebbles may be formed by
taking away one pebble from an aggregate of four ; two pebbles, by an.
equal division of a similar aggregate; and so on.
Every^ arithmetical proposition ; every statement of the result of an
arithmetical operation ; is a statement of one of the modes of formation
of a given number. It affirms that a certain aggregate might have been
formed by putting together certain other aggregates, or by withdrawing
certain portions of some aggregate ; and that, by consequence, we might,
reproduce those aggregates from it, by reversing the process.
REMAINING LAWS OF NATUEE. 431
Thus, when we say that the cube of 12 is 1128, what we .affirm is this:
that if, having a sufficient number of pebbles or of any other objects, we
put them together into the particular sort of parcels or aggregates called
twelves; and put together these twelves again into similar collections;
and, finally, make up twelve of these largest parcels ; the aggregate thua
formed will be such a one as we call 1728; namely, that which (to take
the most familiar of its modes of formation) may be made by joining the
parcel called a thousand pebbles, the parcel called seven hundred pebbles,
the parcel called twenty pebbles, and the parcel called eight pebbles.
The converse proposition that the cube root of 1728 is 12, asserts that
this large aggregate may again be decomposed into the twelve twelves of
twelves of pebbles which it consists of.
The modes of formation of any number are innumerable ; but when we
know one mode of formation of each, allthe rest may be determined de-
ductively. If we know that a is formed from b and c, b from a and e, c
from d and f, and so forth, until we have included all the numbers of any
scale we choose to select (taking care that for each number the mode of
formation be really a distinct one, not bringing us round again to the for-
mer numbers, but introducing a new number), we have a set of propositions
from which we may reason to all the other modes of formation of those
numbers from one another. Having established a chain of inductive truths
connecting together all the numbers of the scale, we can ascertain the forma-
tion of any one of those numbers from any other by merely traveling from
one to the other along the chain. Suppose that we know only the follow-
ing modes of formation: 6=4-1-2,4 = 7—3, 7 = 5-)- 2, 5 = 9— 4. We could
determine how 6 may be formed from 9. For 6=4-1-2 = 7— 3-|-2=5-f2 —
3-1-2=9- 4-f-2— 34-2. It may therefore be formed by taking away 4 and
3, and adding 2 and 2. If we know besides that 2 -|- 2 = 4, we obtain 6 from
9 in a simpler mode, by merely taking away 3.
It is sufficient, therefore, to select one of the various modes of foi-mation
of each number, as a means of ascertaining all the rest. And since things
which are uniform, and therefore simple, are most easily received and re-
tained by the understanding, there is an obvious advantage in selecting a
mode .of formation which shall be alike for all ; in fixing the connotation
of names of number on one uniform principle. The mode in which our
existing numerical nomenclature is contrived possesses this advantage, with
the additional one, that it happily conveys to the mind two. of the modes
of formation of every number. Each number is considered as formed by
the addition of a unit to the number next below it in magnitude, and this
mode of formation is conveyed by the place which it occupies in the series.
And each is also considered as formed by the addition of a number of
units less than ten, and a number of aggregates each equal to one of the
successive powers of ten; and this mode of its formation is expressed by
its spoken name, and by its numerical character.
What renders arithmetic the type of a deductive science, is the fortimate
applicability to it of a law so comprehensive as "The sums of equals are
equals :" or (to express the same principle in less familiar but more charac-
teristic language). Whatever is made up of parts, is made up of the parts
of those parts. This truth, obvious to the senses in all cases which can be
fairly referred to their decision, and so general as to be co-extensive with
nature itself, being true of all sorts of phenomena (for all admit of being
numbered), must be considered an inductive truth, or law of nature, of the
highest order. And every arithmetical operation is an application of this
432 INDUCTION.
law, or of other laws capable of being deduced from it. This is our war-
rant for all calculations. We believe that five and two are equal to seven,
on the evidence of this inductive law, combined with the definitions of those
numbers. We arrive at that conclusion (as all know who i-emember how
they first learned it) by adding a single unit at a time : 5 + 1 = 6, therefore
S + l + l^e + l^V; and again 2 = 1 + 1, therefore 5 + 2=5 + 1 + 1 = 7.
§ 6. Innumerable as are the true propositions which can be formed con-
cerning particular numbers, no adequate conception could be gained, from
these alone, of the extent of the truths composing the science of number.
Such propositions as we have spoken of are the least general of all numer-
ical truths. It is true that even these are co-extensive with all nature ; the
properties of the number four are true of all objects that are divisible into
four equal parts, and all objects are either actually or ideally so divisible.
But the propositions which compose the science of algebra are true, not of
a particular number, but of all numbers ; not of all things under the condi-
tion of being divided in a particular way, but of all things under the condi-
tion of being divided in any way— of being designated by a number at all.
Since it is impossible for different numbers to have any of their modes
of formation completely in common, it is a kind of paradox to say, that all
pi'opositions which can be made concerning numbers relate to their modes
of formation from other numbers, and yet that there are propositions which
are true of all numbers. But this very paradox leads to the real principle
of generalization concerning the properties of numbers. Two difEei'ent
numbers can not be formed in the same manner from the same numbers ;
but they may be formed in the same manner from different numbers; as
nine is formed from three by multiplying it into itself, and sixteen is form-
ed from four by the same process. Thus there arises a classification of
modes of formation, or in the language commonly used by mathematicians,
a classification of Functions. Any number, considered as formed from any
other number, is called a function of it ; and there are as many kinds of
functions as there are modes of formation. The simple functions are by no
means numerous, most functions being formed by the combination of sever-
al of the operations which form simple functions, or by successive repeti-
tions of some one of those operations. The simple functions of any num-
ber X are all reducible to the following forms: x+a, x—a, ax, -, a;", \^x,
(Z
log. X (to the base a), and the same expressions varied by putting x for a
and a for x, wherever that substitution would alter the value : to which,
perhaps, ought to be added sin x, and arc (sin=a!). All other functions
of X are formed by putting some one or more of the simple functions in
<he place of x or a, and subjecting them to the same elementary operations.
In oi'der to carry on general reasonings on the subject of Functions, we
require a nomenclature enabling us to express any two numbers by names
•which, without specifying what particular numbers they are, shall show
what function each is of the other ; or, in other words, shall put in evi-
crence their mode of formation from one another. The system of general
language called algebraical notation does this. The expressions a and
a'+Sa denote, the one any number, the other the number formed from it
in a particular manner. The expressions a, b, n, and («+&)", denote any
three numbers, and a fourth which is formed from them in a certain mode.
The following may be stated as the general problem of the algebraical
calculus : F being a certain function of a given number, to find what f uno-
REMAINING LAWS OF NATURE. 433
tion F will be of any function of that number. For example, a binomial
<i+b is a function of its two parts a and b, and the parts are, in their
turn, functions of a+b: now {a+b)' is a certain function of the binomial ;
what function will this be of a and b, the two parts? The answer to this
question is the binomial theorem. The formula (a+6)"=a*+- a"~'5+
a*~'&'+,etc., shows in what manner the number which is formed by
multiplying a+b into itself n times, might be formed without that process,
■directly from a, b, and n. And of this nature are all the theorems of the
science of number. They assert the identity of the result of different
modes of formation. They affirm that some mode of formation from x,
and some mode of formation from a certain function of x, produce the
same number.
Besides these general theorems or formulae, what remains in the algebra-
ical calculus is the resolution of equations. But the resolution of an equa-
tion is also a theorem. If the equation be x^-{-ax=b, the resolution of this
equation, viz., a;=—^a±-v/i*''+*) is a general proposition, which may be
regarded as an answer to the question, If & is a certain function of x and a
(namely x'+ax), what function is a; of 5 and a? The resolution of equa-
tions is, therefore, a mere variety of the general problem as above stated.
The problem is — Given a function, what function is it of some other func-
tion ? And in the resolution of an equation, the question is, to find what
function of one of its own functions the number itself is.
Such, as above described, is the aim and end of the calculus. As for its
processes, every one knows that they are simply deductive. In demon-
strating an algebraical theorem, or in resolving an equation, we travel from
the datum to the qucesitum by pure ratiocination ; in which the only prem-
ises introduced, besides the original hypotheses, are the fundamental ax-
ioms already mentioned — that things equal to the same thing are equal to
one another, and that the sums of equal things are equal. At each step in
the demonstration or in the calculation, we apply one or other of these
truths, or truths deducible from them, as, that the differences, products,
etc., of equal numbers are equal.
It would be inconsistent with the scale of this work, and not necessary
to its design, to carry the analysis of the truths and processes of algebra
any further ; which is also the less needful, as the task has been, to a very
great extent, performed by other writers. Peacock's Algebra, and Dr.
Whewell's Doctrine of Limits, are full of instruction on the subject. The
profound treatises of a truly philosophical mathematician, Professor De
Morgan, should be studied by every one who desires to comprehend the
evidence of mathematical truths, and the meaning of the obscurer proc-
esses of the calculus, and the speculations of M. Comte, in his Cours de
Philosophie Positive, on the philosophy of the higher branches of mathe-
matics, are among the many valuable gifts for which philosophy is indebted
to that eminent thinker.
§ 1. If the extreme generality, and remoteness not so much from sense
as from the visual and tactual imagination, of the laws of number, renders
it a somewhat difficult effort of abstraction to conceive those laws as being
in reality physical truths obtained by observation ; the same difficulty does
not exist with regard to the laws of extension. The facts of which those
28
434 INDUCTION.
laws are expressions, are of a kind peculiarly accessible to tlie senses, and
suggesting eminently distinct images to the fancy. That geometry is a
strictly physical science would doubtless have been recognized in all ages,
had it not been for the illusions produced by two circumstances. One of
these is the characteristic property, already noticed, of the facts of geom-
etry, that they may be collected from our ideas or mental pictures of ob-
jects as effectually as from the objects themselves. The other is, the de-
monstrative character of geometrical truths ; which was at one time sup-
posed to constitute a radical distinction between them and physical truths j
the latter, as resting on merely probable evidence, being deemed essentially
uncertain and unprecise. The advance of knowledge has, however, made"
it manifest that physical science, in its better understood branches, is quite-
as demonstrative as geometry. The task of deducing its details from a
few comparatively simple principles is found to be any thing but the im-
possibility it was once supposed to be ; and the notion of the superior cer-
tainty of geometry is an illusion, arising from the ancient prejudice which,,
in that science, mistakes the ideal data from which we reason, for a pecul-
iar class of realities, while the corresponding ideal data of any deductive
physical science are recognized as what they really are, hypotheses.
Every theorem in geometry is a law of external nature, and might have
been ascertained by generalizing from observation and experiment, which
in this case resolve themselves into comparison and measurement. But it
was found practicable, and, being practicable, was desirable, to -deduce these
truths by ratiocination from a small number of general laws of nature, the
certainty and universality of which are obvious to the most careless ob-
server, and which compose the first principles and ultimate premises of the
science. Among these general laws must be included the same two which
we have noticed as ultimate principles of the Science of Number also, and
which ai-e applicable to every description of quantity; viz.. The sums of
equals are equal, and Things which are equal to the same thing are equal
to one another; the latter of which may be expressed in a manner more
suggestive of the inexhaustible multitude of its consequences, by the fol-
lowing terms : Whatever is equal to any one of a number of equal magni-
tudes, is equal to any other of them. To these two must be added, in ge-
ometry, a third law of equality, namely, that lines, surfaces, or solid spaces,
which can be so applied to one another as to coincide, are equal. Some
writers have asserted that this law of nature is a mere verbal definition;
that the expression "equal magnitudes " wieaws nothing but magnitudes
which can be so applied to one another as to coincide. But in this opinion
I can not agree. The equality of two geometrical magnitudes can not dif-
fer fundamentally in its nature from the equality of two weights, two de-
grees of heat, or two portions of duration, to none of which would this
definition of equality be suitable. None of these things can be so applied
to one another as to coincide, yet we perfectly understand what we mean
when we call them equal. Things are equal in magnitude, as things are
equal in weight, when they are felt to be exactly similar in respect of the
attribute in which we compare them : and the application of the objects to
each other in the one case, like the balancing them with a pair of scales in
the other, is but a mode of bringing them into a position in which our
senses can recognize deficiencies of exact resemblance that would otherwise
escape our notice.
Along with these three general principles or axioms, the remainder of
the premises of geometry consists of the so-called definitions : that is to
KEMAINING LAWS OF NATURE. 435
say, propositions asserting the real existence of the varions objects therein
designated, together with some one property of each. In some cases more
than one property is commonly assumed, but in no case is more than one
necessary. It is assumed that there are such things in nature as straight
lines, and that any two of them setting out from the same point, diverge
more and more without limit. This assumption (which includes and goes
beyond Euclid's axiom that two straight lines can not inclose a space) is
as indispensable in geometry, and as evident, resting on as simple, familiar,
and universal observation, as any of the other axioms. It is also assumed
that straight lines divei-ge from one another in different degrees ; in other
words, that there are such things as angles, and that they are capable of
being equal or unequal. It is assumed that there is such a thing as a
circle, and that all its radii are equal ; such things as ellipses^nd that
the sums of the focal distances are equal for every point in an ellipse;
such things as parallel lines, and that those lines are everywhere equally
distant.*
§ 8. It is a matter of more than curiosity to consider, to what peculiarity
of the physical truths which are the subject of geometry, it is owing that
they can all be deduced from so small a number of original premises ; why
it is that we can set out from only one characteristic property of each kind
of phenomenon, and with that and two or three general truths relating to
equality, can travel from mark to mark until we obtain a vast body of de-
rivative truths, to all appearance extremely unlike those elementary ones, i
The explanation of this remarkable fact seems to lie in the following cir-
cumstances. In the first place, all questions of position and figure may be
resolved into questions of magnitude. The position and figure of any ob-
ject are determined by determining the position of a sufficient number of
points in it ; and the position of any point may be determined by the mag-
nitude of three rectangular co-ordinates, that is, of the perpendiculars drawn
from the point to three planes at right angles to one another, arbitrarily
selected. By this transformation of all questions of quality into questions
only of quantity, geometry is reduced to the single problem of the meas-
urement of magnitudes, that is, the ascertainment of the equalities which,
exist between them. Now when we consider that by one of the general
axioms, any equality, when ascertained, is proof of as many other equalities
as there are other things equal to either of the two equals; and that by
another of those axioms, any ascertained equality is proof of the equality
of as many pairs of magnitudes as can be formed by the numerous opera:-
* Geometers have usually preferred to define parallel lines by the property of being in the
same plane and never meeting. This, however, has rendered it necessary for them to assume,
as an additioilal axiom, some other property of parallel lines ; and the unsatisfactory manner
in which properties for that purpose have been selected by Euclid and others has always been
deemed the opprobrium of elementary geometiy. Eveq as a verbal definition, equidistance is
a fitter property to characterize parallels by, since it is the attribute really involved in the sig-
nification of the name. If to be in the same plane and never to meet were all that is meant
by being parallel, we should feel no incongruity in speaking of a curve as parallel to its
asymptote. The meaning of parallel lines is, lines which pursue exactly the same direction,
and which, therefore, neither draw nearer nor go farther from one another ; a conception
suggested at once by the contemplation of nature. That the lines will never meet is of course
included in the more comprehensive proposition that they are everywhere equally distant.
And that any straight lines which are in the same plane and not equidistant will certainly
meet, may be demonstrated in the most rigorous manner from the fundamental property of
straight lines assumed in the text, viz., that if they set out from the same point, they diverge
more and more without limit.
436 INDUCTION.
tions which resolve themselves into the addition of the equals to them-
selves or to other equals ; we cease to wonder that in proportion as a sci-
ence is conversant about equality, it should afford a more copious supply
of marks of marks ; and that the sciences of number and extension, which
are conversant with little else than equality, should be the most deductive
of all the sciences.
There are also two or three of the principal laws of space or extension
which are unusually fitted for rendering one position or magnitude a mark
of another, and thereby contributing to render the science largely daduo-
tive. First, the magnitudes of inclosed spaces, whether superficial or solid,
are completely determined by the magnitudes of the lines and angles which
bound them. Secondly, the length of any line, whether straight or curve,
is measured (certain other things being given) by the angle which it sub-
tends, and vici versa. Lastly, the angle which any two straight lines make
with each other at an inaccessible point, is measured by the angles they
severally make with any third line we choose to select. By means of these
general laws, the measurement of all lines, angles, and spaces whatsoever
might be accomplished by measuring a single straight line and a sufficient
number of angles ; which is the plan actually pursued in the trigonometrical
survey of a country ; and fortunate it is that this is practicable, the exact
measurement of long straight lines being always difficult, and often impos-
sible, but that of angles very easy. Three such generalizations as the fore-
going afford such facilities for the indirect measurement of magnitudes
(by supplying us with known lines or angles which are marks of the mag-
nitude of unknown ones, and thereby of the spaces which they inclose),
that it is easily intelligible how from a few data we can go on to Ascertain
the magnitude of an indefinite multitude of lines, angles, and spaces, which
we could not easily, or could not at all, measure by any more direct process.
§ 9. Such are the remarks which it seems necessary to make in this
place, respecting the laws of nature which are the peculiar subject of the
sciences of number and extension. The immense part which those laws
take in giving a deductive character to the other departments of physical
science, is well known ; and is not surprising, when we consider that all
causes operate according to mathematical laws. The effect is always de-
pendent on, or is a function of, the quantity of the agent ; and generally of
its position also. We can not, therefore, reason respecting causation, with-
out introducing considerations of quantity and extension at every step;
and if the nature of the phenomena admits of our obtaining numerical data
of sufficient accuracy, the laws of quantity become the grand instrument for
calculating forward to an effect, or backward to a cause. That in all other
sciences, as well as in geometry, questions of quality are scarcely ever inde-
pendent of questions of quantity, may be seen from the most familiar phe-
nomena. Even when several colors are mixed on a painter's palette, the
comparative quantity of each entirely determines the color of the mixture.
With this mere suggestion of the general causes which render mathe-
matical principles and processes so predominant in those deductive sciences
which afford precise numerical data, I must, on the present occasion, con-
tent myself; referring the reader who desires a more thorough acquaint-
ance with the subject, to the first two volumes of M. Comte's systematic
work.
In the same work, and more particularly in the third volume, are also
fully discussed the limits ofT.he applicability of mathematical principles to
REMAINING LAWS OF NATURE. 437
the improvement of other sciences. Such principles are manifestly inap-
plicable, where the causes on which any class of phenomena depend are so
imperfectly accessible to our observation, that we can not ascertain, by a
proper induction, their numerical laws ; or where the causes are so numer-
ous, and intermixed in so complex a manner with one another, that even
supposing their laws known, the computation of the aggregate effect tran-
scends the powers of the calculus as it is, or is likely to be ; or, lastly, where
the causes themselves are in a state of perpetual fluctuation ; as in physiol-
ogy, and still more, if possible, in the social science. The mathematical so-
lutions of physical questions become progressively more difiicult and im-
perfect, in proportion as the questions divest themselves of their abstract
and hypothetical character, and approach nearer to the degree of complica-
tion actually existing in nature ; insomuch that beyond the limits of astro-
nomical phenomena, and of those most nearly analogous to them, mathe-
matical accuracy is generally obtained " at the expense of the reality of the
inquiry :" while even in astronomical questions, " notwithstanding the ad-
mirable simplicity of their mathematical elements, our feeble intelligence
becomes incapable of following out effectually the logical combinations of
the laws on which the phenomena are dependent, as soon as we attempt to
take into simultaneous consideration more than two or three essential influ-
ences."* Of this, the problem of the Three Bodies has already been cited,
more than once, as a remarkable instance; the complete solution of so com-
paratively simple a question having vainly tried the skill of the most pro-
found mathematicians. We may conceive, then, how chimerical would be
the hope that mathematical principles could be advantageously applied to
phenomena dependent on the mutual action of the innumerable minute par-
ticles of bodies, as those of chemistry, and still more, of physiology; and
for similar reasons those principles remain inapplicable to the still more
complex inquiries, the subjects of which are phenomena of society and
government.
The value of mathematical instruction as a preparation for those more
difiicult investigations, consists in the applicability not of its doctrines, but
of its method. Mathematics will ever remain the most perfect type of the
Deductive Method in general; and the applications of mathematics to the
deductive branches of physics, furnish the only school in which philosophers
can effectually learn the most difficult and important portion of their art,
the employment of the laws of simpler phenomena for explaining and pre-
dicting those of the more complex. These grounds are quite suflScient for
deeming mathematical training an indispensable basis of real scientific ed-
ucation, and regarding (according to the dictum which an old but unau-
thentic tradition ascribes to Plato) one who is ayewfiiTgriTos, as wanting in
one of the most essential qualifications for the successful cultivation of the
higher branches of philosophy.
♦ PhilosopMe Positive, iii., 414:-tl6.
438 INDUCTION.
CHAPTER XXV.
OP THE GROUNDS OP DISBELIEP.
§ 1. The method of arriving at general truths, or general propositions
fit to he believed, and the nature of the evidence on which they are ground-
ed, have been discussed, as far as space and the writer's faculties permit-
ted, in the twenty-four preceding chapters. But the result of the exami-
nation of evidence is not always belief, nor even suspension of judgment;
it is sometimes disbelief. The philosophy, therefore, of induction and ex-
perimental inquiry is incomplete, unless the grounds not only of belief, but
of disbelief, are treated of ; and to this topic we shall devote one, and the
final, chapter.
By disbelief is not here to be understood the mere absence of belief.
The ground for abstaining from belief is simply the absence or insufficiency
of proof; and in considering what is sufficient evidence to support any
given conclusion, we have already, by implication, considered what evidence
is not sufficient for the same purpose. By disbelief is here meant, not the
state of mind in which we form no opinion concerning a subject, but that
in which we are fully persuaded that some opinion is not true; insomuch
that if evidence, even of great apparent strength (whether grounded on
the testimony of others or on our own supposed perceptions), were pro-
duced in favor of the opinion, we should believe that the witnesses spoke
falsely, or that they, or we ourselves if we were the direct percipients, were
mistaken.
That there are such cases, no one is likely to dispute. Assertions for
which there is abundant positive evidence are often disbelieved, on account
of what is called their improbability, or impossibility. And the question
for consideration is what, in the present case, these words mean, and how
far and in what circumstances the properties which they express are suffi-
cient grounds for disbelief.
§ 2. It is to be remarked, in the first place, that the positive evidence
produced in support of an asseition which is nevertheless rejected on the
score of impossibility or improbability, is never such as amounts to full
proof. It is always grounded on some approximate generalization. The
fact may have been asserted by a hundred witnesses ; but there are many
exceptions to the universality of the generalization that what a hundred
witnesses affirm is true. We may seem to ourselves to have actually seen
the fact ; but that we really see what we think we see, is by no means a
universal truth ; our organs may have been in a morbid state; or we may
have inferred something, and imagined that we perceived it. The evi-
dence, then, in the affirmative being never more than an approximate gen-
eralization, all will depend on what the evidence in the negative is. If that
also rests on an approximate generalization, it is a case for comparison of
probabilities. If the approximate generalizations leading to the affirmative
are, when added together, less strong, or, in other words, farther from be
ing universal, than the approximate generalizations which support the neg-
ative side of the question, the proposition is said to be improbable, and is
GROUNDS. OF DISBELIEF. 439
to be disbelieved provisionally. If, bowever, an alleged fact be in contra-
diction, not to any number of approximate generalizations, but to a com-
pleted generalization grounded on a rigorous induction, it is said to be im-
3)0ssible, and is to be disbelieved totally.
This last principle, simple and evident as it appears, is the doctrine
which, on the occasion of an attempt to apply it to the question of the cred-
ibility of miracles, excited so violent a controversy. Hume's celebrated
-doctrine, that nothing is credible which is contradictory to experience, or
at variance with laws of nature, is merely this very plain and harmless
proposition, that whatever is contradictory to a complete induction is in-
credible. That such a maxim as this should either be accounted a danger-
ous heresy, or mistaken for a gi-eat and recondite truth, speaks ill for the
state of philosophical speculation on such subjects.
But does not (it may be asked) the very statement of the proposition
imply a contradiction ? An alleged fact, according to this theory, is not to
be believed if it contradict a complete induction. But it is essential to
the completeness of an induction that it shall not contradict any known
fact. Is it not, then, a petitio principii to say, that the fact ought to be
disbelieved because the induction opposed to it is complete? How can
we have a right to declare the induction complete, while facts, supported
Taj credible evidence, present themselves in opposition to it ?
I answer, we have that right whenever the scientific canons of induction
^ive it to us ; that is, whenever the induction can be complete. We have
it, for example, in a case of causation in which there has been an experi-
mentum cruois. If an antecedent A, superadded to a set of antecedents in
all other respects unaltered, is followed by an effect B which did not exist
before, A is, in that instance at least, the cause of B, or an indispensable
part of its cause ; and if A be tried again with many totally different sets
of antecedents and B still follows, then it is the whole cause. If these ob-
servations or experiments have been repeated so often, and by so many
persons, as to exclude all supposition of error in the observer, a law of na-
ture is established ; and so long as this law is received as such, the asser-
tion that on any particular occasion A took place, and yet B did not follow,
without any counteracting cause, must be disbelieved. Such an assertion
is not to be credited on any less evidence than what would suffice to over-
turn the law. The general truths, that whatever has a beginning has a
■cause, and that when none but the same causes exist, the same effects fol-
low, rest on the strongest inductive evidence possible ; the proposition that
things affirmed by even a crowd of respectable witnesses are true, is but an
approximate generalization ; and — even if we fancy we actually saw or felt
the fact which is in contradiction to the law — what a human being can see
is no more than a set of appearances; from which the real nature of the
phenomenon is merely an inference, and in this inference approximate gen-
eralizations usually have a large share. If, therefore, we make our election
to hold by the law, no quantity of evidence whatever ought to persuade us
that there has occurred any thing in contradiction to it. If, indeed, the
evidence produced is such that it is more likely that the set of observations
and experiments on which the law rests should have been inaccurately per-
formed or incorrectly interpreted, than that the evidence in question should
be false, we may believe the evidence ; but then we must abandon the law.
And since the law was received on what seemed a complete induction, it
•«an only be rejected on evidence equivalent; namely, as being inconsistent
aiot with any number of approximate generalizations, but with some other
440 INDUCTION.
and better established law of nature. This extreme case, of a conflict be-
tween two supposed laws of natui-e, has probably never actually occurre<J
where, in the process of investigating both the laws, the true canons of
scientific induction had been kept in view ; but if it did occur, it must ter-
minate in the total rejection of one of the supposed laws. It would prove
that there must be a flaw in the logical process by which either one or the
other was established ; and if there be so, that supposed general truth i»
no truth at all. We can not admit a proposition as a law of nature, and
yet believe a fact in real contradiction to it. We must disbelieve the al-
leged fact, or believe that we were mistaken in admitting the supposed law.
But in order that any alleged fact should be contradictory to a law of
causation, the allegation must be, not simply that the cause existed with-
out being followed by the effect, for that would be no uncommon occur-
rence ; but that this happened in the absence of any adequate counteract-
ing cause. Now in the case of an alleged miracle, the assertion is the ex-
act opposite of this. It is, that the effect was defeated, not in the absence,,
but in consequence of a counteracting cause, namely, a direct interposition
of an act of the will of some being who has power over nature; and in
particular of a Being, whose will being assumed to have endowed all the
causes with the powers by which they produce their effects, may well be
supposed able to counteract them. A miracle (as was justly remarked by
Brown)* is no contradiction to the law of cause and effect; it is a new ef-
fect, supposed to be produced by the introduction of a new cause. Of the
adequacy of that cause, if present, there can be no doubt ; and the only
antecedent improbabilty which can be ascribed to the miracle, is the im-
probability that any such cause existed.
All, therefore, which Hume has made out, and this he must be consider-
ed to have made out, is, that (at least in the imperfect state of our knowl-
edge of natural agencies, which leaves it always possible that some of the
physical antecedents may have been hidden from us) no evidence can prove
a miracle to any one who did not previously believe theexistence of a be-
ing or beings with supernatural power; or who believes himself to have
full proof that the character of the Being whom he recognizes is inconsist-
ent with his having seen fit to interfere on the occasion in question.
If we do not already believe in supernatural agencies, no miracle can
prove to us their existence. The miracle itself, considered merely as an
extraordinary fact, may be satisfactorily certified by our senses or by testi-
mony ; but nothing can ever prove that it is a miracle ; there is still anoth-
er possible hypothesis, that of its being the result of some unknown nat-
ural cause; and this possibility can not be so completely shut out, as to
leave no alternative but that of admitting the existence and intervention of
a being superior to nature. Those, however, who already believe in such
a being have two hypotheses to choose from, a supernatural and an un-
known natural agency; and they have to judge which of the two is the
most probable in the particular case. In forming this judgment, an im-
portant element of the question will be the conformity of the result to the'
laws of the supposed agent, that is, to the character of the Deity as they
conceive it. But with the knowledge which we now possess of the gen-
eral uniformity of the course of nature, religion, following in the wake of
science, has been compelled to acknowledge the government of the uni-
verse as being on the whole carried on by general laws, and not by special
* See the two remarkable notes (A) and (P), appended to his Inquiry into the Relation of
Cause and Effect.
GROUNDS OF DISBELIEF. 44 j
iiiterpoBitions. To whoever holds this belief, there is a general presump-
tion against any supposition of divine agency not operating through gen-
eral laws, or, in other words, there is an antecedent improbability in every
miracle, which, in order to outweigh it, requires an extraordinary strength
of antecedent probability derived from the special circumstances of the case.
§ 3. It appears from what has been said, that the assertion that a cause
has been defeated of an effect which is connected with it by a completely
ascertained law of causation, is to be disbelieved or not, according to the
probability or improbability that there existed in the particular instance an
adequate counteracting cause. To form an estimate of this, is not more
difficult than of other probabilities. With regard to all known causes ca-
pable of counteracting the given causes, we have generally some previous
knowledge of the frequency or rarity of their occurrence, from which we
may draw an inference as to the antecedent improbability of their having
been present in any particular case. And neither in respect to known nor
unknown causes are we required to pronounce on the probability of their
existing in nature, but only of their having existed at the time and place at
which the transaction is alleged to have happened. We are seldom, there-
fore, without the means (when the circumstances of the case are at all
known to us) of judging how far it is likely that such a cause should have
existed at that time and place without manifesting its presence by some
other marks, and (in the case of an unknown cause) without having hither-
to manifested its existence in any other instance. According as this cir-
cumstance, or the falsity of the testimony, appears more improbable — that
is, conflicts with an appi'oximate generalization of a higher oi-der — we be-
lieve the testimony, or disbelieve it ; with a stronger or a weaker degree of
conviction, according to the preponderance ; at least until we have sifted
the matter further.
So much, then, for the case in which the alleged fact conflicts, or appears
to conflict, with a real law of causation. But a more common case, per-
haps, is that of its conflicting with uniformities of mere co-existence, not
proved to be dependent on causation ; in other words, with the properties
of Kinds. It is with these uniformities principally that the marvelous
stories related by travelers are apt to be at variance ; as of men with tails,
or with wings, and (until confirmed by experience) of flying fish ; or of ice,
in the celebrated anecdote of the Dutch travelers and the King of Siam.
Facts of this description, facts previously unheard of, but which could not
from any known law of causation be pronounced impossible, are what
Hume characterizes as not contrary to experience, but merelj' unconforma
ble to it; and Bentham, in his treatise on Evidence, denominates them facts
disconformable in specie, as distinguished from such as are disconformable
in toto or in degree.
In a case of this description, the fact asserted is the existence of a new
Kind ; which in itself is not in the slightest degree incredible, and only to be
rejected if the improbability that any variety of object existing at the par-
ticular place and time should not have been discovered sooner, be greater
than that of error or mendacity in the witnesses. Accordingly, such asser-
tions, when made by credible persons, and of unexplored places, are not dis-
believed, but at most regarded as requiring confirmation from subsequent
observers ; unless the alleged properties of the supposed new Kind are at
variance with known properties of some larger kind which includes it; or,
in other words, unless, in the new Kind which is assei-ted to exist, some
442 INDUCTION.
properties are said to liave been found disjoined from others which have
always been known to accompany them ; as in the case of Pliny's men, or
any other kind of animal of a structure different from that which has al-
ways been found to co-exist with animal life. On the mode of dealing with,
any such case, little needs be added to what has been said on the same top-
ic in the twenty-second chapter.* When the uniformities of co-existence
which the alleged fact would violate, are such as to raise a strong presump-
tion of their being the result of causation, the fact which conflicts witii
them is to be disbelieved ; at least provisionally, and subject to further in-
vestigation. When the presumption amounts to a virtual certainty, as in,
the case of the general structure of organized beings, the only question re-
quiring consideration is whether, in phenomena so little understood, there
may not be liabilities to counteraction from causes hitherto unknown ; or
whether the phenomena may not be capable of originating in some other
■way, which would produce a different set of derivative uniformities. Where
(as in the case of the flying fish, or the ornithorhynchus) the generalizatioQ
to which the alleged fact would be an exception is very special and of lim-
ited range, neither of the above suppositions can be deemed very improba-
ble ; and it is genei'ally, in the case of such alleged anomalies, wise to sus
pend our judgment, pending the subsequent inquiries which will not fail
to confirm the assertion if it be true. But when the generalization is very-
comprehensive, embracing a vast number and variety of observations, and.
covering a considerable province of the domain of nature ; then, for reasons^
which have been fully explained, such an empirical law comes near to the
certainty of an ascertained law of causation ; and any alleged exception to
it can not be admitted, unless on the evidence of some law of causation
proved by a still more complete induction.
Such uniformities in the course of nature as do not bear marks of be-
ing the results of causation are, as we have already seen, admissible as
universal truths with a degree of credence proportioned to their general-
ity. Those which are true of all things whatever, or at least which are
totally independent of the varieties of Kinds, namely, the laws of number
and extension, to which we may add the law of causation itself, are proba-
bly the only ones, an exception to which is absolutely and permanently in-
credible. Accordingly, it is to assertions supposed to be contradictory ta
these laws, or to some others coming near to them in generality, that the
•word impossibility (at least total impossibility) seems to be generally con-
fined. Violations of other laws, of special laws of causation, for instance,^
are said, by persons studious of accuracy in expression, to be impossible
in the circumstances of the case; or impossible unless some cause had ex-
isted which did not exist in the particular case.f Of no assertion, not in
* Supra, p. 413.
t A writer to whom I have several times referred, gives as the definition of an impossibility,
that which there exists in the world no cause adequate to produce. This definition does not
take in such impossibilities as these — that two and two should make five ; that two straight
lines should inclose a space ; or that any thing should begin to exist without a cause. I can
think of no definition of impossibility comprehensive enough to include all its varieties, ex-
cept the one which I have given : viz., An impossibility is that, the truth of which would con-
flict with a complete induction, that is, with the most conclusive evidence which we possess
of universal truth.
As to the reputed impossibilities which rest on no other grounds than our ignorance of any
cause capable of producing the supposed effects ; very few of them are certainly impossible, or
permanently incredible. The facts of traveling seventy miles an hour, painless surgical oper-
ations, and conversing by instantaneous signals between London and New York, held a highc
place, not many years ago, among such impossibilities.
GROUNDS OF DISBELIEF. 443
contradiction to some of these very general laws, will more than improb-
ability be asserted by any cautious person ; and improbability not of the
highest degree, unless the time and place in which the fact is said to have
occurred, render it almost certain that the anomaly, if real, could not have
been overlooked by other observers. Suspension of judgment is in all
other cases the resource of the judicious inquii-er ; provided the testimony
in favor of the anomaly presents, when well sifted, no suspicious circum-
stances.
But the testimony is scarcely ever found to stand that test, in cases in
which the anomaly is not real. In the instances on record in which a great
number of witnesses, of good reputation and scientific acquirements, have
testified to the truth of something which has turned out untrue, there have
almost always been circumstances which, to a keen observer who had taken
due pains to sift the matter, would have rendered the testimony untrust-
worthy. There have generally been means of accounting for the impres-
sion on the senses or minds of the alleged percipients, by fallacious appear-
ances ; or some epidemic delusion, propagated by the contagious influence
of popular feeling, has been concerned in the case ; or some strong interest
has been implicated — religious zeal, party feeling, vanity, or at least the
passion for the marvelous, in persons strongly susceptible of it. When
none of these or similar circumstances exist to account for the apparent
strength of the testimony ; and where the assertion is not in contradiction
either to those universal laws which know no counteraction or anomaly, or
to the generalizations next in comprehensiveness to them, but would only
amount, if admitted, to the existence of an unknown cause or an anomalous
Kind, in circumstances not so thoroughly explored but that it is credible
that things hitherto unknown may still come to light; a cautious person
will neither admit nor reject the testimony, but will wait for confirmation
at other times and from other unconnected sources. Such ought to have
been the conduct of the King of Siam when the Dutch travelers affirmed
to him the existence of ice. But an ignorant person is as obstinate in his
contemptuous incredulity as he is uni'easonably credulous. Any thing un-
like his own narrow experience he disbelieves, if it flatters no pi'opensity ;
any nursery tale is swallowed implicitly by him if it does.
§ 4. I shall now advert to a very serious misapprehension of the princi-
ples of the subject, which has been committed by some of the writers
against Hume's Essay on Miracles, and by Bishop Butler before them, in
their anxiety to destroy what appeared to them a formidable weapon of
assault against the Christian religion ; and the effect of which is entirely
to confound the doctrine of the Grounds of Disbelief. The mistake con-
sists in overlooking the distinction between (what may be called) improba-
bility before the fact and improbability after it ; or (since, as Mr. Venn
remarks, the distinction of past and future is not the material circumstance)
between the improbability of a mere guess being right, and the improbabil-
ity of an alleged fact being true.
Many events are altogether improbable to us, before they have happened,
or before we are informed of their happening, which are not in the least
incredible when we are informed of them, because not contrary to any,
even approximate, induction. In the cast of a perfectly fair die, the
chances are five to one against throwing ace, that is, ace will be thrown
on an average only once in six throws. But this is no reason against be-
lieving that ace was thrown on a given occasion, if any credible witness
444 INDUCTION.
asserts it ; since though ace is only thrown once in six times, some number
which is only thrown once in six times must have been thrown if the die
was thrown at all. The improbability, then, or, in other words, the unusu-
alness, of any fact, is no reason for disbelieving it, if the nature of the case
renders it certain that either that or something equally improbable, that
;is, equally unusual, did happen. Nor is this all; for even if the other five
sides of the die were all twos, or all threes, yet as ace would still, on the
average, come up once in every six throws, its coming up in a given throw
would be not in any way contradictory to experience. If we disbelieved
all facts which had the chances against them beforehand, we should believe
hardly any thing. We are told that A. B. died yesterday ; the moment
before we were so told, the chances against his having died on that day
may have been ten thousand to one ; but since he was certain to die at
some time or other, and when he died must necessarily die on some par-
ticular day, while the preponderance of chances is very great against every-
day in particular, experience affords no ground for discrediting any testi-
mony which may be produced to the event's having taken place on a given
day.
Yet it has been considered by Dr. Campbell and others, as a complete
answer to Hume's doctrine (that things are incredible which are contrary
to the uniform course of experience), that we do not disbelieve, merely
because the chances were against them, things in strict conformity to the
uniform course of experience; that we do not disbelieve an alleged fact
merely because the combination of causes on which it, depends occurs only
once in a certain number of times. It is evident that whatever is shown
by observation, or can be proved from laws of nature, to occur in a certain
proportion (however small) of the whole number of possible cases, is not
contrary to experience; though we are right in disbelieving it, if some
other supposition respecting the matter in question involves, on the whole,
a less departure from the ordinary course of events. Yet on such grounds
as this have able writers been led to the extraordinary conclusion, that
nothing supported by credible testimony ought ever to be disbelieved.
§ 5. We have considered two species of events, commonly said to be im-
probable ; one kind which are in no way extraordinary, but which, having
an immense preponderance of chances against them, are improbable until
they are affirmed, but no longer ; another kind which, being contrary to
some recognized law of nature, are incredible on any amount of testimony
except such as would be sufficient to shake our belief in the law itself.
But between these two classes of events, there is an intermediate class, con:
sisting of what are commonly termed Coincidences : in other words, those
combinations of chances which present some peculiar and unexpected reg-
ularity, assimilating them, in so far, to the results of law. As if, for exam-
ple, in a lottery of a thousand tickets, the numbers should be drawn in the
exact order of what are called the natural numbers, 1, 2, 3, etc. We have
still to consider the principles of evidence applicable to this case : whether
there is any difference between coincidences and ordinary events, in the
amount of testimony or other evidence necessary to render them credible.
It is certain that on every rational principle of expectation, a combinar
tion of this peculiar sort may be expected quite as often as any other given
series of a thousand numbers ; that with perfectly fair dice, sixes will be
thrown twice, thrice, or any number of times in succession, quite as often
in a thousand or a million throws, as any other succession of numbers fixed
GROUNDS OF DISBELIEF. 445
upon beforehand ; and that no judicious player wo'uld give greater odds
against the one series than against the other. Notwithstanding this, there
is a general disposition to regard the one as much more improbable than
the other, and as requiring much stronger evidence to make it credible.
Such is the force of this impression, that it has led some thinkers to the
conclusion, that nature has greater difficulty in producing regular combi-
nations than irregular ones ; or in other wordfe, that there is some general
tendency of things, some law, which prevents regular combinations from
occurring, or at least from occurring so often as' others. Among these
thinkers may be numbered D'Alembert; who, in an Essay oij Probabilities
to be found in the fifth volume of his Melanges, contends that regular
combinations, though equally probable according to the mathematical theo-
ry with any others, are physically less probable. He appeals to common
sense, or, in other words, to common impressions ; saying, if dice thrown
repeatedly in our presence gave sixes every time, should we not, before the
number of throws had reached ten (not to speak of thousands of millions),
be ready to affirm, with the most positive conviction, that the dice were
false?
The common and natural impression is in favor of D'Alembert : the reg-
ular series would be thought much more unlikely than an irregular. But
this common impression is, I apprehend, merely grounded on the fact, that
scarcely any body remembers to have ever seen one of these peculiar coin-
cidences : the reason of which is simply that no one's experience extends to
any thing like the number of trials, within which that or any other given
combination of events can be expected to happen. The chance of sixes on
a single throw of two dice being ^, the chance of sixes ten times in suc-
cession is 1 divided by the tenth power of 36 ; in other words, such a con-
currence is only likely to happen once in 3,656,158,440,062,976 trials, a
number which no dice-player's experience comes up to a millionth part of.
But if, instead of sixes ten times, any other given succession of ten throws
had been fixed upon, it would have been exactly as unlikely that in any
individual's experience that particular succession had ever occurred ; al-
though this does not seem equally improbable, because no one would be
likely to have remembered whether it had occurred or not, and because the
comparison is tacitly made, not between sixes ten times and any one par-
ticular series of throws, but between all regular and all irregular succes-
sions taken together.
That (as D'Alembert says) if the succession of sixes was actually thrown
before our eyes, we should ascribe it not to chance, but to unfairness in the
dice, is unquestionably true. 'But this arises from a totally different prin-
ciple. We should then be considering, not the probability of the fact in
itself, but the comparative probability with which, when it is known to
have happened, it may be referred to one or to another cause. The regu-
lar series is not at all less likely than the irregular one to be brought about
by chance, but it is much more likely than the irregular one to be pro-
duced by design; or by some general cause operating through the struc-
ture of the dice. It is the nature of casual combinations to produce a
repetition of the same event, as often and no oftener than any other series
of events. But it is the nature of general causes to reproduce, in the same
circumstances, always the same event. Common sense and science alike
dictate that, all other things being the same, we should rather attribute the
effect to a cause which if real would be very likely to produce it, than to a
cause which would be very unlikely to produce it. According to Laplace's
44G INDUCTION.
sixth theorem, which we demonstrated in a former chapter, the difference
of probability arising from the superior efficacy of the constant cause, un-
fairness in the dice, would after a very few throws far outweigh any ante-
cedent probability which there could be against its existence.
D'Alembert should have put the question in another manner. He should
have supposed that we had ourselves previously tried the dice, and knew
by ample experience that they were fair. Another person then tries them
in our absence, and assures us that he threw sixes ten times in succession.
Is the assertion credible or not ? Here the effect to be accounted for is
not the occurrence itself, but the fact of the witness's asserting it. This
may arise either from its having really happened, or fr&m some other
cause. What we have to estimate is the comparative probability of these
two suppositions.
If the witness affirmed that he had thrown any other series of numbers,
supposing him to be a person of veracity, and tolerable accuracy, and to
profess that he took particular notice, we should believe him. But the
ten sixes are exactly as likely to have been really thrown as the other se-
ries. If, therefore, this assertion is less credible than the other, the reason
must be, not that it is less likely than the other to be made truly, but that
it is more likely than the other to be made falsely.
One reason obviously presents itself why what is called a coincidence,
should be oftener asserted falsely than an ordinary combination. It ex-
cites wonder. It gratifies the love of the marvelous. The motives, there-
fore, to falsehood, one of the most frequent of which is the desire to aston-
ish, operate more strongly in favor of this kind of assertion than of the
other kind. Thus far there is evidently more reason for discrediting an
alleged coincidence, than a statement in itself not more probable, but
which if made would not be thought remarkable. There are cases, how-
erer, in which the presumption on this ground would be the other way.
There are some witnesses who, the more extraordinary an occurrence
might appear, would be the more anxious to verify it by the utmost care-
fulness of observation before they would venture to believe it, and still
more before they would assert it to others.
§ 6. Independently, however, of any peculiar chances of mendacity aris-
ing from the nature of the assertion, Laplace cotjtends, that merely on the
general ground of the fallibility of testimony, a coincidence is not credible
on the same amount of testimony on which we should be warranted in be-
lieving an ordinary combination of events. In order to do justice to his
argument, it is necessary to illustrate it by the example chosen by himself.
If, says Laplace, there were one thousand tickets in a box, and one only
has been drawn out, then if an eye-witness affirms that the number drawn
was "zg, this, though the chances were 999 in 1000 against it, is not on that
account the less credible ; its credibility is equal to the antecedent proba-
bility of the witness's veracity. But if there were in the box 999 black
balls and only one white, and the witness affirms that the white ball was
drawn, the case according to Laplace is very different : the credibility of
his assertion is but a small fraction of what it was in the former case ; the
reason of the difference being as follows :
The witnesses of whom we are speaking must, from the nature of the
case, be of a kind whose credibility falls materially short of certainty ; let
us suppose, then, the credibility of the witness in the case in question to
be -^ ; that is, let us suppose that in evei'y ten statements which the wit-
GROUNDS OF DISBELIEF. 447
ness makes, nine on an average are correct, and one incorrect. Let us
now suppose that there have taken place a suificient number of drawings
to exhaust all the possible combinations, the witness deposing in every one.
In one case out of every ten in all these drawings he will actually have
made a false announcement. But in the case of the thousand tickiets these
false announcements will have been distributed impartially over all the
numbers, and of the 999 cases in which No. 79 was not drawn, there will
. have been only one case in which it was announced. On the contrary, in
the case of the thousand balls (the announcement being always either
" black " or " white)," if white was not drawn, and there was a false an-
nouncement, that false announcement must have been white ; and since by
the supposition there was a false announcement once in every ten times,
white will have been announced falsely in one-tenth part of all the cases in
which it was not drawn, that is, in one-tenth part of 999 cases out of ev-
ery thousand. White, then, is drawn, on an average, exactly as often as
No. 79, but it is announced, without having been really drawn, 999 times
as often as No. 79 ; the announcement, therefore, requires a much greater
amount of testimony to render it credible.*
To make this argument valid it must of course be supposed, that the
announcements made by the witness are average specimens of his general
veracity and accuracy ; or, at least, that they are neither more nor less so
in the case of the black and white balls, than in the case of the thousand
tickets. This assumption, however, is not warranted. A person is far less
likely to mistake, who has only one form of error to guard against, than if
he had 999 different errors to avoid. For instance, in the example chosen,
a messenger who might make a mistake once in ten times in reporting the
number drawn in a lottery, might not err once in a thousand times if sent
simply to obseiTe whether a ball was black or white. Laplace's argument,
therefore, is faulty even as applied to his own case. Still less can that case
be received as completely representing all cases of coincidence. Laplace
has so contrived his example, that though black answers to 999 distinct
possibilities, and white only to one, the witness has nevertheless no bias
which can make him prefer black to white. The witness did not know
that there were 999 black balls in the box and only one white ; or if he
did, Laplace has taken care to make all the 999 cases so undistinguishably
alike, that there is hardly a possibility of any cause of falsehood or error
operating in favor of any of them, which would not operate in the same
manner if there were only one. Alter this supposition, and the whole ar-
gument falls to the ground. Let the balls, for instance, be numbered, and
let the white ball be No. 79. Considered in respect of their color, there
are but two things which the witness can be interested in asserting, or can
have dreamed or hallucinated, or has to choose from if he answers at ran-
dom, viz., black and white ; but considered in respect of the numbers at-
tached to them, there are a thousand ; and if his interest or error happens
to be connected with the numbers, though the only assertion he makes is
about the color, the case becomes precisely assimilated to that of the thou-
* Not, hojvever, as might at first sight appear, 999 times as much. A complete analysis of
the cases shows that (always assuming the veracity of the witness to be ^) in 10,000 draw-
ings, the drawing of No. 79 will occur nine times, and be announced incorrectly once ; the
■credibility, therefore, of the announcement of No. 79 is ^,5^ ; while the drawing of a white ball
will occur nine times, and be announced incorrectly 999 times. The credibility, therefore, of
the announcement of white is j^jg, and the ratio of the two 1008 : 10 ; the one announcement
l)eing thus only about a hundred times more credible than the other, instead of 999 times.
448 INDUCTION.
sand tickets. Or instead of the balls suppose a lottery, witb 1000 tickets
and but one prize, and that I hold No. 19, and being interested only in that,
ask the witness not what was the number drawn, but whether it was 79 or
some other. There are now only two cases, as in Laplace's example; yet
he surely would not say that if the witness answered 79, the assertion
would be in an enormous proportion less credible, than if he made the same
answer to the same question asked in the other way. If, for instance (to
put a case supposed by Laplace himself), he has staked a large sum on one
of the chances, and thinks that by announcing its occui-reuce he shall in-
crease his credit; he is equally likely to have betted on any one of the 999
numbers which are attached to black balls, and so far as the chances of
mendacity from this cause are concerned, there will be 999 times as many
chances of his announcing black falsely as white.
Or suppose a regiment of 1000 men, 999 Englishmen and one French-
man, and that of these one man has been killed, and it is not known
which. I ask the question, and the witness answers, the Frenchman. This
was not only as improbable a priori, but is in itself as singular a circum-
stance, as remarkable a coincidence, as the drawing of the white ball; yet
we should believe the statement as readily, as if the answer had been John
Thompson. Because, though the 999 Englishmen were all alike in the
point in which they difPered from the Frenchman, they were not, like the
999 black balls, undistinguishable in every other respect ; but being all dif-
ferent, they admitted as many chances of interest or error, as if each man
had been of a different nation ; and if a lie was told or a mistake made, the
misstatement was as likely to fall on any Jones or Thompson of the set, as
on the Frenchman.
The example of a coincidence selected by D'Alembert, that of sixes
thrown on a pair of dice ten times in succession, belongs, to this sort of
cases rather than to such as Laplace's. The coincidence is here far more
remarkable, because of far rarer occurrence, than the drawing of the white
ball. But though the improbability of its really occurring is greater, the
superior probability of its being announced falsely can not be establish-
ed with the same evidence. The announcement "black" represented 999
cases, but the witness may not have known this, and if he did, the 999
cases are so exactly alike, that there is really only one set of possible causes
of mendacity corresponding to the whole. The announcement " sixes not
drawn ten times," represents, and is known by the witness to represent,
a great multitude of contingencies, every one of which being unlike every
other, there may be a different and a fresh set of causes of mendacity cor-
responding to each.
It appears to me, therefore, that Laplace's doctrine is not strictly true of
any coincidences, and is wholly inapplicable to most; and that to know
whether a coincidence does or does not require more evidence to render it
credible than an ordinary event, we must refer, in every instance, to first
principles, and estimate afresh what is the probability that the given testi-
mony would have been delivered in that instance, supposing the fact which
it asserts not to be true.
With these remarks we close the discussion of the Grounds of Disbelief ;
and along with it, such exposition as space admits, and as the writer has it
in his power to furnish, of the Logic of Induction.
BOOK IV.
OF OPERATIONS SUBSIDIARY TO INDUCTION.
"Clear and distinct ideas are terms which, though familiar and frequent in men's months,
I have reason to think every one who uses does not perfectly understand. And possibly it is
but here and there one who gives himself the trouble to consider^ them so far as to know what
he himself or others precisely mean by them ; I have, therefore, in most places, chose to put
detenninate or determined, instead of clear and distinct, as more likely to direct men's thoughts
to my meaning in this matter." — Locke's Essay on the Human Understanding ; Epistle to
the Reader.
" n ne pent y avoir qu'une m^thode parfaite, qui est la mithode naturelle ; on nomme
ainsiun arrangement dans lequel les Stres du m§me genre seraient plus voisins entre eux que
ceux de tons les autres genres ; les genres du m€me ordre, plus que ceux de tous les autres
ordres ; et ainsi de suite. Cette methode est I'id^al auquel I'histoire naturelle doit tendre ;
car il est Evident que si Ton y parvenait, I'on aurait I'expression exacte et complete de la na-
ture entiSre." — Cuviek, Eigne Animal, Introduction.
"Deux grandes notions philosophiques dominent la theorie fondamentale de la methode
naturelle propreraent dite, savoir la formation des groupes naturels, et ensuite leur succession
hierarchique." — Comte, Cours de Philosophie Positive, 4:2me le9on.
CHAPTER I.
OF OBSEEVATION" AND DESCRIPTION.
§ ] , The inquiry which occupied us in the two preceding Books, has
conducted us to what appears a satisfactory solution of the principal prob-
lem of Logic, according to the conception I have formed of the science.
We have found, that the mental process with which Logic is conversant,
the operation of ascertaining truths by means of evidence, is always, even
when appearances point to a different theory of it, a process of induction.
And we have particularized the various modes of induction, and obtained
a clear view of the principles to which it must conform, in order to lead to
results which can be relied on.
The consideration of Induction, however, does not end with the direct
rules for its performance. Something must be said of those other opera-
tions of the mind, which are either necessarily presupposed in all induction,
or are instrumental to the more difBcult and complicated inductive process-
es. The present Book will be devoted to the consideration of these sub-
sidiary operations ; among which our attention must first be given to those,
which are indispensable preliminaries to all induction whatsoever.
Induction being merely the extension to a class of cases, of something
which has been observed to be true in certain individual instances of the
class; the first place among the operations subsidiary to induction, is
claimed by Observation. This is not, however, the place to lay down rules
for making good observers ; nor is it within the competence of Logic to do
so, but of the art of intellectual Education. Our business with observation
29
450 OPERATIONS SUBSIDIARY TO INDUCTION.
is only in its connection with the appropriate problem of logic, the estima-
tion of evidence. We have to consider, not how or what to observe, but
under what conditions observation is to be relied on ; what is needful, in
order that the fact, supposed to be observed, may safely be received as
true.
§ 2. The answer to this question is very simple, at least in its first as-
pect. The sole condition is, that what is supposed to have been observed
shall really have been observed ; that it be an observation, not an inference.
For in almost every act of our perceiving faculties, observation and infer-
ence are intimately blended. What we are said to observe is usually a
compound result, of which one-tenth may be observation, and the remain-
ing nine-tenths inference.
I affirm, for example, that I hear a man's voice. This would pass, in com-
mon language, for a direct perception. All, however, which is really per-
ception, is that I hear a sound. That the sound is a voice, and that voice
the voice of a man, are not perceptions but inferences. I affirm, again, that
I saw my brother at a certain hour this morning. If any proposition con-
cerning a matter of fact would commonly be said to be known by the di-
rect testimony of the senses, this surely would be so. The truth, however,
is far otherwise. I only saw a certain colored surface ; or rather I had the
tind of visual sensations which are usually produced by a colored surface ;
and from these as marks, known to be such by previous experience, I con-
cluded that I saw my brother. I might have had sensations precisely sim-
ilar, when my brother was not there. I might have seen some other per-
son so nearly resembling him in appearance, as, at the distance, and, with
the degree of attention which I bestowed, to be mistaken for him. I might
have been asleep, and have dreamed that I saw him ; or in a state of nerv-
ous disorder, which brought his image before me in a waking hallucina-
tion. In all these modes, many have been led to believe that they saw per-
sons well known to them, who were dead or far distant. If any of these
suppositions had been true, the affirmation that I saw my brother would
have been erroneous ; but whatever was matter of direct perception, name-
ly the visual sensations, would have been real. The inference only would
have been ill grounded ; I should have ascribed those sensations to a wrong
cause.
Innumerable instances might be given, and analyzed in the same manner,
of what are vulgarly called errors of sense. There are none of them prop-
erly errors of sense ; they are erroneous inferences from sense. When 1
look at a candle through a multiplying glass, I see what seems a dozen
candles instead of one ; and if the real circumstances of the case were skill-
fully disguised, I might suppose that there were really that number ; there
■would be what is called an optical deception. In the kaleidoscope there
really is that deception ; when I look through the instrument, instead of
what is actually there, namely a casual arrangement of colored fragments,
the appearance presented is that of the same combination several times re-
peated in symmetrical arrangement round a point. The delusion is of course
effected by giving me the same sensations which I should have had if such a
symmetrical combination had really been presented to me. If I cross two
of my fingers, and bring any small object, a marble for instance, into con-
tact with both, at points not usually touched simultaneously by one object,
I can hardly, if my eyes are shut, help believing that there are two marbles
instead of one. But it is not my touch in this case, nor my sight in the
OBSEEVATION AND DESCRIPTION. 451
(Other, which is deceived; the deception, whether durable or only momentary,
is in my judgment. From my senses I have only the sensations, and those
are genuine. Being accustomed to have those or similar sensations when,
and only when, a certain arrangement of outward objects is present to my
organs, I have the habit of instantly, when I experience the sensations, in-
ferring the existence of that state of outward things. This habit has be-
come so powerful, that the inference, performed with the speed and certainty
■oi an instinct, is confounded with intuitive perceptions. When it is cor-
rect, I am unconscious that it ever needed proof ; even when I know it to
be incorrect, I can not without considerable effort abstain from making it.
In order to be aware that it is not made by instinct but by an acquired hab-
it, I am obliged to reflect on the slow process through which I learned to
judge by the eye of many things which I now appear to perceive directly
by sight; and on the reverse operation performed by persons learning to
■draw, who with difticulty and labor divest themselves of their acquired
perceptions, and learn afresh to see things as they appear to the eye.
It would be easy to prolong these illustrations, were there any need to ex-
patiate on a topic so copiously exemplified in various popular works. From
the examples already given, it is seen sufficiently, that the individual facts
from which we collect our inductive generalizations are scarcely ever obtained
by observation alone. Observation extends only to the sensations by which
we recognize objects ; but the propositions which we make use of, either
in science or in common life, relate mostly to the objects themselves. In
«very act of what is called observation, there is at least one inference — from,
the sensations to the presence of the object; from the marks or diagnos-
tics, to the entire phenomenon. And hence, among other consequences, fol-
lows the seeming paradox, that a general proposition collected from par-
ticulars is often more certainly true than any one of the particular propo-
sitions from which, by an act of induction, it was inferred. For, each of
those particular (or rather singular) propositions involved an inference,
irom the impression on the senses to the fact which caused that impression ;
and this inference may have been erroneous in any one of the instances,
but can not well have been erroneous in all of them, provided their number
was sufficient to eliminate chance. The conclusion, therefore, that is, the
general proposition, may deserve more complete reliance than it would be
safe to repose in any one of the inductive premises.
The logic of observation, then, consists solely in a correct discrimination
between that, in a result of observation, which has really been perceived,
and that which is an inference from the perception. Whatever portion is
inference, is amenable to the rules of induction already treated of, and re-
quires no further notice here ; the question for us in this place is, when all
which is inference is taken away what remains ? There remains, in the first
place, the mind's own feelings or states of consciousness, namely, its outward
feelings or sensations, and its inward feelings — its thoughts, emotions, and
volitions. Whether any thing else remains, or all else is inference from
this ; whether the mind is capable of directly perceiving or apprehending
any thing except states of its own consciousness — is a problem of meta-
physics not to be discussed in this place. But after excluding all questions
on which metaphysicians differ, it remains true, that for most purposes the
■discrimination we are called upon practically to exercise is that between
sensations or other feelings, of our own or of other people, and inferences
drawn from them. And on the theory of Observation this is all which
aeems necessary to be said for the purposes of the present work.
452 OPERATIONS SUBSIDIARY TO INDUCTION.
§ 3. If, in the simplest observation, or in what passes for such, there is a
large part which is not observation but something else ; so in the simplest
description of an observation, there is, and must always be, much more as-
serted than is contained in the perception itself. We can not describe a
fact, without implying more than the fact. The perception is only of one
individual thing; but to describe it is to affirm a connection between it
and every other thing which is either denoted or connoted by any of the
terms used. To begin with an example, than which none can be conceived
more elementary: I have a sensation of sight, and I endeavor to describe
it by saying that I see something white. In saying this, I do not solely af-
firm my sensation; I also class it. I assert a resemblance between the
thing I see, and all things which I and others are accustomed to call white.
I assert that it resembles them in the circumstance in which they all
resemble one another, in that which is the ground of their being called by
the name. This is not merely one way of describing an observation, but
the only way. If I would either register my observation for my own fu-
ture use, or make it known for the benefit of others, I must assert a resem-
blance between the fact which I have observed and something else. It is
inherent in a description, to be the statement of a resemblance, or resem-
blances.
We thus see that it is impossible to express in words any result of ob-
servation, without performing an act possessing what Dr. Whewell consid-
ers to be characteristic of Induction. There is always something intro-
duced which was not included in the observation itself; some conception
common to the phenomenon with other phenomena to which it is com-
pared. An observation can not be spoken of in language at all without
declaring more than that one observation ; without assimilating it to other
phenomena already observed and classified. But this identification of aa
object — this recognition of it as possessing certain known characteristics —
has never been confounded with Induction. It is an operation which pre-
cedes all induction, and supplies it with its materials. It is a perception of
resemblances, obtained by comparison.
These resemblances are not always apprehended dii'ectly,by merely com-
paring the object observed with some other present object, or with our
recollection of an object which is absent. They are often ascertained
through intermediate marks, that is, deductively. In describing some new
kind of animal, suppose me to say that it measures ten feet in length, from
the forehead to the extremity of the tail. I did not ascertain this by the
unassisted eye. I had a two-foot rule which I applied to the object, and,
as we commonly say, measured it ; an operation which was not wholly man-
ual, but partly also mathematical, involving the two propositions, Five
times two is ten, and Things which are equal to the same thing are equal
to one another. Hence, the fact that the animal is ten feet long is not an
immediate perception, but a conclusion from reasoning ; the minor prem-
ises alone being furnished by observation of the object. Nevertheless, this
is called an observation, or a description of the animal, not an induction re-
specting it.
To pass at once from a very simple to a very complex example : I affirm
that the earth is globular. The assertion is not grounded on direct percep-
tion ; for the figure of the earth can not, by us, be directly perceived, though
the assertion would not be true unless circumstances could be supposed
under which its truth could be so perceived. That the form of the earth
is globular is inferred from certain marks, as for instance from this, that its
OBSERVATION AND DESCEIPTION. 453
•shadow thrown upon the moon is circular; or this, that on the sea, or any
■extensive plain, our horizon is always a circle ; either of which marks is in-
compatible with any other than a globular form. I assert further, that the
earth is that particular kind of a globe which is termed an oblate spheroid ;
because it is found by measurement in the direction of the meridian, that
the length on the surface of the earth which subtends a given angle at its
<jentre, diminishes as we recede from the equator and approach the poles.
But these propositions, that the earth is globular, and that it is an oblate
spheroid, assert, each of them, an individual fact; in its own nature capa-
ble of being perceived by the senses when the requisite organs and the nec-
essary position are supposed, and only not actually perceived because those
organs and that position are wanting. This identification of the earth,
;first as a globe, and next as an oblate spheroid, which, if the fact could have
been seen, would have been called a description of the figure of the earth,
may without impropriety be so called when, instead of being seen, it is in-
ferred. But we could not without impropriety call either of these asser-
tions an induction from facts respecting the earth. They are not general
propositions collected from particular facts, but particular facts deduced
irom general propositions. They are conclusions obtained deductively,
irom premises originating in induction : but of these premises some were
not obtained by observation of the earth, nor had any peculiar reference
to it.
If, then, the truth respecting the figure of the earth is not an induction,
why should the truth respecting the figure of the earth's orbit be so ? The
two cases only differ in this, that the form of the orbit was not, like the
form of the eaith itself, deduced by ratiocination from facts which were
marks of ellipticity, but was got at by boldly guessing that the path was
an elUpse, and finding afterward, on examination, that the observations were
in harmony with the hypothesis. According to Dr. Whewell, however, this
process of guessing and verifying our guesses is not only induction, but the
whole of induction : no other exposition can be given of that logical opera-
tion. That he is wrong in the latter assertion, the whole of the preceding
book has, I hope, suflBciently proved ; and that the process by which the
ellipticity of the planetary orbits was ascertained, is not induction at all,
was attempted to be shown in the second chapter of the same Book.* We
are now, however, prepared to go more into the heart of the matter than at
that earlier period of our inquiry, and to show, not merely what the opera-
tion in question is not, but what it is.
§ 4. "We observed, in the second chapter, that the proposition " the earth
moves in an ellipse," so far as it only serves for the colligation or connect-
ing together of actual observations (that is, as it only aflBrms that the ob-
served positions of the earth may be correctly represented by as many
points in the circumference of an imaginary ellipse), is not an induction,
but a description : it is an induction, only when it affirms that the interme-
diate positions, of which there has been no direct observation, would be
found to correspond to the remaining points of the same elliptic circumfer-
ence. Now, though this real induction is one thing, and the description
another, we are in a very different condition for making the induction be-
fore we have obtained the description, and after it. For inasmuch as the
description, like all other descriptions, contains the assertion of a resem-
* Supra, boot iii., chap, ii., § 3, 4, 5.
454 OPERATIONS SUBSIDIARY TO INDUCTION.
blance between the pbenomenon described and something else; in pointing
out something which the series'of observed places of a planet resembles, it
points out something in which the several places themselves agree. If the
series of places correspond t(i as many points of an ellipse, the places them-
selves agree in being situated in that ellipse. We have, therefore, by the-
same process which gave us the description, obtained the requisites for an
induction by the Method of Agreement. The successive observed places^
of the earth being considered as effects, and its motion as the cause which
produces them, we find that those effects, that is, those places, agree in the
circumstance of being in an ellipse. We conclude that the remaining ef-
fects, the places which have not been observed, agree in the same circum-
stance, and that the law of the motion of the earth is motion in an ellipse.
The Colligation of Facts, therefore, by means of hypotheses, or, as Dr.
Whewell prefers to say, by means of Conceptions, instead of being, as he
supposes, Induction itself, takes its proper place among operations subsidr
iary to Induction. All Induction supposes that we have previously com-
pared the requisite number of individual instances, and ascertained in what
circumstances they agree. The Colligation of Facts is no other than this
preliminary operation. When Kepler, after vainly endeavoring to connect
the observed places of a planet by various hypotheses of circular motion,
at last tried the hypotheses of an ellipse and found it answer to the phe-
nomena; what he really attempted, first unsuccessfully and at last success-
fully, was to discover the circumstance in which all the observed positions,
of the planet agreed. And when he in like manner connected another set
of observed facts, the periodic times of the different planets, by the propo-
sition that the squares of the times are proportional to the cubes of the
distances, what he did was simply to ascertain the property in which the
periodic times of all the different planets agreed.
Since, therefore, all that is true and to the purpose in Dr. Whewell's
doctrine of Conceptions might be fully expressed by the more familiar
term Hypothesis ; and since his Colligation of Facts by means of appro-
priate Conceptions, is but the ordinary process of finding by a comparison
of phenomena, in what consists their agreement or resemblance ; I would
willingly have confined myself to those better understood expressions, and
persevered to the end in the same abstinence which I have hitherto ob-
served from ideological discussions; considering the mechanism of our
thoughts to be a topic distinct from and irrelevant to the principles and
rules by which the trustworthiness of the results of thinking is to be esti-
mated. Since, however, a work of such high preten.sions, and, it must also
be said, of so much real merit, has rested the whole theory of Induction
upon such ideological considerations, it seems necessary for others who
follow to claim for themselves and their doctrines whatever position may
properly belong to them on the same metaphysical ground. And this is'
the object of the succeeding chapter.
ABSTRACTION. 455
CHAPTER II.
OF ABSTRACTION, OK THE FORMATION OF CONCEPTIONS.
§1. The metaphysical inquiry into the nature and composition of what
have been called Abstract Ideas, oi-, in other words, of the notions which
answer in the mind to classes and to general names, belongs not to Logic,,
but to a different science, and our purpose does not require that we should
enter upon it hei'e. We are only concerned with the universally acknowl-
edged fact, that such notions or conceptions do exist. The mind can con-
ceive a multitude of individual things as one assemblage or class ; and gen-
eral names do really suggest to us certain ideas or mental representations,
otherwise we could not use the names with consciousness of a meaning.
Whether the idea called up by a general name is composed of the various
circumstances in which all the individuals denoted by the name agree, and
of no others (which is the doctrine of Locke, Brown, and the Conceptual-
ists) ; or whether it be the idea of some one of those individuals, clothed in
its individualizing peculiarities, but with the accompanying knowledge that
those peculiarities are not properties of the class (which is the doctrine of
Berkeley, Mr. Bailey,* and the modern Nominalists) ; or whether (as held by
Mr. James Mill) the idea of the class is that of a miscellaneous assemblage
of individuals belonging to the class; or whether, finally, it be any one or
any other of all these, according to the accidental circumstances of the
case; certain it is, that some idea or mental conception is suggested by a.
general name, whenever we either hear it or employ it with consciousness-
of a meaning. And this, which we may call, if we please, a general idea,,
represents in our minds the whole class of things to which the name is
applied. Whenever we think or reason concerning the class, we do so by
means of this idea. And the voluntary power which the mind has, of at-
tending to one part of what is present to it at any moment, and neglecting
another part, enables us to keep our reasonings and conclusions respecting
the class unaffected by any thing in the idea or mental image which is not
really, or at least which we do not really believe to be common, to the
whole class.f
There are, then, such things as general conceptions, or conceptions by
means of which we can think generally ; and when we form a set of phe-
nomena into a class, that is, when we compare them with one another to
ascertain in what they agree, some general conception is implied in this-
* Mr. Bailey has given the best statement of this theory. "The general name," he says,,
"raises up the image sometimes of one individual of the class formerly seen, sometimes of
another, not unfrequently of many individuals in succession ; and it sometimes suggests an
image made up of elements from several different objects, by a latent process of which I am
not conscious." (Letters on the Philosophy of the Human Mind, 1st series, letter 22.) But
Mr. Bailey must allow that we carry on inductions and ratiocinations respecting the class, by
means of this idea or conception of some one individual in it. This is all I require. The
name of a class calls up some idea, through which we can, to all intents and pui-poses, think
of the class as such, and not solely o( an individual member of it.
1 1 have entered rather fully into this question in chap. xvii. of An Examination of Sir
WVliam Hamilton's Philosophy, headed "The Doctrine of Concepts or General Notions,"
which contains my last views on the subject
456 OPERATIONS SUBSIDIARY TO INDUCTION-
mental operation. And inasmuch as such a comparison is a necessary prfr
liminary to Induction, it is most true that Induction could not go on with-
out general conceptions.
§ 2. But it does not therefore follow that these general conceptions must
have existed in the mind previously to the comparison. It is not a law of
our intellect, that in comparing things with each other and taking note
of their agreement we merely recognize as realized in the outward world
something that we already had in dur minds. The conception originally
found its way to us as the result of such a comparison. It was obtained
(in metaphysical phrase) by abstraction from individual things. These
things may be things which we perceived or thought of on former occa-
sions, but they may also be the things which we are perceiving or thinking
of on the very occasion. When Kepler compared the observed places of
the planet Mars, and found that they agreed in being points of an elliptic
circumference, he applied a general conception which was already in his
mind, having been derived from his former experience. But this is by no
means universally the case. When we compare several objects and find
them to agree in being white, or when we compare the various species of
ruminating animals and find them to agree in being cloven-footed, we have
just as much a general conception in our minds as Kepler had in his: we
have the conception of " a white thing," or the conception of " a cloven-
footed animal." But no one supposes that we necessarily bring these con-
ceptions with us, and superinduce them (to adopt Dr.Whewell's expres-
sion) upon the facts : because in these simple cases every body sees that
the very act of comparison which ends in our connecting the facts by
means of the conception, may be the source from which we derive the con-
ception itself. If we had never seen any white object or had never seen
any cloven-footed animal before, we should at the same time and by the
same mental act acquire the idea, and employ it for the colligation of the
observed phenomena. Kepler, on the contrary, really had to bring the
idea with him, and superinduce it upon the facts ; he could not evolve it
out of them : if he had not already had the idea, he would not have been
able to acquire it by a comparison of the planet's positions. But this in-
ability was a mere accident; the idea of an ellipse could have been ac-
quired from the paths of the planets as effectually as from any thing else,
if the paths had not happened to be invisible. If the planet had left a
visible track, and we had been so placed that we could see it at the proper
angle, we might have abstracted our original idea of an ellipse from the
planetary orbit. Indeed, every conception which can be made the instru-
ment for connecting a set of facts, might have been originally evolved from
those very facts. The conception is a conception of something; and that
which it is a conception of, is really in the facts, and might, under some
supposable circumstances, or by some supposable extension of the faculties
which we actually possess, have been detected in them. And not only is
this always in itself possible, but it actually happens in almost all cases in
which the obtaining of the right conception is a matter of any considera-
ble difficulty. For if there be no new conception required ; if one of those
already familiar to mankind will serve the purpose, the accident of being
the first to whom the right. one occurs, may happen to almost any body;
at least in the case of a set of phenomena which the whole scientific world
are engaged in attempting to connect. The honor, in Kepler's case, was
that of the accurate, patient, and toilsome calculations by which he com-
ABSTBACTION. 45 >
pared the results that followed from his different guesses, with the obser«
vations of Tycho Brahe; but the merit was very small of guessing an
ellipse ; the only wonder is that men had not guessed it before, nor could
they have failed to do so if there had not existed an obstinate a priori
prejudice that the heavenly bodies must move, if not in a circle, in some
combination of circles.
The really difficult cases are those in which the conception destined to
create light and order out of darkness and confusion has to be sought for
among the very phenomena which it afterward serves to arrange. Why,,
according to Dr. Whewell himself, did the ancients fail in discovering the
laws of mechanics, that is, of equilibrium and of the communication of mo-
tion ? Because they had not, or at least had not clearly, the ideas or con-
ceptions of pressure and resistance, momentum, and uniform and accelera^
ting force. And whence could they have obtained these ideas except from
the very facts of equilibrium and motion ? The tardy development of sev-
eral of the physical sciences, for example, of optics, electricity, magnetism,,
and the higher generalizations of chemistry, he ascribes to the fact that
mankind had not yet possessed themselves of the Idea of Polarity, that is,,
the idea of opposite properties in opposite directions. But what was there
to suggest such an idea, until, by a separate examination of several of these
different branches of knowledge, it was shown that the facts of each of them
did present, in some instances at least, the curious phenomenon of oppositfr
properties in opposite directions? The thing was superficially manifest
only in two cases, those of the magnet and of electrified bodies ; and there
the conception was encumbered with the circumstance of material poles^
or fixed points in the body itself, in which points this opposition of proper-
ties seemed to be inherent. The first comparison and abstraction had led
only to this conception of poles ; and if any thing corresponding to that con-
ception had existed in the phenomena of chemistry or optics, the difficulty
now justly considered so great, would have been extremely small. The ob-
scurity arose from the fact, that the polarities in chemistry and optics were
distinct species, though of the same genus, with the polarities in electricity
and magnetism ; and that in order to assimilate the phenomena to one anoth-
er, it was necessary to compare a polarity without poles, such for instance as
is exemplified in the polarization of light, and the polarity with (apparent)
poles, which we see in the magnet ; and to recognize that these polarities,,
while different in many other respects, agree in the one character which is.
expressed by the phrase, opposite properties in opposite directions. From
the result of such a comparison it was that the minds of scientific men
formed this new general conception ; between which^ and the first confused
feeling of an analogy between some of the phenomena of light and those of
electricity and magnetism, there is a long interval, filled up by the labors,
and more or less sagacious suggestions of many superior minds.
The conceptions, then, which we employ for the colligation and methodi-
zation of facts, do not develop themselves from within, but are impressed
upon the mind from without ; they are never obtained otherwise than by
way of comparison and abstraction, and, in the most important and the-
most numerous cases, are evolved by abstraction from the very phenomena
which it is their office to colligate. I am far, however, from wishing to im-
ply that it is not often a very difficult thing to perform this process of ab-
straction well, or that the success of an inductive operation does not, in many
cases, principally depend on the skill with which we perform it. Bacon
was quite justified in designating as one of the principal obstacles to good
458 OPERATIONS SUBSIDIARY TO INDUCTION.
induction, general conceptions wrongly formed, " notiones temerfe h rebus
•abstractae ;" to which Dr. Whewell adds, that not only does bad abstraction
make bad induction, but that, in order to perform induction well, we must
have abstracted well ; our general conceptions must be " clear " and " ap-
propriate " to the matter in hand.
§ 3. In attempting to show what the difficulty in this matter really is,
■and how it is surmounted, I must beg the reader, once for all, to bear this
in mind ; that although, in discussing the opinions of a different school of
3)hiIosophy, I am willing to adopt their language, and to speak, therefore,
of connecting facts through the instrumentality oiE a conception, this tech-
nical phraseology means neither more nor less than what is commonly call-
ed comparing the facts with one another and determining in what they
agree. Nor has the technical expression even the advantage of being met-
aphysically correct. The facts are not connected, except in a merely met-
aphorical acceptation of the term. The ideas of the facts may become
-connected, that is, we may be led to think of them together; but this oon-
fiequence is no more than what maybe produced by any casual association.
What really takes place, is, I conceive, more philosophically expressed by
the common word Comparison, than by the phrases "to connect" or "to
■superinduce." For, as the general conception is itself obtained by a com-
parison of particular phenomena, so, when obtained, the mode in which we
apply it to other phenomena is again by comparison. We compare phe-
nomena with each other to get the conception, and we then compare those
and other phenomena with the conception. We get the conception of an
animal (for instance) by comparing different animals, and when we after-
ward see a creature resembling an animal, we compare it with our general
•conception of an animal ; and if it agrees with that general conception, we
include it in the class. The conception becomes the type of comparison.
And we need only consider what comparison is, to see that where the
•objects are more than two, and still more when they are an indefinite num-
ber, a type of some sort is an indispensable condition of the comparison.
When we have to arrange and classify a great number of objects according
to their agreements and differences, we do not make a confused attempt to
•compare all with all. We know that two things are as much as the mind
can easily attend to at a time, and we therefore fix upon one of the objects,
either at hazard or because it offers in a peculiarly striking manner some
important character, and, taking this as our standard, compare it with one
■object after another. If we find a second object which presents a remark-
able agreement with the first, inducing us to class them together, the ques-
tion instantly arises, in what particular circumstances do they agree ? and
to take notice of these circumstances is already a fii'st stage of abstraction,
giving rise to a general conception. Having advanced thus far, when we
now take in hand a third object we naturally ask ourselves the question,
not merely whether this third object agrees with the first, but whether it
agrees with it in the same circumstances in which the second did? in other
words, whether it agrees with the general conception which has been ob-
tained by abstraction from the first and second ? Thus we see the tenden-
cy of general conceptions, as soon as formed, to substitute themselves as
types, for whatever individual objects previously answered that purpose in
■our comparisons. We may, perhaps, find that no considerable number of
■other objects agree with this first general conception ; and that we must
•drop the conception, and beginning again with a different individual case,
ABSTRACTION. , 459
proceed by fresh comparisons to a different general conception. Some-
times, again, we find that the same conception will serve, by merely leaving
out some of its circumstances ; and by this higher effort of abstraction, we
obtain a still more general conception ; as in the case formerly referred to,
the scientific world rose from the conception of poles to the general concep-
tion of opposite properties in opposite directions ; or as those South-Sea
islanders, whose conception of a quadruped had been abstracted from hogs
(the only animals of that description which they had seen), when they after-
ward compared that conception with other quadrupeds, dropped some of
the circumstances, and arrived at the more general conception which Eu-
ropeans associate with the term.
These brief remarks contain, I believe, all that is well grounded in the
■doctrine, that the conception by which the mind arranges and gives unity
to phenomena must be furnished by the mind itself, and that we find the
right conception by a tentative process, trying first one and then another
until we hit the mark. The conception is not furnished by the mind until
it has been furnished to the mind ; and the facts which supply it are some-
times extraneous facts, but more often the very facts which we are attempt-
ing to arrange by it. It is quite true, howevei', that in endeavoring to
arrange the facts, at whatever point we begin, we never advance three
steps without forming a general conception, more- or less distinct and pre-
cise; and that this general conception becomes the clue which we instant-
ly endeavor to trace through the rest of the facts, or rather, becomes the
standard with which we thenceforth compare them. If we are not satis-
fied with the agreements which we discover among the phenomena by com-
paring them with this type, or with some still more general conception
which by an additional stage of abstraction we can form from the type;
we change our path, and look out for other agreements; we recommence
the comparison from a different starting-point, and so generate a different
set of general conceptions. This is the tentative process which Dr. Whe-
well speaks of ; and which has not unnaturally suggested the theory, that
the conception is supplied by the mind itself ; since the different concep-
tions which the mind successively tries, it either already possessed from
its previous experience, or they were supplied to it in the first stage of the
corresponding act of comparison ; so that, in the subsequent part of the
process, the conception manifested itself as something compared with the
phenomena, not evolved from them.
§ 4. If this be a correct account of the instrumentality of general con-
ceptions in the comparison which necessarily precedes Induction, we are
now able to translate into our own language what Dr. Whewell means by
saying that conceptions, to be subservient to Induction, must be " clear "
and " appropriate."
If the conception corresponds to a real agreement among the phenome-
na; if the comparison which we have made of a set of objects has led us to
■class them according to real resemblances and differences ; the conception
which does this can not fail to be appropriate, for some purpose or other.
The question of appropriateness is relative to the particular object we
have in view. As soon as, by our comparison, we have ascertained some
agreement, something which can be predicated in common of a number of
objects ; we have obtained a basis on which an inductive process is capa-
ble of being founded. But the agreements, or the ulterior consequences
to which those agreements lead, may be of very different degrees of impor-
460 OPERATIONS SUBSIDIAEY TO INDUCTION.
tance. If, for instance, we only compare animals according to their color,
and class those together which are colored alike, we form the general con-
ceptions of a white animal, a black animal, etc., which are conceptions le-
gitimately formed ; and if an induction were to be attempted concerning
the causes of the colors of animals, this comparison would be the proper
and necessary preparation for such an induction, but would not help us to-
ward a knowledge of the laws of any other of the properties of animals ;
while if, with Cuvier, we compare and class them according to the struc-
ture of the skeleton, or, with Blainville, according to the nature of their
outward integuments, the agreements and differences which are observable
in these respects ai-e not only of much greater importance in themselves,
but are marks of agreements and differences in many other important par-
ticulars of the structure and mode of life of the animals. If, therefore, the-
study of their structure and habits be our object, the conceptions gener-
ated by these last comparisons are far more " appropriate " than those gen-
erated by the former. Nothing, other than this, can be meant by the ap-
propriateness of a conception.
When Dr. Whewell says that the ancients, or the school-men, or any
modern inquirers, missed discovering the real law of a phenomenon because
they applied to it an inappropriate instead of an appropriate conception j
he can only mean that in comparing various instances of the phenomenoUj
to ascertain in what those instances agreed, they missed the important
points of agreement; and fastened upon such as were either imaginary,,
and not agreements at all, or, if real agreements, were comparatively tri-
fling, and had no connection with the phenomenon, the law of which was
sought.
Aristotle, philosophizing on the subject of motion, remarked that certain
motions apparently take place spontaneously; bodies fall to the ground,,
flame ascends, bubbles of air rise in water, etc. ; and these he called nat-
ural motions ; while others not only never take place without external in-
citement, but even when such incitement is applied, tend spontaneously to
cease ; which, to distinguish them from the former, he called violent mo-
tions. Now, in comparing the so-called natural motions with one another,
it appeared to Aristotle that they agreed in one circumstance, namely, that
the body which moved (or seemed to move) spontaneously, was moving
toward its own place; meaning thereby the place from whence it originally
came, or the place where a great quantity of matter similar to itself was
assembled. In the other class of motions, as when bodies are thrown up in
the air, they are, on the contrary, moving from their own place. Now,
this conception of a body moving toward its own place may justly be con-
sidered inappropriate ; because, though it expresses a circumstance really
found in some of the most familiar instances of motion apparently spon-
taneous, yet, first, there are many other cases of such motion, in which that
circumstance is absent; the motion, for instance, of the earth and planets.
Secondly, even when it is present, the motion, on closer examination, would
often be seen not to be spontaneous ; as, when air rises iu water, it does
not rise by its own nature, but is pushed up by the superior weight of the
water which presses upon it. Finally, there are many cases in which the
spontaneous motion takes place in the contrary direction to what the theory
considers as the body's own place ; for instance, when a fog rises from a
lake, or when water dries up. The agreement, therefore, which Aristotle
selected as his principle of classification, did not extend to all cases of the
phenomenon he wanted to study, spontaneous motion ; while it did include
ABSTRACTION. 461
cases of the absence of the phenomenon, cases of motion not spontaneoua
The conception was hence " inappropriate." We may add that, in the case
in question, no conception would be appropriate ; there is no agreement
which runs through all the ca^s of spontaneous or apparently spontaneous
motion and no others ; they can not be brought under one law ; it is a case
of Plurality of Causes.*
§ 5. So much for the first of Dr. Whewell's conditions, that conceptions
must be appropriate. The second is, that they shall be " clear :" and let us
oonsider what this implies. Unless the conception corresponds to a real
agreement, it has a worse defect than that of not being clear : it is not ap-
plicable to the case at all. Among the phenomena, therefore, which we are
attempting to connect by means of the conception, we must suppose that
there really is an agreement, and that the conception is a conception of
that agreement. In order, then, that it may be clear, the only requisite is,
that we shall know exactly in what the agreement consists ; that it shall
have been carefully observed, and accurately remembered. We are said
not to have a clear conception of the resemblance among a set of objects,
when we have only a general feeling that they resemble, without having
analyzed their resemblance, or perceived in what points it consists, and
fixed in our memory an exact recollection of those points. This want of
■clearness, or, as it may be otherwise called, this vagueness in the general
conception, may be owing either to our having no accurate knowledge of
the objects themselves, or merely to our not having carefully compared
them. Thus a person may have no clear idea of a ship because he has
never seen one, or because he remembers but little, and that faintly, of
what he has seen. Or he may have a perfect knowledge and remembrance
of many ships of various kinds, frigates among the rest, but he may have
no clear but only a confused idea of a frigate, because he has never been
told, and has not compared them suflSciently to have remarked and remem-
bered, in what particular points a frigate differs from some other kind of
ship.
It is not, however, necessary, in order to have clear ideas, that we should
know all the common properties of the things which we class together.
That would be to have our conception of the class complete as well as
clear. It is sufficient if we never class things together without knowing
exactly why we do so — without having ascertained exactly what agree-
ments we are about to include in our conception ; and if, after having thus
fixed our conception, we never vary from it, never include in the class any
* Other examples of inappropriate conceptions are given by Dr. Whewell (Phil. Ind. Sc.
ii., 185) as follows: "Aristotle and his followers endeavored in vain to account for the me-
chanical relation of forces in the lever, by applying the inappropriate geometrical concep-
tions of the properties of the circle : they failed in explaining the/orm of the luminous spot
made by the sun shining through a hole, because they applied the inappropriate conception
of a circular quality in the sun's light : they speculated to no pui-pose about the elementary
composition of bodies, because they assumed the inappropriate conception of likeness between
the elements and the compound, instead of the genuine notion of elements merely determining
the qualities of the compound." But in these cases there is more than an inappropriate con-
ception ; there is a false conception ; one which has no prototype in nature, nothing corre-
sponding to it in facts. This is evident in the last two examples, and is equally true in the
first ; the "properties of the circle" which were referred to, being purely fantastical. There
is, therefore, an error beyond the wrong choice of a principle of generalization ; there is a.
false assumption of matters of fact. The attempt is made to resolve certain laws of nature
into a more general law, that law not being one which, though real, is inappropriate, but one
wholly imaginaiy.
462 OPERATIONS SUBSIDIARY TO INDUCTION.
thing which has not those common properties, nor exclude from it anj
thing which has. A clear conception means a determinate conception;
one which does not fluctuate, which is not one thing to-day and another
to-morrow, but remains fixed and invariable, except when, from the prog-
ress of our knowledge, or the correction of some error, we consciously add
to it or alter it. A person of clear ideas is a person who always knows in
virtue of what properties his classes are constituted ; what attributes are
connoted by his general names.
The principal requisites, therefore, of clear conceptions, are habits of at-
tentive observation, an extensive experience, and a memory which receives
and retains an exact image of what is observed. And in proportion as
any one has the habit of observing minutely and comparing carefully a
particular class of phenomena, and an accurate memory for the results of
the observation and comparison, so will his conceptions of that class of
phenomena be clear ; provided he has the indispensable habit (naturally,
however, resulting from those other endowments), of never using general
names without a precise connotation.
As the clearness of our conceptions chiefly depends on the carefulness
and accuracy of our observing and comparing faculties, so their appropri-
ateness, or rather the chance we have of hitting upon the appropriate con-
ception in any case, mainly depends on the activity of the same faculties.
He who by habit, grounded on sufficient natural aptitude, has acquired a
readiness in accurately observing and comparing phenomena, will perceive
so many more agreements, and will perceive them so much more rapidly
than other people, that the chances are much greater of his perceiving, in
any instance, the agreement on which the important consequences depend.
§ 6. It is of so much importance that the part of the process of investi-
gating truth, discussed in this chapter, should be rightly understood, that
I think it is desirable to restate the results we have arrived at, in a some-
what different mode of expression.
We can not ascertain general truths, that is, truths applicable to classes,
unless we have formed the classes in such a manner that general truths
can be affirmed of them. In the formation of any class, there is involved
a conception of it as a class, that is, a conception of certain circumstances
as being those which characterize the class, and distinguish the objects
composing it from all other things. When we know exactly what these
circumstances are, we have a clear idea (or conception) of the class, and of
the meaning of the general name which designates it. The primary condi-
tion implied in having this clear idea, is that the class be really a class;
that it correspond to a real distinction ; that the things it includes really
do agree with one another in certain particulars, and differ, in those same
particulars, from all other things. A person without clear ideas is one
who habitually classes together, under the same general names, things
which have no common properties, or none which are not possessed also
by other things ; or who, if the usage of other people prevents him from
actually misclassing things, is unable to state to himself the common prop-
erties in virtue of which he classes them rightly.
But is it not the sole requisite of classification that the classes should be
real classes, framed by a legitimate mental process ? Some modes of class-
ing things are more valuable than others for human uses, whether of spec-
ulation or of practice ; and our classifications are not well made, unless the
things which they bring together not only agree with each other in some-
ABSTRACTION. 46a
thing which distinguishes them from all other things, but agree with each
other and differ from other things in the very circumstances which are of
primary importance for the purpose (theoretical or practical) which we
have in view, and which constitutes the problem before us. In other
words, our conceptions, though they may be clear, are not appropriate for
our purpose, unless the properties we comprise in them are those which
will help us toward what we wish to understand — i. e., either those which go
deepest into the nature of the things, if our object be to understand that,
or those which are most closely connected with the particular property
which we are endeavoring to investigate.
We can not, therefore, frame good general conceptions beforehand.
That the conception we have obtained is the one we want, can only be
known when we have done the work for the sake of which we wanted it ;
when we completely understand the general character of the phenomena,
or the conditions of the particular property with which we concern our-
selves. General concep'tions formed without this thorough knowledge, are
Bacon's "notiones temerfe k rebus abstractae." Yet such premature con-
ceptions we must be continually making up, in our progress to something
better. They are an impediment to the progress of knowledge, only when
they are permanently acquiesced in. When it has become our habit to
group things in wrong classes — in groups which either are not really class-
es, having no distinctive points of agreement (absence of clear ideas), or
which are not classes of which any thing important to our purpose can be
predicated (absence of appropriate ideas) ; and when, in the belief that
these badly made classes are those sanctioned by nature, we refuse to ex-
change them for others, and can not or will not make up our general con-
ceptions from any other elements ; in that case all the evils which Bacon
ascribes to his " notiones temerfe abstractse " really occur. This was what
the ancients did in physics, and what the world in general does in morals
and politics to the present day.
It would thus, in my view of the matter, be an inaccurate mode of ex-
pression to say, that obtaining appropriate conceptions is a condition pre-
cedent to generalization. Throughout the whole process of comparing
phenomena with one another for the purpose of generalization, the mind is
trying to make up a conception ; but the conception which it is trying to
make up is that of the really important point of agreement in the phenom-
ena. As we obtain more knowledge of the phenomena themselves, and of
the conditions on which their important properties depend, our views on
this subject naturally alter; and thus we advance from a less to a more
" appropriate " general conception, in the. progress of our investigations.
We ought not, at the same time, to forget that the really important
agreement can not always be discovered by mere comparison of the very
phenomena in question, without the aid of a conception acquired elsewhere ;
as in the case, so often referred to, of the planetary orbits.
The search for the agreement of a set of phenomena is in truth very
similar to the search for a lost or hidden object. At first we place our-
selves in a sufficiently commanding position, and cast our eyes round us,
and if we can see the object it is well ; if not, we ask ourselves mentally
what are the places in which it may be hid, in order that we may there
search for it : and so on, until we imagine the place where it really is. And
here too we require to have had a previous conception, or knowledge, of
those different places. As in this familiar process, so in the philosophical
operation which it illustrates, we first endeavor to find the lost object or
464 OPERATIONS SUBSIDIARY TO INDUCTION.
recognize the common attribute, without coirjecturally invoking the aid of
any previously acquired conception, or, in other words, of any hypothesis.
Having failed in this, we call upon our imagination for some hypothesis of
a possible place, or a possible point of resemblance, and then look to see
whether the facts agree with the conjecture.
For such cases something more is required than a mind accustomed to
accurate observation and comparison. It must be a mind stored with gen-
eral conceptions, previously acquired, of the sorts which bear affinity to the
subject of the particular inquiry. And much will also depend on the nat-
ural strength and acquired culture of what has been termed the scientific
imagination; on the faculty possessed of mentally arranging known ele-
ments into new combinations, such as have not yet been observed in nar
ture, though not contradictory to any known laws.
But the variety of intellectual habits, the purposes which they serve, and
the modes in which they may be fostered and cultivated, are considerations
belonging to the Art of Education : a subject far wider than Logic, and
-which this treatise does not profess to discuss. Here, therefore, the pres-
ent chapter may properly close.
CHAPTER m.
OF NAMING, AS SUBSIDIABT TO nSTDtTCTION,
§ 1. It does not belong to the present undertaking to dwell on the im-
portance of language as a medium of human intercourse, whether for pur-
poses of sympathy or of information. Nor does our design admit of more
than a passing allusion to that great property of names, on which their func-
tions as an intellectual instrument are, in reality, ultimately dependent;
their potency as a means of forming, and of riveting, associations among
our other ideas ; a subject on which an able thinker* has thus written:
" Names are impressions of sense, and as such take the strongest hold on
the mind, and of all other impressions can be most easily recalled and re-
tained in view. They therefore serve to give a point of attachment to all
the more volatile objects of thought and feeling. Impressions that when
passed might be dissipated forever, are, by their connection with language,
always within reach. Thoughts, of themselves, are perpetually slipping out
of the field of immediate mental visic^IT'^buirihe nameabiiJes with us, and
the utterance of it restores theni,in a moment. Words are the custodiers
of every product of mind less impressive than themselves. All extensions
of human knowledge, all new generalizations, are fixed and spread, even un-
intentionally, by the use of words. The child growing up learns, along
with the vocables of his mother-tongue, that things which he would have
believed to be different are, in important points, the same. Without any
formal instruction, the language in which we grow up teaches us all the
common philosophy of the age. It directs us to observe and know things
which we should have overlooked ; it supplies us with classifications ready
made, by which things are arranged (as far as the light of by-gone genera-
tions admits) with the objects to which they bear the greatest total resem-
blance. The number of general names in a language, and the degree of
* Professor Bain.
NAMING. 465 ,
generality of those names, afford a test of the knowledge of the era, and of
the intellectual insight which is the birthright of any one born into it."
It is not, however, of the functions of Names, considered generally, that
we have here to treat, but only of the manner and degree in which they are
directly instrumental to the investigation of truth ; in other words, to the
process" of induction.
§ 2. Observation and Abstraction, the operations which formed the sub-
ject of the two foregoing chapters, are conditions indispensable to induc-
tion ; there can be no induction where they are not. It has been imagined
that Naming is also a condition equally indispensable. There are thinkers
who have held that language is not solely, according to a phrase generally
current, an instrument of thought, but the instrument ; that names, or some-
thing equivalent to them, some species of artificial signs, are necessary to
reasoning; that there could be no inference, and consequently no induction,
without them. But if the nature of reasoning was correctly explained in
the earlier part of the present work, this opinion must be held to be an ex-
aggeration, though of an important truth. If reasoning be from particulars
to particulars, and if it consist in recognizing one fact as a mark of another,
or a mark of a mark of another, nothing is required to render reasoning
possible, except senses and association ; senses to perceive that two facts
are conjoined ; association, as the law by which one of those two facts raises
up the idea of the other.* For these mental phenomena, as well as for the
belief or expectation which follows, and by which we recognize as having
taken place, or as about to take plaee, that of which we have perceived a
mark, there is evidently no need of language. And this inference of one
particular fact from another is a case of induction. It is of this sort of in-
duction that brutes are capable ; it is in this shape that uncultivated minds
make almost all their inductions, and that we all do so in the cases in which
familiar experience forces our conclusions upon us without any active proc-
ess of inquiry on our part, and in which the belief or expectation follows
the suggestion of the evidence with the promptitude and certainty of an
instinct.f
§ 3. But though inference of an inductive character is possible without
the use of signs, it could never, without them, be carried much beyond the
very simple cases which we have just described, and which form, in aU
probability, the limit of the reasonings of those animals to whom conven-
tional language is unknown. Without language, or something equivalent
to it, there could only be as much reasoning from experience as can take
place without the aid of general propositions. Now, though in strictness
* This sentence having been erroneously understood as if I had meant to assert that belief is
nothing but an irresistible association, I think it necessary to observe that I express no theory
respecting the ultimate analysis either of reasoning or of belief, two of the most obscure points
in analytical psychology. I am speaking not of the powers themselves, but of the previous
conditions necessary to enable those powers to exert themselves : of which conditions I am
■contending that language is not one, senses and association being sufficient without it. The
irresistible association theory of belief, and the difficulties connected with the subject, have
■been discussed at length in the notes to the new edition of Mr. James Mill's Analysis of the
^Phenomena of the Human Mind.
t Mr. Bailey agrees with me in thinking that whenever " from something actually present
to my senses, conjoined with past experience, I feel satisfied that something has happened, or
will happen, or is happening, beyond the sphere of my personal observation," I may with strict
propriety be said to reason : and of course to reason inductively, for demonstrative reasoning
is excluded by the circumstances of the case. (The Theory of Seasoning, 2d ed., p. 27.)
30
466 OPERATIONS SUBSIDIARY TO INDUCTION.
we may reason from past experience to a fresh individual case without th*
intermediate stage of a general proposition, yet without general propositions
we should seldom remember what past experience we have had, and scarce-
ly ever what conclusions that experience will warrant. The division of the
inductive process into two parts, the first ascertaining what is a mark of
the given fact, the second whether in the new case that mark exists, is
natural, and scientifically indispensable. It is, indeed, in a majority of
cases, rendered necessary by mere distance of time. The experience by
which we are to guide our judgments may be other people's experience,
little of which can be communicated to us otherwise than by language;,
when it is our own, it is generally experience long past ; unless, therefore,
it were recorded by means of artificial signs, little of it (except in cases in-
volving our intenser sensations or emotions, or the subjects of our daily and
hourly contemplation) would be retained in the memory. It is hardly nec-
essary to add, that when the inductive inference is of any but the most
direct and obvious nature — when it requires several observations or exper-
iments, in varying circumstances, and the comparison of one of these with
another — it is impossible to proceed a step, without the artificial memory
which words bestow. Without words, we should, if we had often seen A
and B in immediate and obvious conjunction, expect B whenever we saw
A; but to discover their conjunction when not obvious, or to determine
whether it is i-eally constant or only casual, and whether there is reason to
expect it under any given change of circOmstances, is a process far too com-
plex to be performed without some contrivance to make our remembrance
of our own mental operations accurate. Now, language is such a contriv-
ance. When that instrument is called to our aid, the difficulty is reduced
to that of making our remembrance of the meaning of words accurate.
This being secured, whatever passes through our minds may be remem-
bered accurately, by putting it carefully into words, and committing the
words either to writing or to memory.
The function of Naming, and particularly of General Names, in Induc-
tion, may be recapitulated as follows. Every inductive inference which is
good at all, is good for a whole class of cases ; and, that the inference may
have any better warrant of its correctness than the mere clinging together
of two ideas, a process of experimentation and comparison is necessary; in
which the whole class of cases must be brought to view, and some uniform-
ity in the course of nature evolved and ascertained, since the existence
of such a uniformity is required as a justification for drawing the infer-
ence in even a single case. This uniformity, therefore, may be ascertained
once for all ; and if, being ascertained, it can be remembered, it will serve
as a formula for making, in particular cases, all such inferences as the pre-
vious experience will warrant. But we can only sscure its being remem-
bered, or give ourselves even a chance of carrying in our memory any con-
siderable number of such uniformities, b)"- registering them through the
medium of permanent signs ; which (being, from the nature of the case,,
signs not of an individual fact, but of a uniformity, that is, of an indefinite
number of facts similar to one another) are general signs; universals; gen-
eral names, and general propositions.
§ 4. And here I can not omit to notice an oversight committed by some
eminent thinkers ; who have said that the cause of our using general names
is the infinite multitude of individual objects, which, making it impossible
to have a name for each, compels us 'to make one name serve for many.
IIEQUISITES OF LANGUAGE. 46T
This is a very limited view of the function of general names. Even if
there were a name for every individual object, we should require general
names as much as we now do. Without them we could not express the
result of a single comparison, nor record any one of the uniformities ex-
isting in nature; and should be hardly better off in respect to Induction
than if we had no names at all. With none but names of individuals (or,
in other words, proper names), we might, by pronouncing the name, sug-
gest the idea of the object, but we could not assert any proposition ; ex-
cept the unmeaning ones formed by predicating two proper names one of
another. It is only by means of general names that we can convey any
information, predicate any attribute, even of an individual, much more of
a class. Rigorously speaking, we could get on without any other general
names than the abstract names of attributes; all our propositions might
be of the form " such an individual object possesses such an attribute," or
"such an attribute is always (or never) conjoined with such another attri-
bute." In fact, however, mankind have always given general names to
objects as well as attributes, and indeed before attributes : but the general
names given to objects imply attributes, derive their whole meaning from
attributes ; and are chiefly useful as the language by means of which we
predicate the attributes which they connote.
It remains to be considered what principles are to be adhered to in
giving general names, so that these names, and the general propositions in
which they fill a place, may conduce most to the purposes of Induction.
CHAPTER IV.
OF THE EBQUISITES OP A PHILOSOPHICAL LANGUAGB, AND THE PRINCI-
PLES OP DEFINITION.
§ 1. In order that we may possess a language perfectly suitable for the
investigation and expression of general truths, there are two principal, and
several minor requisites. The first is, that every general name should
have a meaning, steadily fixed, and precisely determined. When, by the
fulfillment of this condition, such names as we possess are fitted for the
due performance of their functions, the next requisite, and the second in
order of importance, is that we should possess a name wherever one is
needed ; wherever there is any thing to be designated by it, which it is of
importance to express.
The former of these requisites is that to which our attention will be ex-
clusively directed in the present chapter.
§ 2. Every general name, then, must have a certain and knowable mean-
ing. Now the meaning (as has so often been explained) of a general con-
notative name, resides in the connotation ; in the attribute on account of
which, and to express which, the name is given. Thus, the name animal
being given to all things which possess the attributes of sensation and
voluntary motion, the word connotes those attributes exclusively, and they
constitute the whole of its meaning. If the name be abstract, its denota-
tion is the same with the connotation of the corresponding concrete; it
designates directly the attribute, which the concrete term implies. To give
a precise meaning to general names is, then, to fix with steadiness the
468 OPERATIONS SUBSIDIARY TO INDUCTION.
attribute or attributes connoted by each concrete general name, and de.
noted by the corresponding abstract. Since abstract names, in the order
of their creation, do not precede but follow concrete ones, as is proved by
the etymological fact that they are almost always derived from them ; we
may consider their meaning as determined by, and dependent on, the mean-
ing of their concrete ; and thus the problem of giving a distinct meaning
to general language, is all included in that of giving a precise connotation
to all concrete general names.
This is not difficult in the case of new names ; of the technical terms
created by scientific inquirers for the purposes of science or art. But
when a name is in common use, the difficulty is greater; the problem in
this case not being that of choosing a convenient connotation for the name,
but of ascertaining and fixing the connotation with which it is already
used. That this can ever be a matter of doubt, is a sort of paradox. But
the vulgar (including in that term all who have not accurate habits of
thought) seldom know exactly what assertion they intend to make, what
common property they mean to express, when they apply the same "name to
a number of different things. All which the name expresses with them,
when they predicate it of an object, is a confused feeling of resemblance
between that object and some of the other things which they have been
accustomed to denote by the name. They have applied the name Stone
to various objects previously seen ; they see a new object, which appears .
to them somewhat like the former, and they call it a stone, without asking
themselves in what respect it is like, or what mode or degree of resem-
blance the best authorities, or even they themselves, require as a warrant
for using the name. This rough general impression of resemblance is,
however, made up of particular circumstances of resemblance ; and into
these it is the business of the logician to analyze it; to ascertain what
points of resemblance among the different things commonly called by the
name, have produced in the common mind this vague feeling of likeness ;
have given to the things the similarity of aspect, which has made them a
class, and has caused the same name to be bestowed upon them.
But though general names are imposed by the vulgar without any more
definite connotation than that of a vague resemblance ; .general proposi-
tions come in time to be made, in which predicates are applied to those
names, that is, general assertions are made concerning the whole of the
things which are denoted by the name. And since by each of these prop-
ositions some attribute, more or less precisely conceived, is of course pred-
icated, the ideas of these various attributes thus become associated with
the name, and in a sort of uncertain way it comes to connote them ; there
is a hesitation to apply the name in any new case in which any of the at-
tributes familiarly predicated of the class do not exist. And thus, to
common minds, the propositions which they are in the habit of hearing or
uttering concerning a class make up in a loose way a sort of connotation
for the class name. Let us take, for instance, the word Civilized. How
few could be found, even among the most educated persons, who would
undertake to say exactly what the term Civilized connotes. Yet there is
a feeling in the minds of all who use it, that they are using it with a mean-
ing; and this meaning is made up, in a confused manner, of every thing
which they have heard or read that civilized men or civilized communities
are, or may be expected to be.
It is at this stage, probably, in the progress of a concrete name, that the
corresponding abstract name generally comes into use. Under the notion
REQUISITES OF LANGUAGE. 469
that the concrete name must of course convey a meaning, or, in other words,
that there is some property common to all things which it denotes, people
give a name to this common property ; from the concrete Civilized, they
form the abstract Civilization. But since most people have never com-
pared the different things which are called by the concrete name, in such a
manner as to ascertain what properties these things have in common, or
whether they have any ; each is thrown back upon the marks by which he
himself has been accustomed to be guided in his application of the term ;
and these, being merely vague hearsays and current phrases, are not the
same in any two persons, nor in the same person at different times. Hence
the word (as Civilization, for example) which professes to be the designa-
tion of the unknown common property, conveys scarcely to any two minds
the same idea. No two persons agree in the things they predicate of it ;
and when it is itself predicated of any thing, no other person knows, nor
does the speaker himself know with precision, what he means to assert.
Many other words which could be named, as the word honor, or the word
gentleman, exemplify this uncertainty still more strikingl)'.
It needs scarcely be observed, that general propositions of which no
one can tell exactly what they assert, can not possibly have been brought
to the test of a correct induction. Whether a name is to be used as
an instrument of thinking, or as a means of communicating the result of
thought, it is imperative to determine exactly the attribute or attributes
which it is to express ; to give it, in short, a fixed and ascertained connota-
tion.
§ 3. It would, however, be a complete misunderstanding of the proper of-
fice of a logician in dealing with terms already in use, if we were to think
that because a name has not at present an ascertained connotation, it is
competent to any one to give it such a connotation at his own choice. The
meaning of a terqi actually in use is not an arbitrary quantity to be fixed,
hut an unknown quantity to be sought.
In the first place, it is obviously desirable to avail ourselves, as far as
possible, of the associations already connected with the name; not enjoin-
ing the employment of it in a manner which conflicts with all previous
habits, and especially not so as to require the rupture of those strongest
of all associations between names, which are created by familiarity with
propositions in which they are predicated of one another. A philosopher
would have little chance of having his example followed, if he were to give
such a meaning to his terms as should require us to call the North Ameri-
can Indians a civilized people, or the higher classes in Europe savages ; or
to say that civilized people live by hunting, and savages by agriculture.
Were there no other reason, the extreme diflSculty of effecting so complete
a revolution in speech would be more than a sufficient one. The endeavor
should be, that all generally received propositions into which the term en-
ters, should be at least as true after its meaning is fixed, as they were be-
fore; and that the concrete name, therefore, should not receive such a con-
notation as shall prevent it from denoting things which, in common lan-
guage, it is currently affirmed of. The fixed and precise connotation which
it receives should not be in deviation from, but in agreement (as far as it
goes) with, the vague and fluctuating connotation which the term already
had.
To fix the connotation of a concrete name, or the denotation of the cor-
responding abstract, is to define the name. When this can be done with-
4'70 OPERATIONS SUBSIDIARY TO INDUCTION.
out rendering any received assertions inadmissible, the name can be de-
fined in accordance with its received use, which is vulgarly called defining
not the name but the thing. What is meant by the improper expression
of defining a thing (or rather a class of things — for nobody talks of defin-
ing an individual), is to define the name, subject to the condition that it
shall denote those things. This, of course, supposes a comparison of the
things, feature by feature and property by property, to ascertain what at-
tributes they agree in ; and not unf requently an operation strictly induc^
tive, for the purpose of ascertaining some unobvious agreement, which is
the cause of the obvious agreements.
For, in order to give a connotation to a name, consistently with its de-
noting certain objects, we have to make our selection from among the vari.
ous attributes in which those objects agree. To ascertain in what they do
agree is, therefore, the first logical operation requisite. When this has
been done as far as is necessary or practicable, the question arises, which
of these, common attributes shall be selected to be associated with the
name. For if the class which the name denotes be a Kind, the common
properties are innumerable ; and even if not, they are often extremely nu-
merous. Our choice is first limited by the preference to be given to prop-
erties which are well known, and familiarly predicated of the class ; but
even these are often too numerous to be all included in the definition, and,
besides, the properties most generally known may not be those which serve
best to mark out the class from all others. We should therefore select
from among the common properties (if among them any such are to be
found) those on which it has been ascertained by experience, or proved by
deduction, that many others depend ; or at least which are sure marks of
them, and from whence, therefore, many others will follow by inference.
We thus see that to frame a good definition of a name already in use, is
not a matter of choice but of discussion, and discussion not merely respect-
ing the usage of language, but respecting the properties of things, and
even the origin of those properties. And hence every enlargement of
our knowledge of the objects to which the name is applied, is liable to
suggest an improvement in the definition. It is impossible to frame a per-
fect set of definitions on any subject, until the theory of the"~ subject is per-
fect ; and as science makes progress, its definitions are also progressive.
§ 4. The discussion of Definitions, in so far as it does not turn on the
use of words but on the properties of things, Dr. Whewell calls the Expli-
cation of Conceptions. The act of ascertaining, better than before, in what
particulars any phenomena which are classed together agree, he calls in his
technical phraseology, unfolding the general conception in virtue of which
they are so classed. Making allowance for what appears to me the dark-
ening and misleading tendency of this mode of expression, several of his
remarks are so much to the purpose, that I shall take the liberty of tran-
scribing them.
He observes,* that many of the controversies which have had an impor-
tant share in the formation of the existing body of science, have "assumed
the form of a battle of Definitions. For example, the inquiry concerning
the laws of falling bodies led to the question whether the proper definition
of a uniform force is that it generates a velocity proportional to the space
f I'om rest, or to the time. The controversy of the vis viva was what was
* Novum Organum Renovatvm, pp. 35-37.
REQUISITES OF LANGUAGE. 471
the proper definition of the measure of force. A principal question in the
classification of minerals is, what is the definition of a mineral species.
Physiologists have endeavored to throw light on their subject by defining
.organization, or some similar term." Questions of the same nature were
long open and are not yet completely closed, respecting the definitions of
Specific Heat, Latent Heat, Chemical Combination, and Solution.
"It is very important for us to observe, that these controversies have
never been questions of insulated and arbitrary definitions, as men seem
often tempted to imagine them to have been. In all cases there is a tacit
assumption of some proposition which is to be expressed by means of the
definition, and which gives it its importance. The dispute concerning the
definition thus acquires a real value, and becomes a question concerning
true and false. Thus, in the discussion of the question, What is a uniform
force? it was taken for granted that gravity is a uniform force. In the
debate of the vis viva, it was assumed that in the mutual action of bodies
the whole effect of the force is unchanged. In the zoological definition of
.species (that it consists of individuals which have, or may have, sprung
from the same parents), it is presumed that individuals so related resemble
«ach other more than those which are excluded by such a definition ; or,
perhaps, that species so defined have permanent and definite differences.
A definition of organization, or of some other term which was not employed
to express some principle, would be of no value.
"The establishment, therefore, of a right definition of a term, may be a
useful step in the explication of our conceptions ; but this will be the case
then only when we have under our consideration some proposition in which,
the term is employed. For then the question really is, how the conception
shall be understood and defined in order that the proposition may be true.
"To unfold our conceptions by means of definitions has never been serv-
iceable to science, except when it has been associated with an immediate
use of the definitions. The endeavor to define a Uniform Force was cora-
t)ined with the assertion that gravity is a uniform force; the attempt to
•define Accelerating Force was immediately followed by the doctrine that
accelerating forces may be compounded; the process of defining Momen-
tum was connected with the principle that momenta gained and lost are
•equal ; naturalists would have given in vain the definition of Species which
we have quoted, if they had not also given the characters of species so sepa-
rated Definition may be the best mode of explaining our conception,
but that which alone makes it worth while to explain it in any mode, is the
•opportunity of using it in the expression of truth. When a definition is
propounded to us as a useful step in knowledge, we are always entitled to
^sk what principle it serves to enunciate."
In giving, then, an exact connotation to the phrase, " a uniform force,"
the condition was understood, that- the phrase should continue to denote
gravity. The discussion, therefore, respecting the definition, resolved itself
into this question. What is there of a uniform nature in the motions pro-
duced by gravity ? By observations and comparisons, it was found that
what was uniform in those motions was the ratio of the velocity acquired
to the time elapsed ; equal velocities being added in equal times. A uni-
form force, therefore, was defined a force which adds equal velocities in
equal times. So, again, in defining momentum. It was already a received
•doctrine that, when two objects impinge upon one another, the momentum
lost by the one is equal to that gained by the other. This proposition it
was deemed necessary to preserve, not from the motive (which operates in
472 OPERATIONS SUBSIDIARY TO INDUCTION.
many other cases) that it was firmly fixed in popular belief ; for the propo.
sition in question had never been heard of by any but the scientifically in-
structed. But it was felt to contain a truth ; even a superficial observation
of the phenomena left no doubt that in the propagation of motion from
one body to another, there was something of which the one body gained
precisely what the other lost ; and the word momentum had been invented
to express this unknown something. The settlement, therefore, of the defi-
nition of momentum, involved the determination of the question, What is
that of which a body, when it sets another body in motion, loses exactly
as much as it communicates? And when experiment had shown that this
something was the product of the velocity of the body by its mass, or quan-
tity of matter, this became the definition of momentum.
The following remarks,* therefore, ai-e perfectly just: "The business of
definition is part of the business of discovery To define, so that our
definition shall have any scientific value, requires no small portion of that
sagacity by which truth is detected When it has been clearly seen
what ought to be our definition, it must be pretty well known what truth
we have to state. The definition, as well as the discovery, supposes a de-
cided step in our knowledge to have been made. The writers on Logic,
in the Middle Ages, made Definition the last stage in the progress of knowl-
edge ; and in this arrangement at least, the history of science, and the phi-
losophy derived from the history, confirm their speculative views." For
in order to judge finally how the name which denotes a class may best be
defined, we must know all the properties common to the class, and all the
relations of causation or dependence among those properties.
If the properties which are fittest to be selected as marks of other com-
mon properties are also obvious and familiar, and especially if they bear a
great part in producing that general air of resemblance which was the
original inducement to the formation of the class, the definition will then
be most felicitous. But it is often necessary to define the class by some
property not familiarly known, provided that property be the best mark of
those which are known. M. De Blainville, for instance, founded his defini-
tion of life on the process of decomposition and recomposition which in-
cessantly takes place in every living body, so that the particles composing
it are never for two instants the same. This is by no means one of the
most obvious properties of living bodies ; it might escape altogether the
notice of an unscientific observer. Yet great authorities (independently of
M. De Blainville, who is himself a first-rate authority) have thought that no
other property so well answers the conditions required for the definition.
§ 5. Having laid down the principles which ought for the most part to
be observed in attempting to give a precise connotation to a term in use,
I must now add, that it is not always practicable to adhere to those princi'
pies, and that even when practicable, it is occasionally not desirable.
Cases in which it is impossible to comply with all the conditions of a
precise definition of a name in agreement with usage, occur very frequent-
ly. There is often no one connotation capable of being given to a word,
so that it shall still denote every thing it is accustomed to denote ; or that
all the propositions into which it is accustomed to enter, and which have
any foundation in truth, shall remain true. Independently of accidental
ambiguities, in which the different meanings have no connection with one
* Novum Organum Renovatum, pp. 39, 40.
REQUISITES OF LANGUAGE. 473
another ; it continually happens that a word is used in two or more senses
derived from each other, but yet radically distinct. So long as a term is
vague, that is, so long as its connotation is not ascertained and permanent-
ly fixed, it is constantly liable to be applied by extension from one thing to
another, until it reaches things which have little, or even no, resemblance
to those which were first designated by it.
"Suppose," says Dugald Stewart, in his Philosophical Assays* "that
the letters A, B, C, D, E, denote a series of objects ; that A possesses some
one quality in common with B ; B a quality in common with C ; C a qual-
ity in common with D ; D a quality in common with E ; while at .the same
time, no quality can be found which belongs in common to any three ob-
jects in the series. Is it not conceivable, that the afiinity between A and B
may produce a transference of the name of the first to the second ; and
that, in consequence of the other aflSnities which connect the remaining ob-
jects together, the same name may pass in succession from B to C ; from
C to D ; and from D to E ? In this manner, a common appellation will
arise between A and E, although the two objects may, in their nature and
properties, be so widely distant from each other, that no stretch of im-
agination can conceive how the thoughts were led from the former to the
latter. The transitions, nevertheless, may have been all so easy and grad-
ual, that, were they successfully detected by the fortunate ingenuity of a
theorist, we should instantly recognize, not only the verisimilitude, but the
truth of the conjecture : in the same way as we admit, with the confidence
■of intuitive conviction, the certainty of the well-known etymological process
which connects the Latin preposition e or ex with the English substantive
stranger, the moment that the intermediate links of the chain are submitted
to our examination."!
The applications which a word acquires by this gradual extension of it
from one set of objects to another, Stewart, adopting an expression from
Mr. Payne Knight, calls its transitive applications ; and after briefly illustra-
ting such of them as are the result of local or casual associations, he pro-
ceeds as follows :J
" But although by far the greater part of the transitive or derivative ap-
plications of words depend on casual and unaccountable caprices of the
feelings or the fancy, there are certain cases in which they open a very in-
* P. 217, 4to edition.
t "E, ex, extra, extranens, etranger, stranger."
Another etymological example sometimes cited is the derivation of the English uncle from
the Latin aims. It is scarcely possible for two words to bear fewer ontward marks of rela-
tionship, yet there is but one step between them, avus, avunculus, uncle. So pilgrim, fron)
«yer ; per agrum, peragrinus, peregrinus, pellegrino, pilgrim.
Professor Bain gives some apt examples of these transitions of meaning. "The word
'damp' primarily signified moist, humid, wet. But the property is often accompanied with
the feeling of cold or chilliness, and hence the idea of cold is strongly suggested by the word.
This Is not all. Proceeding upon the superadded meaning, we speak of damping a man's
ardor, a metaphor where the cooling is the only circumstance concerned ; we go on still fur-
ther to designate the iron slide that shuts off the draft of a stove, 'the damper,' the primary
meaning being now entirely dropped. 'D17,' in like manner, through signifying the absence
of moisture, water, or liquidity, is applied to sulphuric acid containing water, although not
thereby ceasing to be a moist," wet, or liquid substance." So in the phrases, dry sherry, or
Champagne.
"'Street,' originally a paved way, with or without houses, has been extended to roads
iined with houses, whether paved or nnpaved. 'Impertinent' signified at first irrelevant,
aUen to the purpose in hand : through which it has come to mean, meddling, intrusive, uih
mannerly, insolent." (Logic, ii., 173, 174.)
:t Pp. 226, 227.
474 OPERATIONS SUBSIDIARY TO INDUCTION.
teresting field of philosophical speculation. Such are those, in which an
analogous transference of the corresponding term may be remarked uni-
versally, or very generally, in other languages ; and in which, of course, the-
uniformity of the result must be ascribed to the essential principles of the
human frame. Even in such cases, however, it will by no means be always
found, on examination, that the various applications of the same term have-
arisen from any common quality or qualities in the objects to which they
relate. In the greater number of instances, they may be traced to some
natural and universal associations of ideas, founded in the common facul-
ties, comijion organs, and common condition of the human race Ac-
cording to the different degrees of intimacy and strength in the associa-
tions on which the transitions of language are founded, very different ef-
fects may be expected to arise. Where the association is slight and casu-
al, the several meanings will remain distinct from each other, and will often,,
in process of time, assume the appearance of capricious varieties in the use
of the same arbitrary sign. W7iere the association is so natural and ha-
bitual as to become virtually indissoluble, the transitive meanings will coa-
lesce in one complex conception; and every new transition will become a
more comprehensive generalization of the term in question.''''
I solicit particular attention to the law of mind expressed in the last sen-
tence, and which is the source of the perplexity so often experienced in de-
tecting these transitions of meaning. Ignorance of that law is the shoal Ott
which some of the most powerful intellects which have adorned the human
race have been stranded. The inquiries of Plato into the definitions of
some of the most general terms of moral speculation are characterized by
Bacon as a far nearer approach to a true inductive method than is else-
where to be found among the ancients, and are, indeed, almost perfect ex-
amples of the preparatory process of comparison and abstraction; but,
from being unaware of the law just mentioned, he often wasted the powers^
of this great logical instrument on inquiries in which it could realize no re-
sult, since the phenomena, whose common properties he so elaborately en-
deavored to detect, had not really any common properties. Bacon himself
fell into the same error in his speculations on the nature of heat, in which
he evidently confounded under the name hot, classes of phenomena whiob
have no property in common. Stewart certainly overstates the matter
when he speaks of " a prejudice which has descended to modern times from
the scholastic ages, that when a word admits of a variety of significations,,
these different significations must all be species of the same genus, and
must consequently include some essential idea common to every individual
to which the generic term can be applied;"* for both Aristotle and his-
followers were well aware that there are such things as ambiguities of
language, and delighted in distinguishing them. But they never suspected
ambiguity in the cases where (as Stewart remarks) the association on which
the transition of meaning was founded is so natural and habitual, that the-
two meanings blend together in the mind, and a real transition becomes an
apparent generalization. Accordingly they wasted infinite pains in endeav-
oring to find a definition which would serve for several distinct meanings-
at once; as in an instance noticed by Stewart himself, that of " causation;
the ambiguity of the word which, in the Greek language corresponds to-
the English word cause, having suggested to them the vain attempt of tra-
cing the common idea which, in the case of any effect, belongs to the effi^
* Essays, p. 214.
REQUISITES OF LANGUAGE. 475
eient, to the matter, to the form, and to the end. The idle generalities "
(he adds) " we meet with in other philosophers, about the ideas of the good,
the^^, and the becoming, have taken their rise from the same undue influ-
ence of popular epithets on the speculations of the learned."*
Among the words which have undergone so many successive transitions
of meaning that every trace of a property common to all the things they
are applied to, or at least common and also peculiar to those things, has
been lost, Stewart considers the word Beautiful to be one. And (without
attempting to decide a question which in no respect belongs to logic) I can
not but feel, with him, considerable doubt whether the word beauttful con-
notes the same property when we speak of a beautiful color, a beautiful
face, a beautiful scene, a beautiful character, and a beautiful poem. The
word was doubtless extended from one of these objects to another on ac-
count of a resemblance between them, or, more probably, between the emo-
tions they excited ; and, by this progressive extension, it has at last reach-
ed things very remote from those objects of sight to which there is no
doubt that it was first appropriated ; and it is at least questionable wheth-
er there is now any property common to all the things which, consistently
with usage, may be called beautiful, except the property of agreeableness,
which the term certainly does connote, but which can not be all that people
usually intend to express by it, since there are many agreeable things which
are never called beautiful. If such be the case, it is impossible to give to
the word Beautiful any fixed connotation, such that it shall denote all the
objects which in common use it now denotes, but no others. A fixed con-
notation, however, it ought to have ; for, so long as it has not, it is unfit to
be used as a scientific term, and is a perpetual source of false analogies and
erroneous generalizations.
This, then, constitutes a case in exemplification of our remark, that even
when there is a property common to all the things denoted by a name, to
erect that property into the definition and exclusive connotation of the name
is not always desirable. The various things called beautiful unquestionably
resemble one another in being agreeable ; but to make this the definition of
beauty, and so extend the word Beautiful to all agreeable things, would be
to drop altogether a portion of meaning which the word really, though in-
distinctly, conveys, and to do what depends on us toward causing those
qualities of the objects which the word previously, though vaguely, pointed
at, to be overlooked and forgotten. It is better, in such a case, to give a
fixed connotation to the term by restricting, than by extending its use;
rather excluding from the epithet Beautiful some things to which it is com-
monly considered applicable, than leaving out of its connotation any of the
qualities by which, though occasionally lost sight of, the general mind may
have been habitually guided in the commonest and most interesting appli-
cations of the term. For there is no question that when people call any
thing beautiful, they think they are asserting more than that it is merely
agreeable. They think they are ascribing a peculiar sort of agreeableness,
analogous to that which they find in some other of the things to which they
are accustomed to apply the same name. If, therefore, there be any pe-
cuUar sort of agreeableness which is common though not to all, yet to the
principal things which are called beautiful, it is better to limit the denota-
tion of the term to those things, than to leave that kind of quality without
a term to connote it, and thereby divert attention from its peculiarities.
* Essays, p. 213.
4T6 OPERATIONS SUBSIDIARY TO INDUCTION.
§ 6. The last remark exemplifies a rule of terminology, which is of great
importance, and which has hardly yet been recognized as a rule, but by a
few thinkers of the present century. In attempting to rectify the use of a
vague term by giving it a fixed connotation, we must take care not to dis-
card (unless advisedly, and on the ground of a deeper knowledge of the
subject) any portion of the connotation which the word, in however indis-
tinct a manner, previously carried with it. For otherwise language loses
one of its inherent and most valuable properties, that of being the conser-
vator of ancient experience ; the keeper-alive of those thoughts and obser-
vations of former ages, which may be alien to the tendencies of the passing
time. This function of language is so often overlooked or undervalued,
that a few observations on it appear to be extremely required.
Even when the connotation of a term has been accurately fixed, and still
more if it has been left in the state of a vague unanalyzed feeling of resem-
blance; there is a constant tendency in the word, through familiar use, to
part with a portion of its connotation. It is a well-known law of the mind,
that a word originally associated with a very complex cluster of ideas, is
far from calling up all those ideas in the mind, every time the word is used ;
it calls up only one or two, from which the mind runs on by fresh associa-
tions to another set of ideas, without waiting for the suggestion of the re-
mainder of the complex cluster. If this were not the case, processes of
thought could not take place with any thing like the rapidity which we
know they possess. Very often, indeed, when we are employing a word in
our mental operations, we are so far from waiting until the complex idea
which corresponds to the meaning of the word is consciously brought be-
fore us in all its parts, that we run on to new trains of ideas by the other
associations which the mere word excites, without having realized in our
imagination any part whatever of the meaning ; thus using the word, and
even using it well and accurately, and carrying on important processes of
reasoning by means of it, in an almost mechanical manner; so much so,
that some metaphysicians, generalizing from an extreme case, have fancied
that all reasoning is but the mechanical use of a set of terms according to
a certain form. We may discuss and settle the most important interests
of towns or nations, by the application of general theorems or practical
maxims previously laid down, without having had consciously suggested to
us, once in the whole process, the houses and green fields, the thronged
market-places and domestic hearths, of which not only those towns and na^
tions consist, but which the words town and nation confessedly mean.
Since, then, general names come in this manner to be used (and even to
do a portion of their work well) without suggesting to the mind the whole
of their meaning, and often with the suggestion of a very small, or no part
at all of that meaning ; we can not wonder that words so used come in time
to be no longer capable of suggesting any other of the ideas appropriated
to them, than those with which the association is most immediate and
strongest, or most kept \ip by the incidents of life; the remainder being
lost altogether; unless the mind, by often consciously dwelling on them,
keeps up the association. Words naturally retain much more of their
meaning to persons of active imagination, who habitually represent to them-
selves things in the concrete, with the detail which belongs to them in the
actual world. To minds of a different description, the only antidote to this
corruption of* language is predication. The habit of predicating of the
name, all the various properties which it originally connoted, keeps up the
association between the name and those properties.
REQUISITES OF LANGUAGE. 477
But in order that it may do so, it is necessary that the predicates should
themselves retain their association with the properties which they several-
ly connote. For the propositions can not keep the meaning of the words
alive, if the meaning of the propositions themselves should die. And noth-
ing is more common than for propositions to be mechanically repeated;
mechanically retained in the memory, and their truth undoubtingly assented
to and relied on, while yet they carry no meaning distinctly home to the
mind ; and while the matter of fact or law of nature which they originally
expressed is as much lost sight of, and practically disregarded, as if it never
had been heard of at all. In those subjects which are at the same time
familiar and complicated, and especially in those which are so in as great a
degree as moral and social subjects are, it is a matter of common remark
how many important propositions are believed and repeated from habit,
while no account could be given, and no sense is practically manifested, of
the truths which they convey. Hence it is, that the traditional maxims of
old experience, though seldom questioned, have often so little effect on the
conduct of life ; because their meaning is never, by most persons, really felt,
until personal experience has brought it home. And thus also it is that so
, many doctrines of religion, ethics, and even politics, so full of meaning and
reality to first converts, have manifested (after the association of that mean-
ing with the verbal formulas has ceased to be kept up by the controversies
which accompanied their first introduction) a tendency to degenerate rap-
idly into lifeless dogmas ; which tendency, all the efforts of an education
expressly and skillfully directed to keeping the meaning alive, are barely
sufficient to counteract.
Considering, then, that the human mind, in different generations, occu-
pies itself with different things, and in one age is led by the circumstances
which surround it to fix more of its attention upon one of the properties
of a thing, in another age upon another ; it is natural and inevitable that
in every age a certain portion of our recorded and traditional knowledge,
not being continually suggested by the pursuits and inquiries with which
mankind are at that time engrossed, should fall asleep, as it were, and fade
from the memory. It would be in danger of being totally lost, if the prop-
ositions or formulas, .the results of the previous experience, did 'not remain,
as forms of words it may be, but of words that once really conveyed, and
are still supposed to convey, a meaning : which meaning, though suspended,
may be historically traced, and when suggested, may be recognized by
minds of the necessary endowments as being still matter of fact, or truth.
While the formulas remain, the meaning may at any time revive ; and as,
on the one hand, the formulas progressively lose the meaning they were in-
tended to convey, so, on the other, when this forgetfulness has reached its
height and begun to produce obvious consequences, minds arise which from
the contemplation of the formulas rediscover the truth, when truth it was,
which was contained in them, and announce it again to mankind, not as a
discovery, but as the meaning of .that which they have been taught, and
still profess to believe.
Thus there is a perpetual oscillation in spiritual truths, and in spiritual
doctrines of any significance, even when not truths. Their meaning is
almost always in a process either of being lost or of being recovered.
Whoever has attended to the history of the more serious convictions of
mankind — of the opinions by which the general conduct of their lives is,
or as they conceive ought to be, more especially regulated — is aware that
even when recognizing verbally the same doctrines, they attach to them at
478 OPERATIONS SUBSIDIARY TO INDUCTION.
different periods a greater or a less quantity, and even a different kind of
meaning. The words in tlieir original acceptation connoted, and the prop-
ositions expressed, a complication of outward facts and inward feelings, to
different portions of which the general mind is more particularly alive in dif-
ferent generations of mankind. To common minds, only that portion of the
meaning is in each generation suggested, of which that generation possesses
the counterpart in its own habitual experience. But the words and. prop-
ositions lie ready to suggest to any mind duly prepared the remainder of
the meaning. Such individual minds are almost always to be found ; and
the lost meaning, revived by them, again by degrees works its way into the
general mind.
The arrival of this salutary reaction may, however, be materially retarded
by the shallow conceptions and incautious proceedings of mere logicians.
It sometimes happens that toward the close of the downward period, when
the words have lost part of their significance, and have not yet begun to
recover it, persons arise whose leading and favorite idea is the importance
of clear conceptions and precise thought, and the necessity, therefore, of
definite language. These persons, in examining the old formulas, easily
perceive that words are used in them without a meaning ; and if they are
not the sort of persons who are capable of rediscovering the lost significa-
tion, they naturally enough dismiss the formula, and define the name with-
out reference to it. In so doing they fasten down the name to what it
connotes in common use at the time when it conveys the smallest quantity
of meaning; and introduce the practice of employing it, consistently and
uniformly, according to that connotation. The word in this way acquires
an extent of denotation far beyond what it had before ; it becomes extend-
ed to many things to which it was previously, in appearance capriciously,
refused. Of the propositions in which it was formerly used, those which
were true in virtue of the forgotten part of its meaning are now, by the
clearer light which the definition diffuses, seen not to be true according to
the definition ; which, however, is the recognized and sufficiently correct
expression of all that is perceived to be in the mind of any one by whom,
the term is used at the present day. The ancient formulas are consequent-
ly treated as prejudices ; and people are no longer taught as before, though
not to understand them, yet to believe that there is truth in them. They
no longer remain in the general mind surrounded by respect, and ready at
any time to suggest their original meaning. "Whatever truths they contain
are not only, in these circumstances, rediscovered far more slowly, but,
when rediscovered, the prejudice with which novelties are regarded is now,
in some degree at least, against them, instead of being on their side.
An example may make these remarks more intelligible. In all ages, ex-
cept where moral speculation has been silenced by outward compulsion, or
where the feelings which prompt to it still continue to be satisfied by the
traditional doctrines of an established faith, one of the subjects which have
most occupied the minds of thinking persons is the inquiry, What is vir-
tue ? or, What is a virtuous character ? Among the different theories on
the subject which have, at different times, grown up and obtained partial
currency, every one of which reflected as in the clearest mirror the express
image of the age which gave it birth ; there was one, according to which
virtue consists in a correct calculation of our own personal interests, either
in this world only, or also in another. To make this theory plausible, it
was of course necessary that the only beneficial actions which people in
general were accustomed to see, or were therefore accustomed to praise.
REQUISITES OF LANGUAGE. 479
should be such as were, oi* at least might without contradicting obvious
facts be supposed to be, the result of a prudential regard to self-interest ;
so that the words really connoted no more, in common acceptation, than
was set down in the definition.
Suppose, now, that the partisans of this theory had contrived to introduce
a consistent and undeviating use of the term according to this definition.
Suppose that they had seriously endeavored, and had succeeded in the en-
deavor, to banish the word disinterestedness from the language ; had ob-
tained the disuse of all expressions attaching odium to selfishness or com-
mendation to self-sacrifice, or which implied generosity or kindness to be
any thing but doing a benefit in order to receive a greater personal advan-
tage in return. Need we say that this abrogation of the old formulas for
the sake of preserving clear ideas and consistency of thought, would have
been a great evil? while the very inconsistency incurred by the co-exist-
ence of the formulas with philosophical opinions which seemed to condemn
them as absurdities, operated as a stimulus to the re - examination of the
subject and thus the very doctrines originating in the oblivion into which
a part of the truth had fallen, were rendered indirectly, but powerfully,
instrumental to its revival.
The doctrine of the Coleridge school, that the language of any people
among whom culture is of old date, is a sacred deposit, the property of all
ages, and which no one age should consider itself empowered to alter—
borders indeed, as thus expressed, on an extravagance ; but it is grounded
an a truth, frequently overlooked by that class of logicians who think more
of having a clear than of having a comprehensive meaning ; and who per-
ceive that every age is adding to the truths which it has received from its
predecessors, but fail to see that a counter process of losing truths al-
ready possessed, is also constantly going on, and requiring the most sedu-
lous attention to counteract it. Language is the depository of the accumu-
lated body of experience to which all former ages have contributed their
part, and which is the inheritance of all yet to come. We have no right to
prevent ourselves from transmitting to posterity a larger portion of this
inheritance than we may ourselves have profited by. However much we
may be able to improve on the conclusions of our forefathers, we ought to
be careful not inadvertently to let any of their premises slip through our
fingers. It may be good to alter the meaning of a word, but it is bad to let
any part of the meaning drop. Whoever seeks to introduce a more correct
use of a term with which important associations are connected, should be re-
quired to possess an accurate acquaintance with the history of the particular
word, and of the opinions which in different stages of its progress it served
to express. To be qualified to define the name, we must know all that has
ever been known of the properties of the class of objects which are, or
•originally were, denoted by it. For if we give it a meaning according to
which any proposition will be false which has ever been generally held to
be true, it is incumbent on us to be sure that we know and have considered
all which those who believed the proposition understood by it.
480 OrERATIONS SUBSIDIARY TO INDUCTION.
CHAPTER V.
ON THE NATURAL HISTOET OP THE VARIATIONS IN THE MEANING OP
TERMS.
§ 1. It is not only iu the mode which has now been pointed out, namely
by gradual inattention to a portion of the ideas conveyed, that words in
common use are liable to shift their connotation. The truth is, that the
connotation of such words is perpetually varying; as might be expected
from the manner in which words in common use acquire their connotation.
A technical term, invented for purposes of art or science, has, from the first,
the connotation given to it by its inventor ; but a name which is in every
one's mouth before any one thinks of defining it, derives its connotation
only from the circumstances which are habitually brought to mind when it
is pronounced. Among these circumstances, the properties common to the
things denoted by the name, have naturally a principal place; and would
have the sole place, if language were regulated by convention rather than
by custom and accident. But besides these common properties, which if
they exist are certainly present whenever the name is employed, any other
circumstance may casually be found along with it, so frequently as to be-
come associated with it in the same manner, and as strongly, as the common
properties themselves. In proportion as this association forms itself, peo-
ple give up using the name in cases in which those casual circumstances do
not exist. They prefer using some other name, or the same name with
some adjunct, rather than employ an expression which will call up an idea
they do not want to excite. The circumstance originally casual, thus be-
comes regularly a part of the connotation of the word.
It is this continual incorporation of circumstances originally accident-
al, into the permanent signification of words, which is the cause that there
are so few exact synonyms. It is this also which renders the dictionary
meaning of a word, by universal remark so imperfect an exponent of its
real meaning. The dictionary meaning is marked out in a broad, blunt
way, and probaby includes all that was originally necessary for the correct
employment of the terra ; but in process of time so many collateral asso-
ciations adhere to words, that whoever should attempt to use them with
no other guide than the dictionary, would confound a thousand nice dis-
tinctions and subtle shades of meaning which dictionaries take no account
of; as we notice in the use of a language in conversation or writing by a
foreigner not thoroughly master of it. The history of a word, by showing
the causes which determine its use, is in these cases a better guide to its
employment than any definition ; for definitions can only show its meaning
at the particular time, or at most the series of its successive meanings, but
its history may show the law by which the succession was produced. The
word gentleman, for instance, to the correct employment of which a dic-
tionary would be no guide, originally meant simply a man born in a certain
rank. _ From this it came by degrees to connote all such qualities or ad-
ventitious circumstances as were usually found to belong to persons of that
rank. This consideration at once explains why in one of its vulgar accep-
tations it means any one who lives without labor, in another without man-
VARIATIONS IN MEANING OF TERMS. 48j
ual labor, and in its more elevated signification it has in every age signified
the conduct, character, habits, and outward appearance, in whomsoevei
found, which, according to the ideas of that age, belonged or were expect-
ed to belong to persons born and educated in a high social position.
It continually happens that of two words, whose dictionary meanings
are either the same or very slightly different, one will be the proper word
to use in one set of circumstances, another in another, without its being
possible to show how the custom of so employing them originally grew up.
The accident that one of the words was used and not the other on a par-
ticular occasion or in a particular social circle, will be suiBcient to produce
so strong an association between the word and some specialty of circum-
stances, that mankind abandon the use of it in any other case, and the
specialty becomes part of its signification. The tide of custom first drifts-
the word on the shore of a particular meaning, then retires and leaves it
there.
An instance in point is the remarkable change which, in the English lan-
guage at least, has taken place in the signification of the word loyalty^
That word originally meant in English, as it still means in the language
from whence it came, fair, open dealing, and fidelity to engagements ; in
that sense the quality it expressed was part of the ideal chivalrous or
knightly character. By what process, in England, the term became re-
stricted to the single case of fidelity to the throne, I am not sufficiently
versed in the history of courtly language to be able to pronounce. The
interval between a loyal chevalier and a loyal subject is certainly great.
I can only suppose that the word was, at some period, the favorite term at
court to express fidelity to the oath of allegiance ; until at length those who-
wishei to speak of any other, and as it was probably deemed, inferior sort
of fidelity, either did not venture to use so dignified a term, or found it
convenient to employ some other in order to avoid being misunderstood.
§ 2. Cases are not unfrequent in which a circumstance, at first casually
incorporated into the connotation of a word which originally had no refer-
ence to it, in time wholly supersedes the original meaning, and becomes
not merely a part of the connotation, but the whole of it. This is exem-
plified in the word pa.ga.D, paganus; which originally, as its etymology im-
ports, was equivalent to villager; the inhabitant of a pagus, or village.
At a particular era in the extension of Christianity over the Roman em-
pire, the adherents of the old religion, and the villagers or country people,
were nearly the same body of individuals, the inhabitants of the towns hav-
ing been earliest converted ; as in our own day, and at all times, the great-
er activity of social intercourse renders them the earliest recipients of new
opinions and modes, while old habits and prejudices linger longest among
the country people ; not to mention that the towns were more immediate-
ly under the direct influence of the Government, which at that time had
embraced Christianity. From this casual coincidence, the word paganus
carried with it, and began more and more steadily to suggest, the idea of
a worshiper of the ancient divinities; until at length it suggested that
idea so forcibly that people who did not desire to suggest the idea avoided
using the word. But when paganus had come to connote heathenism, the
very unimportant circumstance, with- reference to that fact, of the place of
residence, was soon disregarded in the employment of the word. As there
was seldom any occasion for making separate assertions respecting hea-
thens who lived in the country, there was no need for a separate word to
31
482 OPERATIONS SUBSIDIARY TO INDUCTION.
denote them ; and pagan came not only to mean heathen, but to mean that
exclusively. " -1.7..
A case still more familiar to most readers is that of the word villain or
villein. This term, as every body knows, had in the Middle Ages a conno-
tation as strictly defined as a word could have, being the proper legal des-
ignation for those persons who were the subjects of the less onerous forms
of feudal bondage. The scorn of the semi-barbarous military aristocracy
for these their abject dependants, rendered the act of likening any person
to this class of people a mark of the greatest contumely ; the same scorn
led them to ascribe to the same people all manner of hateful qualities, which
doubtless also, in the degrading situation in which they were held, were
•often not unjustly imputed to them. These circumstances combined to at-
tach to the term villain ideas of crime and guilt, in so forcible a manner
that the application of the epithet even to those to whom it legally belong-
•ed became an affront, and was abstained from whenever no affront was in-
tended. From that time guilt was part of the connotation ; and soon be-
came the whole of it, since mankind were not prompted by any urgent mo>
tive to continue making a distinction in their language between bad men
of servile station and bad men of any other rank in life.
These and similar instances in which the original signification of a term
is totally lost — another and an entirely distinct meaning being first ingraft-
ed upon the former, and finally substituted for it — afford examples of the
double movement which is always taking place in language : two counter-
movements, one of Generalization, by which words are perpetually losing
portions of their connotation, and becoming of less meaning and more gen-
eral acceptation ; the other of Specialization, by which other, or even these
same words, are continually taking on fresh connotation ; acquiring addi-
tional meaning by being restricted in their employment to a part only of
the occasions on which they might properly be used before. This double
movement is of sufficient importance in the natural history of language
(to which natural history the aitificial modifications ought always to have
some degree of reference), to justify our dwelling a little longer on the
nature of the twofold phenomenon, and the causes to which it owes its
existence.
§ 3. To begin with the movement of generalization. It might seem un-
necessary to dwell on the changes in the meaning of names which take
place merely from their being used ignorantly, by persons who, not having
properly mastered the received connotation of a word, apply it in a looser
and wider sense than belongs to it. This, however, is a real source of al-
terations in the language ; for when a word, from being often employed in
cases where one of the qualities which it connotes does not exist, ceases to
suggest that quality with certainty, then even those who are undet no mis-
take as to the proper meaning of the word, prefer expressing that meaning
in some other way, and leave the oj-iginal word to its fate. The word
'Squire, as standing for an owner of a landed estate ; Parson, as denoting
not the rector of the parish, but clergymen in general ; Artist, to denote
only a painter or sculptor ; are cases in point. Such cases give a clear in-
sight into the process of the degeneration of languages in periods of his-
tory when literary culture was suspended; and we are now in danger of
experiencing a similar evil through the superficial extension of the same
culture. So many persons without any thing deserving the name of edu-
cation have become writers by profession, that written language may al-
VARIATIONS IN MEANING OF TERMS. 483
most be said to be principally wielded by persons ignorant of the proper
-use of the instrument, and who are spoiling it more and more for those
who understand it. Vulgarisms, which creep in nobody knows how, are
-daily depriving the English language of valuable modes of expressing
thought. To take a present instance: the verb transpire formerly con-
veyed very expressively its correct meaning, viz., to become known through
unnoticed channels — to exhale, as it were, into publicity through invisible
pores, hke a vapor or gas disengaging itself. But of late a practice has
•commenced of employing this word, for the sake of finery, as a mere .syno-
nym of to happen : " the events which have transpired in the Crimea,"
meaning the incidents of the war. This vile specimen of bad English is
already seen in the dispatches of noblemen and viceroys ; and the time is
apparently not far distant when nobody will understand the word if used
in its proper sense. In other cases it is not the love of finery, but simple
want of education, which makes writers employ words in senses unknown
to genuine English. The use of " aggravating " for " provoking," in my
boyhood a vulgarism of the nursery, has crept into almost all newspapers,
and into many books ; and when the word is used in its proper sense, as
when writers on criminal law speak of aggravating and extenuating cir-
cumstances, their meaning, it is probable, is already misunderstood. It is
a great error to think that these corruptions of language do no harm.
Those who are struggling with the diflBcnlty (and who know by experience
how great it already is) of expressing one's self clearly with precision, find
their resources continually narrowed by illiterate writers, who seize and
twist from its purpose some form of speech which once served to convey
briefly and compactly an unambiguous meaning. It would hardly be be-
lieved how often a writer is compelled to a circumlocution by the single
vulgarism, introduced during the last few years, of using the word alone
as an abverb, only not being fine enough for the rhetoric of ambitious ig-
norance. A man will say " to which I am not alone bound by honor but
also by law," unaware that what he has unintentionally said is, that he is
not alone bound, some other person being bound with him. Formerly, if
any one said, " I am not alone responsible for this," he was understood to
mean (what alone his words mean in correct English), that he is not the
sole person responsible; but if he now used such an expression, the reader
would be confused between that and two other meanings : that he is not
only responsible but something more ; or that he is responsible not only
for this but for something besides. The time is coming when Tennyson's
<Enone could not say, " I will not die alone," lest she should be supposed
to mean that she would not only die but do something else.
The blunder of writing predicate for predict has become so widely dif-
fused that it bids fair to render one of the most useful terms irwthe sci-
entific vocabulary of Logic unintelligible. The mathematical and logical
terra " to eliminate " is undergoing a similar destruction. All who are ac-
quainted either with the proper use of the word or with its etymology
know that to eliminate a thing is to thrust it out: but those who know
nothing about it, except that it is a fine-looking phrase, use it in a sense
precisely the reverse, to denote, not turning any thing out, but bringing it
in. They talk of eliminating some truth, or other useful result, from a
mass of details.* A similar permanent deterioration in the language is
* Though no such evil consequences as take place in these instances are likely to arise from
the modem freak of writing sanatory instead of sanitary, it deserves notice as a charming
specimen of pedantry ingrafted upon ignorance. Those who thus undertake to correct the
484 OPERATIONS SUBSIDIARY TO INDUCTION.
in danger of being produced by the blanders of translators. The writers
of telegrams, and the foreign correspondents of newspapers, have gone on
so long ti'anslating demander by " to demand," without a suspicion that it
means only to ask, that (the context generally showing that nothing els©
is meant) English readers are gradually associating the English word de-
maud with sitnple asking, thus leaving the language without a term to
express a demand in its proper sense. In like manner, " transaction," the
French word for a compromise, is translated into the English word trans-
action ; while, curiously enough, the inverse change is taking place in
France, where the word " compromis " has lately begun to be used for ex-
pressing the same idea. If this continues, the two countries will have ex-
changed phrases.
Independently, however, of the generalization of names through their
ignorant misuse, there is a tendency in the same direction consistently
with a perfect knowledge of their meaning ; arising from the fact, that the
number of things known to us, and of which we feel a desire to speak,
multiply faster than the names for them. Except on subjects for which
there has been constructed a scientific terminology, with which unscientifi6
persons do not meddle, great difficulty is generally found in bringing a
new name into use ; and independently of that difficulty, it is natural to
prefer giving to -a new object a name which at least expresses its resem-
blance to something already known, since by predicating of it a name en-
tirely new we at first convey no information. In this manner the name of
a species often becomes the name of a genus ; as salt, for example, or oil/
the former of which words originally denoted only the muriate of soda,
the latter, as its etymology indicates, only olive-oil ; but which now de-
note large and diversified classes of substances resembling these in some
of their qualities, and connote only those common qualities, instead of
the whole of the distinctive properties of olive-oil and sea-salt. The words
glass and soap are used by modern chemists in a similar manner, to denote
genera of which the substances vulgarly so called are single species. And
it often happens, as in those instances, that the term keeps its special sig-
nification in addition to its more general one, and becomes ambiguous, that
is, two names instead of one.
These changes, by which words in ordinary use become more and more
generalized, and less and less expressive, take place in a still greater degree
with the words which express the complicated phenomena of mind and so-
ciety. Historians, travelers, and in general those who speak or write con-
cerning moral and social phenomena with which they are not familiarly ac-
quainted, are the great agents in this ifiodification of language. The vo-
cabulary of all except unusually instructed as well as thinking persons, is,
on such-subjects, eminently scanty. They have a certain small set of words
to which they are accustomed, and which they employ to express phenom-
ena the most heterogeneous, because they have never sufficiently analyzed
the facts to which those words correspond in their own country, to have
attached perfectly definite ideas to the words. The first English conquer-
ors of Bengal, for example, carried with them the phrase landed proprietor
into a country where the rights of individuals over the soil were extremely
different in degree, and even in nature, from those recognized in England.
Applying the term with all its English associations in such a state of
spelling of the classical English writers, are not aware that the meaning of sanatory, if there
were such a word in the language, would have reference not to the preservation of health, but
to the cure of disease.
VARIATIONS IN MEANING OF TERMS. 485
things ; to one who had only a limited right they gave an absolute right,
from another because he had not an absolute right they took away all
right, drove whole classes of people to ruin and despaii-, filled the country
with banditti, created a feeling that nothing was secure; and produced, with
the best intentions, a disorganization of society which had not been pro-
duced in that country by the most ruthless of its barbarian invaders. Yet
the usage of persons capable of so gross a misapprehension determines the
meaning of language ; and the words they thus misuse grow in generality,
until the instructed are obliged to acquiesce; and to employ those words
(first freeing them from vagueness by giving them a definite connotation)
as generic terms, subdividing the genera into species.
§ 4. While the more rapid growth of ideas than of names thus creates a
perpetual necessity for making the same names serve, even if imperfect-
ly, on a greater number of occasions; a counter-operation is going on,, by
which names become on the contrary restricted to fewer occasions, by tak-
ing on, as it were, additional connotation, from circumstances not originally
included in the meaning, but which have become connected with it in the
mind by some accidental cause. We have seen above, in the words pagan
and villain, remarkable examples of the specialization of the meaning of
words from casual associations, as well as of the generalization of it in a
new direction, which often follows.
Similar specializations are of frequent occurrence in the history even of
scientific nomenclature. " It is by no means uncommon," says Dr. Paris,
in his Pharmacologia,* " to find a word which is used to express general
characters subsequently become the name of a specific substance in which
such characters are predominant; and we shall find that some important
anomalies in nomenclature may be thus explained. The term Apaevkov,
from which the word Arsenic is derived, was an ancient epithet applied to
those natural substances which possessed strong and acrimonious proper-
ties ; and as the poisonous quality of arsenic was found to be remarkably
powerful, the term was especially applied to Orpiment, the form in which
this metal most usually occurred. So the term Verbena (quasi Serbena)
originally denoted all those herbs that were held sacred on account of their
being employed in the rites of sacrifice, as we learn from the poets ; but as
one herb was usually adopted upon these occasions, the word Verbena came
to denote that particular herb only, and it is transmitted to us to this day
under the same title, viz., Verbena or Vervain, and indeed until lately it en-
joyed the medical reputation which its sacred origin conferred upon it, for
it was worn suspended around the neck as an amulet. Vitriol, in the orig-
inal application of the word, denoted any crystalline body with a certain
degree of transparency {pitrum) ; it is hardly necessary to observe that the
term is now appropriated to a particular species : in the same manner.
Bark, which is a general term, is applied to express one genus, and by way
of eminence it has the article The prefixed, as Tlie bark ; the same obser-
vation will apply to the word Opium, which, in its primitive sense, signifies
any juice (ottoc, Succus), while it now only denotes one species^yiz., that of
the poppy. So, again, Elaterium was used by Hippocrates to signify vari-
ous internal applications, especially purgatives, of a violent and drastic na-
ture (from the word i\a.vv<a, agito, moveo, stimulo), but by succeeding au-
thors it was exclusively applied to denote the active matter which subsides
* Historical Introduction, vol. i. , pp. 66-68.
486 OPERATIONS SUBSIDIARY TO INDUCTION.
from the juice of the wild cucumber. The word Feeula, again, originally-
meant to imply any substance which was derived by spontaneous subsid-
ence from a liquid (from fmx, the grounds or settlement of any liquor) ;.,
afterward it was applied to Starch, which is deposited in this manner by
agitating the flour of wheat in water ; and, lastly, it has been applied to a
peculiar vegetable principle, which, like starch, is insoluble in cold, but com-
pletely soluble in boiling water, with which it forms a gelatinous solution.
This indefinite meaning of the word feeula has created numerous mistake*
in pharmaceutic chemistry ; Elaterium, for instance, is said to be feeula,.
and, in the original sense of the word, it is properly so called, inasmuch as
it is procured from a vegetable juice by spontaneous subsidence, but in the-
limited and modern acceptation of the term it conveys an erroneous idea ;.
for instead of the active principle of the juice residing in feeula, it is a pe-
culiar proximate principle, sui generis, to which I have ventured to bestow
the name of Matin. For the same reason, much doubt and obscurity in-
volve the meaning of the word Extract, because it is applied generally to
any substance obtained by the evaporation of a vegetable solution, and
specifically to a peculiar proximate principle, possessed of certain charac-
ters, by which it is distinguished from every other elementary body."
A generic term is always liable to become thus limited to a single spe-
cies, or even individual, if people have occasion to think and speak of that
individual or species much oftener than of any thing else which is contain-
ed in the genus. Thus by cattle, a stage-coachman will understand horses;
beasts, in the language. of agriculturists, stands for oxen; and birds, with
some sportsmen, for partridges only. The law of language which operates
in these trivial instances is the very same in conformity to which the terms
QtoQ, Deus, and God, were adopted from Polytheism by Christianity, to ex-
press the single object of its own adoration. Almost all the terminology
of the Christian Church is made up of words originally used in a much
more general acceptation : Ecclesia, Assembly ; Bishop, Episcopus, Overseer ;
Priest, Presbyter, Elder ; Deacon, Diaconus, Administrator ; Sacrament, a
vow of allegiance ; Evangelium, good tidings ; and some words, as Minister y
are still used both in the general and in the limited sense. It would be in-
teresting to trace the progress by which author came, in its most familiar
sense, to signify a writer, and ■Koiiyn\^, or maker, a poet.
Of the incorporation into the meaning of a term, of circumstances acci-
dentally connected with it at some particular period, as in the case of Pa-
gan, instances might easily be multiplied. Physician (^uo-iVoc, or natural-
ist) became, in England, synonymous with a healer of diseases, because
until a comparatively late period medical practitioners were the only natu-
ralists. Glerc, or clericus, a scholar, came to signify an ecclesiastic, because
the clergy were for many centuries the only scholars.
Of all ideas, however, the most liable to cling by association to any thing
with which they have ever been connected by proximity, are those of our
pleasures and pains, or of the things which we habitually contemplate as
sources of our pleasures or pains. The additional connotation, therefore,
which a woi:d soonest and most readily takes on, is that of agreeableness
or painfulness, in their various kinds and degrees ; of being a good or bad
thing ; desirable or to be avoided ; an object of hatred, of dread, contempt,
admiration, hope, or love. Accordingly there is hardly a single name, ex-
pressive of any moral or social fact calculated to call forth strong affections-
either of a favorable or of a hostile nature, which does not carry with it de-
cidedly and irresistibly a connotation of those strong affections, or, at the
TERMINOLOGY AND NOMENCLATURE. 48'i!
least, of approbation or censure ; insomuch tiiat to employ those names la
conjunction with others by which the contrary sentiments were expressed,,
would produce the effect of a paradox, or even a contradiction in terms.
Tlie baneful influence of a connotation thus acquired, on the prevailing hab-
its of thought, especially in morals and politics, has been well pointed out.
on many occasions by Bentham. It gives rise to the fallacy of " question-beg-
ging names." The very property which we are inquiring whether a thing-
possesses or not, has become so associated *ith the name of the thing as to-
be part of its meaning, insomuch that by merely uttering the name we as-
sume the point which was to be made out ; ore of the most frequent sources-
of apparently self-evident propositions.
Without any further multiplication of examples to illustrate the changes-
which usage is continually making in the signification of terms, I shall add,,
as a practical rule, that the logician, not being able to prevent such transfor-
mations, should submit to them with a good grace when they are irrevocably
effected, and if a definition is necessary, define the word according to its new
meaning ; retaining the former as a second signification, if it is needed, and
if there is any chance of being able to preserve it either in the language of
philosophy or in common use. Logicians can not make the meaning of any
but scientific terms ; that of all other words is made by the collective hu-
man race. But logicians can ascertain clearly what it is which, working
obscurely, has guided the general mind to a particular employment of a
name; and when they have found this, they can clothe it in such distinct
and permanent terras, that mankind shall see the meaning which before
they only felt, and shall not suffer it to be afterward forgotten or misappre-
hended.
CHAPTER VI.
THE PEmCIPLBS OF A PHILOSOPHICAL LANGUAGE FUKTHBE CONSIDEEED..
§ 1. Wb have, thus far, considered only one of the requisites of a lan-
guage adapted for the investigation of truth ; that its terms shall each of
them convey a determinate and unmistakable meaning. There are, howev-
er, as we have already remarked, other requisites ; some of them important
only in the second degree, but one which is fundamental, and barely yields,
in point of importance, if it yields at all, to the quality which we have al-
ready discussed at so much length. That the language may be fitted for
its purposes, not only should every word perfectly express its meaning, but,
there should be no important meaning without its word. Whatever we
have occasion to think of often, and for scientific purposes, ought to have
a name appropriated to it.
This requisite of philosophical language may be considered under three
different heads ; that number of separate conditions being involved in it.
§ 2, First, there ought to be all such names, as are needful for making-
such a record of individual observations that the words of the record shall
exactly show what fact it is which has been observed. In other words,,
there should be an accurate Descriptive Terminology.
The only things which we can observe directly being our own sensations,,
or other feelings, a complete descriptive language would be one in which
there should be a name for every variety of elementary sensation or feel-
488 OPERATIONS SUBSIDIARY TO INDUCTION.
ing. Combinations of sensations or feelings may always be described, if
we have a name for each of the elementary feelings which "compose them;
Tiut brevity of description, and clearness (which often depends very much
on brevity), are greatly promoted by giving distinctive names not to the
■elements alone, but also to all combinations which are of frequent recur-
rence. On this occasion I can not do better than quote from Dr. Whe-
■well* some of the excellent remarks which he has made on this important
branch of our subject.
" The meaning of [descriptive] technical terms can be fixed in the first
Instance only by convention, and can be made intelligible only by present-
ing to the senses that which the terms are to signify. The knowledge of
a color by its name can only be taught through the eye. No description
oan convey to a hearer what we mean by apple-green or French gray.
It might, perhaps, be supposed that, in the first example, the terra apple,
referring to so familiar an object, sufficiently suggests the color intended.
But it may easily be seen that this is not true; for apples are of many dif-
ferent hues of green, and it is only by a conventional selection that we can
appropriate the term to one special shade. When this appropriation is
once made, the terra refers to the sensation, and not to the parts of the
term ; for these enter into the compound merely as a help to the meraory,
whether the suggestion be a natural connection as in ' apple-green,' or a
casual one as in 'French gray.' In order to derive due advantage from
technical terras of the kind, they must be associated immediately with the
perception to which they belong ; and not connected with it through the
vague usages of common language. The meraory must retain the sensa^
tion ; and the technical word must be understood as directly as the most
familiar word, and more distinctly. When we find such terms as tin-white
or pinchbeck-brown, the metallic color so denoted ought to start up in our
memory without delay or search.
" This, which it is most important to recollect with respect to the sim-
pler properties of bodies, as color and form, is no less true with respect to
more compound notions. In all cases the term is fixed to a peculiar mean-
ing by convention ; and the student, in order to use the word, must be com-
pletely familiar with the convention, so that he has no need to frame con-
jectures from the word itself. Such conjectures would always be insecure,
and often erroneous. Thus the term papilionaceous applied to a flower is
employed to indicate, not only a resemblance to a butterfly, but a resem-
blance arising from five petals of a certain peculiar shape and arrangement;
and even if the resemblance were much stronger than it is in such cases,
yet, if it were produced in a different way, as, for example, by one petal, or
two only, instead of a ' standard,' two « wings,' and a ' keel ' consisting of
two parts more or less united into one, we should be no longer justified in
speaking of it as a ' papilionaceous ' flower."
When, however, the thing named is, as in this last case, a combination
of simple sensations, it is not necessary, in order to learn the meaning of
the word, that the student should refer back to the sensations themselves ;
it may be comraunicated to him through the medium of other words ; the
terras, in short, may be defined. But the names of elementary sensations,
or elementary feelings of any sort, can not be defined ; nor is there any
mode of making their signification known but by making the learner ex-
perience the sensation, or referring him, through some known mark, to his
* History of Scientific Ideas, ii., 110, 111.
TERMINOLOGY AND NOMENCLATURE. 48»
remembi-nnce of having experienced it before. Hence it is only the im-
pressions on the outward senses, or those inward feelings which are con-
nected in a very obvious and uniform manner with outward objects, that
are really susceptible of an exact descriptive language. The countless va-
riety of sensations which arise, for instance, from disease, or from peculiar
physiological states, it would be in vain to attempt to name ; for as no one
can judge whether the sensation I have is the same with his, the name can
not have, to us two, real community of meaning. The same may be said,
to a considerable extent, of purely mental feelings. But in some of the
sciences which are conversant with external objects, it is scarcely possible
to surpass the perfection to which this quality of a philosophical language
has been carried.
"The formation* of an exact and extensive descriptive language for
botany has been executed with a degree of skill and felicity, which, before
it was attained, could hardly have been dreamed of as attainable. Eveiy
part of a plant has been named ; and the form of every part, even the most
minute, has had a large assemblage of descriptive terms appropriated to
it, by means of which the botanist can convey and receive knowledge of
form and structure, as exactly as if each minute part were presented to
him vastly magnified. This acquisition was part of the Linntean re-
form 'Tournefort,' says DecandoUe, 'appears to have been the first
who really perceived the utility of fixing the sense of terms in such a way
as always to employ the same word in the same sense, and always to ex-
press the same idea by the same words; but it was Linnaeus who really
created and fixed this botanical language, and this is his fairest claim to-
glory, for by this fixation of language he has shed clearness and precision
over aU parts of the science.'
"It is not necessary here to give any detailed account of the terms of
botany. The fundamental ones have been gradually introduced, as the
parts of plants were more carefully and minutely examined. Thus the
flower was necessarily distinguished into the calyx, the corolla, the sta-
mens, and the pistils; the sections of the corolla were termed petals by
Columna; those of the calyx were called sepals by Necker. Sometimes
terras of greater generality were devised ; as perianth, to include the calyx
and corolla, whether one or both of these were present ; pericarp, for the-
part inclosing the grain, of whatever kind it be, fruit, nut, pod, etc. And
it may easily be imagined, that descriptive terms may, by definition and
combination, become very numerous and distinct. Thus leaves may b&
called pinnatifid,pinnaiipartite, pinnatisect, pinnatilohate, palmatifid, pal-
matipartite, etc., and each of these words designates different combinations-
of the modes and extent of the divisions of the leaf with the divisions of
its outline. In some cases, arbitrary numerical relations are introduced
into the definition : thus, a leaf is called bilobate, when it is divided into-
two parts by a notch ; but if the notch go to the middle of its length, it
is bifid; if it go near the base of the leaf, it is bipartite; if to the base, it
is bisect. Thus, too, a pod of a cruciferous plant is a siliqua, if it is four
times as long as it is broad, but if it be shorter than this it is a silicula.
Such terras being established, the form of the very complex leaf or frond
of a fern (Hymenophyllum Wilsotii) is exactly conveyed by the foUowing^
phrase : ' fronds rigid pinnate, pinnae recurved subunikteral, pinnatifid, the ,
segments linear undivided or bifid, spinuloso-serrate.'
* History of Scientific Ideas, ii. , 111-113.
490 OPERATIONS SUBSIDIARY TO INDUCTION.
"Other characters, as well as form, are conveyed with the like precision;
Color by means of a classified scale of colors This was done with
most precision by Werner, and his scale of colors is still the most usual
standard of naturalists. Werner also introduced a more exact terminology
with regard to other characters which are important in mineralogy, as lustre,
hardness. But Mohs improved upon this step by giving a numerical scale
of hardness, in which talc is 1 , gypsum 2, calc spar 3, and so on Some
properties, as specific gravity, by their definition give at once a numerical
measure ; and others, as crystalline form, require a very considerable array
of mathematical calculation and reasoning, to point out their relations and
gradations."
§ 3. Thus far of Descriptive Terminology, or of the language requisite
for placing on record our observation of individual instances. But when
we proceed from this to Induction, or rather to that comparison of ob-
served instances which is the preparatory step toward it, we stand in need
of an additional and a different sort of general names.
Whenever, for purposes of Induction, we find it necessary to introduce
(in Dr. Whewell's phraseology) some new general conception ; that is,
whenever the comparison of a set of phenomena leads to the recognition
in them of some common circumstance, which, our attention not having
been directed to it on any former occasion, is to us a new phenomenon ; it
is of importance that this new conception, or this new result of abstraction,
should have a name appropriated to it ; especially if the circumstance it
involves be one which leads to many consequences, or which is likely to
he found also in other classes of phenomena. No doubt, in most cases of
the kind, the meaning might be conveyed by joining together several
words already in use. But when a thing has to be often spoken of, thei'e
:are more reasons than the saving of time> and space, for speaking of it in
the most concise manner possible. What darkness would be spread over
geometrical demonstrations, if wherever the word eircle is used, the defini-
tion of a circle were inserted instead of it. In mathematics and its appli-
cations, where the nature of the processes demands that the attention
should be strongly concentrated, but does not require that it should be
widely diffused, the importance of concentration also in the expressions
has always been duly felt; and a mathematician no sooner finds that he
•shall often have occasion to speak of the same two things together, than he
-at once creates a term to express them whenever combined : just as, in his
algebraical operations, he substitutes for (a" -1-6°) :^, or for t-\ — |--j-|- etc.,
1 0 C Co
the single letter P, Q, or S; not solely to shorten his symbolical ex-
pressions, but to simplify the purely intellectual part of his operations, by
■enabling the mind to give its exclusive attention to the relation between
the quantity S and the other quantities which enter into the equation,
without being distracted by thinking unnecessarily of the parts of which
•S is itself composed.
But there is another reason, in addition to that of promoting perspicui-
ty, for giving a briej and compact name to each of the more considerable
results of abstraction which are obtained in the course of our intellectual
phenomena. By naming them, we fix our attention upon them ; we keep
them more constantly before the mind. The names are remembered, and
being remembei-ed, suggest their definition ; while if instead of specific
TERMINOLOGY AND NOMENCLATURE. 491
and characteristic names, the meaning had been expressed by putting to-
gether a number of other names, that particular combination of words al-
ready in common use for other purposes would have had nothing to make
itself remembered by. If we want to render a particular combination of
ideas permanent in the mind, there is nothing which clinches it like a
name specially devoted to express it. If mathematicians had been obliged
to speak of " that to which a quantity, in increasing or diminishing, is al-
ways approaching nearer, so that the difference becomes less than any as-
•signable quantity, but to which it never becomes exactly equal," instead
of expressing all this by the simple phrase, " the limit of a quantity," we
should probably have long remained without most of the important truths
which have been discovered by means of the relation between quantities of
various kinds and their limits. If instead of speaking of momentum, it
had been necessary to say, " the product of the number of units of velocity
in the velocity by the number of units of mass in the mass," many of the
dynamical truths now apprehended by means of this complex idea would
probably have escaped notice, for want of recalling the idea itself with
sufficient readiness and familiarity. And on subjects less remote from the
topics of popular discussion, whoever wishes to draw attention to some
new or unfamiliar distinction among things, will find no way so sure as to
invent or select suitable names for the express purpose of marking it.
A volume devoted to explaining what the writer means by civilization,
does not raise so vivid a conception of it as the single expression, that Civ-
ilization is a different thing from Cultivation; the compactness of that
brief designation for the contrasted quality being an equivalent for a long
discussion. So, if we would impress forcibly upon the understanding and
memory the distinction between the two different conceptions of a repre-
sentative government, we cdn not more effectually do so than by saying
that Delegation is not Representation. Hardly any original thoughts on
mental or social subjects ever make their way among mankind, or assume
their proper importance in the minds even of their inventors, until aptly-
selected words or phrases have, as it were, nailed them down and held
them fast.
§ 4. Of the three essential parts of a philosophical language, we have
now mentioned two : a terminology suited for describing with precision
the individual facts observed ; and a name for every common property of
any importance or interest, which we detect by comparing those facts ; in-
cluding (as the concretes corresponding to those abstract terms) names for
the classes which we artificially construct in virtue of those properties, or
as many of them, at least, as we have frequent occasion to predicate any
thing of.
But there is a sort of classes, for the recognition of which no such elab-
orate process is necessary ; because each of them is marked out from all
others not by some one property, the detection of which may depend on a
■difficult act of abstraction, but by its properties generally. I mean, the
Kinds of things, in the sense which, in this treatise, has been specially at-
tached to that term. By a Kind, it will be remembered, we mean one of
those classes which are distinguished from all others not by one or a few
definite properties, but by an unknown multitude of them ; the combina-
tion of properties on which the class is grounded, being a mere index to
an indefinite number of other distinctive attributes. The class horse is a
Kind, because the things which agree in possessing the characters by which
492 OPERATIONS SUBSIDIARY TO INDUCTION.
we recognize a horse, agi-ee in a great number of other properties, as we
know, and, it can not be doubted, in many more than we know. Animal,
again, is a Kind, because no definition that could be given of the name-
animal could eitlier exhaust the properties common to all animals, or sup-
ply premises from which the remainder of those properties "COuld be in-
ferred. But a combination of properties which does not give evidence of
the existence of any other independent peculiarities, does not constitute a
Kind. White horse, therefore, is not a Kind ; because horses which agree
in whiteness, do not agree in any thing else, except the qualities common
to all horses, and whatever may be the causes or effects of that particular
color.
On the principle that there should be a name for every thing which we
have frequent occasion to make assertions about, there ought evidently to-
be a name for every Kind ; for as it is the very meaning of a Kind that
the individuals composing it have an indefinite multitude of properties in
common, it follows that, if not with our present knowledge, yet with that
which we may hereafter acquire, the Kind is a subject to which there will-
have to be applied many predicates. The third component element of a
philosophical language, therefore, is that there shall be a name for every
Kind. In other words, there must not only be a terminology, but also a
nomenclature.
The words Nomenclature and Terminology are employed by most au-
thors almost indiscriminately ; Dr. Whewell being, as far as I am aware,
the first writer who has regularly assigned to the two words different
meanings. The distinction, however, which he has drawn between them
being real and important, his example is likely to be followed ; and (as is-
apt to be the case when such innovations in language are felicitously made)
a vague sense of the distinction is found to have influenced the employ-
ment of the terms in common practice, before the expediency had beea
pointed out of discriminating them philosophically. Every one would say
that the reform effected by Lavoisier and Guyton-Morveau in the language
of chemistry consisted in the introduction of a new nomenclature, not of a
new terminology. Linear, lanceolate, oval, or oblong, serrated, dentate, or
crenate leaves, are expressions forming part of the terminology of botany^
while the names "Viola odorata," and "TJlex Europasus," belong to its^
nomenclature.
A nomenclature may be defined, the collection of the names of all the
Kinds with which any branch of knowledge is conversant; or more prop-
erly, of all the lowest Kinds, or infirmce, species — those which may be sub-
divided indeed, but not into Kinds, and which generally accord with what
in natural history are termed simply species. Science possesses two splen-
did examples of a systematic nomenclature; that of plants and animals,,
constructed by Linnaeus and his successors, and that of chemistry, which
we owe to the illustrious group of chemists who flourished in France to-
ward the close of the eighteenth century. In these two departments, not
only has every known species, or lowest Kind, a name assigned to it, but
when new lowest Kinds are discovered, names are at once given to them
on a uniform principle. In other sciences the nomenclature is not at pres-
ent constructed on any system, either because the species to be named are
not numerous enough to require one (as in geometry, for example), or be-
cause no one has yet suggested a suitable principle for such a system, as
in mineralogy ; in which the want of a scientiflcally constructed nomencla-
ture is now the principle cause which retards the progress of the science.
TERMINOLOGY AND NOMENCLATURE. 493
§ 5. A word which carries on its face that it belongs to a nomenclature,
seems at first sight to differ from other concrete general names in this —
that its meaning does not reside in its connotation, in the attributes im-
plied in it, but in its denotation, that is, in the particular group of things
which it is appointed to designate ; and can not, therefore, be unfolded by
means of a definition, but must be made known in another way. This
opinion, however, appears to me erroneous. Woi'ds belonging to a no-
menclature differ, I conceive, from other words mainly in this, that besides
the ordinary connotation, they have a peculiar one of their own : besides
■connoting certain attributes, they also connote that those attributes are
distinctive of a Kind. The term " peroxide of iron," for example, belong-
ing by its form to the systematic nomenclature of chemistry, bears on its
face that it is the name of a peculiar Kind of substance. It moreover con-
notes, like the name of any other class, some portion of the properties
•common to the class ; in this instance the pi-operty of being a compound
of iron and the largest dose of oxygen with which iron will combine.
These two things, the fact of being such a compound, and the fact of being
a Kind, constitute the connotation of the name peroxide of iron. When
we say of the substance before us, that it is the peroxide of iron, we there-
by assert, first, that it is a compound of iron and a maximum of oxygen,
and next, that the substance so composed is a peculiar Kind of substance.
Now, this second part of the connotation of any word belonging to a
nomenclature is as essential a portion of its meaning as the first part, while
the definition only declares the first ; and hence the appearance that the
signification of such terms can not be conveyed by a definition : which ap-
pearance, however, is fallacious. The name Viola odorata denotes a Kind,
of which a certain number of characters, suflBcient to distinguish it, are
enunciated in botanical works. This enumeration of characters is surely,
as in other cases, a definition of the name. N"o, say some, it is not a defi-
nition, for the name Viola odorata does not mean those characters; it means
that particular group of plants, and the characters are selected from among
a much greater number, merely as marks by which to recognize the group.
But to this I reply, that the name does not mean that group, for it would
be applied to that group no longer than while the group is believed to be
an inflma species ; if it were to be discovered that several distinct Kinds
have been confounded under this one name, no one would any longer ap-
ply the name Viola odorata to the whole of the group, but would apply it,
if retained at all, to one only of the Kinds retained therein. What is im-
perative, therefore, is not that the name shall denote one particular collec-
tion of objects, but that it shall denote a Kind, and a lowest Kind. The
form of the name declares that, happen what will, it is to denote an infima
species; and that, therefore, the properties which it connotes, and which
are expressed in the definition, are to be connoted by it no longer than
while we continue to believe that those properties, when found together,
indicate a Kind, and that the whole of them are found in no more than one
Kind.
With the addition of this peculiar connotation, implied in the form of
every word which belongs to a systematic nomenclature ; the set of char-
acters which is employed to discriminate each Kind from all other Kinds
(and which is a real definition) constitutes as completely as in any oth-
er case the whole meaning of the term. It is no objection to say that
(as is often the case in natural history) the set of characters may be
changed, and another substituted as being better suited for the purpose
4g4 OPERATIONS SUBSIDIARY TO INDUCTION.
of distinction, while tbe word, still continuing to denote the same group or
things, is not considered to have changed its meaning. For this is no more
than may happen in the case of any other general name : we may, in re-
forming its connotation, leave its denotation untouched ; and it is general-
ly desirable to do so. The connotation, however, is not the less for this
the real meaning, for we at once apply the name wherever the characters
set down in the definition are found ; and that which exclusively guides
us in applying the term, must constitute its signification. If we find, con-
trary to our previous belief, that the characters are not peculiar to one spe-
cies, we cease to use the term co-extensively with the characters ; but thea
it is because the other portion of the connotation fails ; the condition that
the class must be a Kind. The connotation, therefore, is still the meaning ;
the set of descriptive characters is a true definition ; and the meaning is
unfolded, not indeed (as in other cases) by the definition alone, but by the
definition and the form of the word taken together.
§ 6. We have now analyzed what is implied in the two principal requisites
"of a philosophical language ; first, precision, or definiteness; and, secondly,
completeness. Any further remarks on the mode of constructing a nomen-
clature must be deferred until we treat of Classification ; the mode of naming
the Kinds of things being necessarily subordinate to the mode of arranging
those Kinds into larger classes. With respect to the minor requisites of
terminology, some of them are well stated and illustrated in the "Aphorisms
concerning the Language of Science,'' included in Dr. Whewell's Philosophy
of the Inductive Sciences. These, as being of secondary importance in the
peculiar point of view of Logic, I shall not farther refer to, but shall confine
my observations to one more quality, which, next to the two already treat-
ed of, appears to be the most valuable which the language of science can
possess. Of this quality a general notion may be conveyed by the follow-
ing aphorism :
Whenever the nature of the subject permits our reasoning processes to
be, without danger, carried on mechanically, the language should be con-
structed on as mechanical principles as possible ; while, in the contrary
case, it should be so constructed that there shall be the greatest possible ob-
stacles to a merely mechanical use of it.
I am aware that this maxim requires much explanation, which I shall at
once proceed to give. At first, as to what is meant by using a language
mechanically. The complete or extreme case of the mechanical use of lan-
guage, is when it is used without any consciousness of a meaning, and with
only the consciousness of using certain visible or audible marks in con-
formity to technical rules previously laid down. This extreme case is no-
where realized except in the figures of arithmetic, and still more the sym-
bols of algebra, a language unique in its kind, and approaching as nearly to
perfection, for the purposes to which it is destined, as can, perhaps, be
said of any creation of the human mind. Its perfection consists in the
completeness of its adaptation to a purely mechanical use. The symbols are
mere countei'S, without even the semblance of a meaning apart from the
convention which is renewed each time they are employed, and which is al-
tered at each renewal, the same symbol a or x being used on different oc-
casions to represent things which (except that, like all things, they are sus-
ceptible of being numbered) have no property in common. Thei-e is noth-
ing, therefore, to distract the mind from the set of mechanical operations
which are to be performed upon the symbols, such as squaring both sides;
TERMINOLOGY AND NOMENCLATURE. 495
of the equation, multiplying or dividing them by the same or by equivalent
symbols, and so forth. Each of these operations, it is true, corresponds to
a syllogism ; represents one step of a ratiocination relating not to the sym-
bols, but to the things signified by them. But as it has been found practi-
cable to frame a technical form, by conforming to which we can make sui'e
of finding the conclusion of the ratiocination, our end can be completely at-
tained without our ever thinking of any thing but the symbols. Being
thus intended to work merely as mechanism, they have the qualities which
mechanism ought to have. They are of the least possible bulk, so that they
take up scarcely any room, and waste no time in their manipulation ; they
are compact, and fit so closely together that the eye can take in the whole
at once of almost every operation which they are employed to perform.
These admirable properties of the symbolical language of mathematics,
have made so strong an impression on the minds of many thinkers, as to
have led them to consider the symbolical language in question as the ideal
type of philosophical language generally ; to think that names in general, or
(as they are fond of calling them) signs, are fitted for the purposes of
thought in proportion as they can be made to approximate to the compact-
ness, the entire unmeaningness, and the capability of being used as counters
without a thought of what they represent, which are chai'acteristic of the a
and i, the x and y, of algebra. This notion has led to sanguine views of
the acceleration of the progress of science by means which, I conceive, can
not possibly conduce to that end, and forms part of that exaggerated esti-
mate of the influence of signs, which has contributed in no small degree to
prevent the real laws of our intellectual operations from being rightly un-
derstood.
In the first place, a set of signs by which we reason without consciousness
of their meaning, can be sei'viceable, at most, only in our deductive opera-
tions. In our direct inductions we can not for a moment dispense with a
distinct mental image of the phenomena, since the whole operation turns
on a perception of the particulars in which those phenomena agree and dif-
fer. But, further, this reasoning by counters is only suitable to a very lim-
ited portion even of our deductive processes. In our reasonings respecting
numbers, the only general principles which we ever have occasion to intro-
duce are these, Things which are equal to the same thing are equal to one
another, and The sums or differences of equal things are equal ; with thei;-
various corollaries. Not only can no hesitation ever arise respecting the ap-
plicability of these principles, since they are true of all magnitudes what-
ever; but every possible application of which they are susceptible, may be
reduced to a technical rule ; and such, in fact, the rules of the calculus are.
But if the symbols represent any other things than mere numbers, let us
say even straight or curve lines, we have then to apply theorems of geom-
etry not true of all lines without exception, and to select those which are
true of the lines we are reasoning about. And how can we do this unless
we keep completely in mind what particular lines these are? Since ad-
ditional geometrical truths may be introduced into the ratiocination in any
stage of its progress, we can not suffer ourselves, during even the smallest
part of it, to use the names mechanically (as we use algebraical symbols)
without an image annexed to them. It is only after ascertaining that the
solution of a question concerning lines can be made to depend on a previous
question concerning numbers, or, in other words, after the question has been
(to speak technically) reduced to an equation, that the unmeaning signs be-
come available, and that the nature of the facts themselves to which the in-
496 OPERATIONS SUBSIDIARY TO INDUCTION.
vestigation relates can be dismissed from the mind. Up to the establish-
ment of the equation, the language in which mathematicians carry on their
reasoning does not differ in character from that .employed by close reason-
€rs on any other kind of subject.
I do not deny that every correct ratiocination, when thrown into the syl-
logistic shape, is conclusive from the mere form of the expression, provided
none of the terms used be ambiguous ; and this is one of the circumstances
-which have led some writers to think that if all names were so judicious-
ly constructed and so carefully defined as not to admit of any ambiguity,
the improvement thus made in language would not only give to the con-
clusions of every deductive science the same certainty with those of mathe-
matics, but would reduce all reasonings to the application of a technical
iorm, and enable their conclusiveness to be rationally assented to after a
merely mechanical process, as is undoubtedly the case in algebra. But, if
we except geometry, the conclusions of which are already as certain and
«xact as they can be made, there is no science but that of number, in which
the practical validity of a reasoning can be apparent to any person who has
looked only at the reasoning itself. Whoever has assented to what was
said in the last Book concerning the case of the Composition of Causes,
and the still stronger case of the entire supersession of one set of laws by
another, is aware that geometry and algebra are the only sciences of which
the propositions are categorically true ; the general propositions of all oth-
er sciences are true only hypothetically, supposing that no counteracting
cause happens to interfere. A conclusion, therefore, however correctly de-
duced, in point of form, from admitted laws of nature, will have no other
than an hypothetical certainty. At every step we must assure ourselves
that no other law of nature has superseded, or intermingled its operation
with, those which are the premises of the reasoning ; and how can this be
done by merely looking at the words ? We must not only be constantly
thinking of the phenomena themselves, but we must be constantly studying
them ; making ourselves acquainted with the peculiarities of every case to
which we attempt to apply our general principles.
The algebraic notation, considered as a philosophical language, is per-
fect in its adaptation to the subjects for which it is commonly employ-
ed, namely those of which the investigations have already been reduced
to the ascertainment of a relation between numbers. But, admirable as
it is for its own purpose, the properties by which it is rendered such
are so far from constituting it the ideal model of philosophical language
in general, that the more nearly the language of any other branch of
science approaches to it, the less fit that language is for its own proper
functions. On all other subjects, instead of contrivances to prevent our at-
tention from being distracted by thinking of the meaning of our signs, we
ought to wish for contrivances to make it impossible that we should ev^r
lose sight of that meaning even for an instant.
With this view, as much meaning as possible should be thrown into the
formation of the word itself; the aids of derivation and analogy being
made available to keep alive a consciousness of all that is signified by it.
In this respect those languages have an immense advantage which form their
compounds and derivatives from native roots, like the German^ and not from
those of a foreign or dead language, as is so much the case with English,
French, and Italian ; and the best are those which form them according to
fixed analogies, corresponding to the relations between the ideas to be ex-
pressed. All languages do this more or less, but especially, among modern
CLASSIFICATION. 497
European languages, the German ; while even that is inferior to the Greek,
in which the relation between the meaning of a derivative word and that
of its primitive is in general clearly marked by its mode of formation, ex-
cept in the case of words compounded with prepositions, which are often,
in both those languages, extremely anomalous.
But all that can be done, by the mode of constructing words, to prevent
them from degenerating into sounds passing through the mind without any
distinct apprehension of what they signify, is far too little for the necessity
of the case. "Words, however well constructed originally, are always tend-
ing, Uke coins, to have their inscription worn off by passing from hand to
hand ; and the only possible mode of reviving it is to be ever stamping
it afresh, by living in the habitual contemplation of the phenomena them-
selves, and not resting in our familiarity with the words that express them.
If any one, having possessed himself of the laws of phenomena as recorded
in words, whether delivered to him originally by others, or even found out
by himself, is content from thenceforth to live among these formulae, to
think exclusively of them, and of applying them to cases as they arise, with-
out keeping up his acquaintance with the realities from which these laws
were collected — not only will he continually fail in his practical efforts, be-
cause he will apply his formulae without duly considering whether, in this
■case and in that, other laws of nature do not modify or supersede them ;
but the formulae themselves will progressively lose their meaning to him,
and he will cease at last even to be capable of recognizing with certainty
whether a case falls within the contemplation of his formula or not. It is,
in short, as necessary, on all subjects not mathematical, that the things on
which we reason should be conceived by us in the concrete, and " clothed
in circumstances," as it is in algebra that we should keep all individualiz-
ing peculiarities sedulously out of view.
With this remark we close our observations on the Philosophy of Lan-
CHAPTER VII.
OF CLASSIFICATION, AS SUBSIDIARY TO INDUCTION.
§ 1. There is, as has been frequently remarked in this work, a classifi-
cation of things, which is inseparable from the fact of giving them general
names. Every name which connotes an attribute, divides, by that very
fact, all things whatever into two classes, those which have the attribute
and those which have it not ; those of which the name can be predicated,
and those of which it can not. And the division thus made is not merely
a division of such things as actually exist, or are known to exist, but of all
such as may hereafter be discovered, and even of all which can be imagined.
On this kind of Classification we have nothing to add to what has previ-
ously been said. The Classification which requires to be discussed as a sep-
arate act of the mind, is altogether different. In the one, the arrangement
of objects in groups, and distribution of them into compartments, is a mere
incidental effect consequent on the use of names given for another purpose,
namely that of simply expressing some of their qualities. In the other, the
arrangement and distribution are the main object, and the naming is sec-
ondary" to, and purposely conforms itself to, instead of governing, that
more important operation.
32
498 OPERATIONS SUBSIDIARY TO INDUCTION.
Classification, thus regarded, is a contrivance for the best possible orders
ing of the ideas of objects in our minds ; for causing the ideas to accom-
pany or succeed one another in such a way as shall give us the greatest
command over our knowledge already acquired, and lead most directly to*
the acquisition of more. The general problem of Classification, in refer-
ence to these purposes, may be stated as follows : To provide that things
shall be thought of in such groups, and those groups in such an order, as-
will best conduce to the remembrance and to the ascertainment of their
laws.
Classification thus considered, differs from classification in the wider
sense, in having reference to real objects exclusively, and not to all that are
imaginable : its object being the due co-ordination in our minds of those
things only, with the properties of which we have actually occasion to make
ourselves acquainted. But, on the other hand, it embraces all really ex-
isting objects. We can not constitute any one class properly, except in
reference to a general division of the whole of nature ; we can not deter-
mine the group in which any one object can most conveniently be placed,,
without taking into consideration all the varieties of existing objects, all at
least which have any degree of affinity with it. No one family of plants
or animals could have been rationally constituted, except as part of a sys-
tematic arrangement of all plants or animals; nor could such a general ar-
rangement have been properly made, without first determining the exact
place of plants and animals in a general division of nature.
§ 2. There is no property of objects which may not be taken, if we
please, as the foundation for a classification or mental grouping of those
objects ; and in our first attempts we are likely to select for that purpose
properties which are simple, easily conceived, and perceptible on a first
view, without any previous process of thought. Thus Tournefort's ar-
rangement of plants was founded on the shape and divisions of the corolla;,
and that which is commonly called the Linnsean (though Linnaeus also sug-
gested another and more scientific arrangement) was grounded chiefly on
the number of the stamens and pistils.
But these classifications, which are at first recommended by the facility
they afford of ascertaining to what class any individual belongs, are seldom
much adapted to the ends of that Classification which is the subject of our
present remarks. The Linnsean arrangement answers the purpose of mak-
ing us think together of all those kinds of plants which possess the same
number of stamens and pistils ; but to think of them in that manner is of
little use, since we seldom have any thing to afiirm in common of the plants
which have a given number of stamens and pistils. If plants of the class
Pentandria, order Monogynia, agreed in any other properties, the habit of
thinking and speaking of the plants under a common designation would
conduce to our remembering those common properties so far as they were
ascertained, and would dispose us to be on the lookout for such of thera
as were not yet known. But since this is not the case, the only purpose of
thought which the Linnsean classification serves is that of causing us to re-
member, better than we should otherwise have done, the exact number of
stamens and pistils of every species of plants. Now, as this property is of
, little importance or interest, the remembering it with any particular accu-
racy is of no moment. And, inasmuch as, by habitually thinking of plants
in those groupSj we are prevented from habitually thinking of them in
groups which have a greater number of properties in common, the effect of
CLASSIFICATION. 499
|neh a classification, when systematically adhered to, upon our habits of
thought, must be regarded as mischievous.
The ends of scientific classification are best answered, when the objects
are formed into groups respecting which a greater number of general prop-
ositions can be made, and those propositions more important, than could
be made i-especting any other groups into which the same things could be
distributed. The properties, therefore, according to which objects are
classified, should, if possible, be those which are causes of many other prop-
erties; or, at any rate, which are sure marks of them. Causes are prefera-
ble, both as being the surest and most direct of marks, and as being them-
selves the properties on which it is of most use that our attention should
be strongly fixed. But the property which is the cause of the chief pecul-
iarities of a class, is unfortunately seldom fitted to serve also as the diag-
nostic of the class. Instead of the cause, we must generally select some of
its more prominent effects, which may serve as marks of the other effects
and of the cause.
A classification thus formed is properly scientific or philosophical, and
is commonly called a Natural, in contradistinction to a Technical or Arti-
ficial, classification or arrangement. The phrase Natural Classification
seems most peculiarly appropriate to such arrangements as correspond, in
the groups which they form, to the spontaneous tendencies of the mind,
by placing together the objects most similar in their general aspect ; in op-
position to those technical systems which, arranging things according to
their agreement in some circumstance arbitrarily selected, often throw into
the same group objects which in the general aggregate of their properties
present no resemblance, and into different and remote groups, others which
have the closest similarity. It is one of the most valid recommendations
of any classification to the character of a scientific one, that it shall be a
natural classification in this sense also ; for the test of its scientific charac-
ter is the number and importance of the properties which can be asserted
in common of all objects included in a group; and properties on which the
general aspect of the things depends are, if only on that ground, impor-
tant, as well as, in most cases, numerous. But, though a strong recommen-
dation, this circumstance is not a sine qua non; since the most obvious
properties of things may be of trifling importance compared with others
that are not obvious. I have seen it mentioned as a great absurdity in
the Linnsean classification, that it places (which by-the-way it does not)
the violet by the side of the oak ; it certainly dissevers natural affinities,
and brings together things quite as unlike as the oak and the violet are.
But the difference, apparently so wide, which renders the juxtaposition of
those two vegetables so suitable an illustration of a bad arrangement, de-
pends, to the common eye, mainly on mere size and texture ; now if we
made it our study to adopt the classification which would involve the least
peril of similar rapprochements, we should return to the obsolete division
into trees, shrubs, and herbs, which though of primary importance with re-
gard to mere general aspect, yet (compared even with so petty and unob-
vious a distinction as that into dicotyledons and monocotyledons) answers
to so few differences in the other properties of plants, that a classification
founded on it (independently of the indistinctness of the lines of demarka-
tion) would be as completely artificial and technical as the Linnsean.
Our natural groups, therefore, must often be founded not on the obvi-
ous but on the unobvious properties of things, when these are of greater
importance. But in such cases it is essential that there should be some
500 OPERATIONS SUBSIDIARY TO INDUCTION.
other property or set of properties, more readily recognizable by the ob»
server, which co-exist with, and may be received as marks of, the proper-
ties which are the real groundwork of the classification. A natural ar-
rangement, for example, of animals, must be founded in the main on their
internal structure, but (as M. Comte remarks) it would be absurd that we
should not be able to determine the genus and species of an animal with-
out first killing it. On this ground, the preference, among zoological clas-
sifications, is probably due to that of M. De Blainville, founded on the dif-
ferences in the external integuments ; differences which correspond, much
more accurately than might be supposed, to the really important varieties,
both in the other parts of the structure, and in the habits and history of
the animals.
This shows, more strongly than ever, how extensive a knowledge of the
properties of objects is necessary for making a good classification of them.
And as it is one of the uses of such a classification that by drawing atten-
tion to the properties on which it is founded, and which, if the classifica-
tion be good, are marks of many others, it facilitates the discovery of those
others ; we see in what manner our knowledge of things, and our classifi-
cation of them, tend mutually and indefinitely to the improvement of each
other.
We said just now that the classification of objects should follow those
of their properties which indicate not only the most numerous, but also
the most important peculiarities. What is here meant by importance ?
It has reference to the particular end in view ; and the same objects, there-
fore, may admit with propriety of several different classifications. Each
science or art forms its classification of things according to the properties
which fall within its special cognizance, or of which it must take account
in order to accomplish its peculiar practical end. A farmer does not di-
vide plants, like a botanist, into dicotyledonous and monocotyledonous, but
into useful plants and weeds. A geologist divides fossils, not like a zoolo-
gist, into families corresponding to those of living species, but into fossils
of the paleozoic, mesozoic, and tertiary periods, above the coal and below
the coal, etc. Whales are or are not fish according to the purpose for
which we are considering them. " If we are speaking of the internal struc-
ture and physiology of the animal, we must not call them fish ; for in these
respects they deviate widely from fishes ; they have warm blood, and pro-
duce and suckle their young as land quadrupeds do. But this would not
prevent our speaking of the whale-fishery, and calling such animals fish on
all occasions connected with this employment ; for the relations thus arising
depend upon the animal's living in the water, and being caught in a man-
ner similar to other fishes. A plea that human laws which mention fish do
not apply to whales, would be rejected at once by an intelligent judge."*
These different classifications are all good, for the purposes of their own
particular departments of knowledge or practice. But when we are study-
ing objects not for any special practical end, but for the sake of extending
our knowledge of the whole of their properties and relations, we must con-
sider as the most important attributes those which contribute most, either
by themselves or by their effects, to rendei'-the things like one another, and
unlike other things ; which give to the class composed of them the most
mai'ked individuality ; which fill, as it were, the largest space in their ex-
istence, and would most impress the attention of a spectator who knew all
* Nov. Org. Renov., pp. 286, 287.
CLASSIFICATION. 501
their properties but was not specially interested in any. Classes formed
on this principle may be called, in a more emphatic manner than any oth-
ers, natural groups.
§ 3. On the subject of these groups Dr. Whewell lays down a theory,
grounded on an important truth, which he has, in some respects, expressed
and illustrated very felicitously, but also, as it appears to me, with some
admixture of error. It will be advantageous, for both these reasons, to
extract the statement of his doctrine in the very words he has used.
"Natural groups," according to this theory,* are "given by Type, not
by Definition." And this consideration accounts for that " indefiniteness
and indecision which we frequently find in the descriptions of such groups,
and which must appear so strange and inconsistent to any one who does
not suppose these descriptions to assume any deeper ground of connection
than an arbitrary choice of the botanist. Thus in the family of the rose-
tree, we are told that the ovules are very rarely erect, the stigmata usually
simple. Of what use, it might be asked, can such loose accounts be ? To
which the answer is, that they are not inserted in order to distinguish the
species, but in order to describe the family, and the total relations of the
ovules and the stigmata of the family are better known by this general
statement. A similar observation may be made with regard to the Anoma-
lies of each group, which occur so commonly, that Dr. Lindley, in his In-
troduction to the Natural System of Botany, makes the 'Anomalies' an
article in each family. Thus, part of the character of the Rosacese is, that
they have alternate stipulate leaves, and that the albumen is obliterated;
but yet in Lowea, one of the genera of this family, the- stipulse are absent;
and the albumen is present in another, Neillia. This implies, as we have
already seen, that the artificial character (or diagnosis, as Mr. Lindley calls
it) is imperfect. It is, though very nearly, yet not exactly, commensurate
with the natural group ; and hence in certain cases this character is made
to yield to the general weight of natural affinities.
"These views — of classes determined by characters which can not be
expressed in words — of propositions which state, not what happens in all
cases, but only usually — of particulars which are included in a class, though
they transgress the definition of it, may probably surprise the reader.
They are so contrary to many of the received opinions respecting the use
of definitions, and the nature of scientific propositions, that they will prob-
ably appear to many persons highly illogical and unphilosophical. But a
disposition to such a judgment arises in a great measure from this, that
the mathematical and mathematico - physical sciences have, in a great de-
gree, determined men's views of the general nature and form of scientific
truth ; while Natural History has not yet had time or opportunity to exert
its due influence upon the current habits of philosophizing. The appar-
ent indefiniteness and inconsistency of the classifications and definitions of
Natural History belongs, in a far higher degree, to all other except mathe-
matical speculations ; and the modes in which approximations to exact dis-
tinctions and general truths have been made in Natural History, may be
worthy our attention, even for the light they throw upon the best modes
of pursuing truth of all kinds.
" Though in a Natural group of objects a definition can no longer be of
any use as a regulative principle, classes are not therefore left quite loose,
* History of Scientific Ideas, ii., 120-122.
602 OPERATIONS SUBSIDIARY TO INDUCTION.
without any certain standard or guide. The class is steadily fixed, though
not precisely limited ; it is given, though not circumscribed ; it is deter-
mined, not by a boundary-line without, but by a central point within ; not
by what it strictly excludes, but by what it eminently includes ; by an ex-
ample, not by a precept ; in short, instead of a Definition we have a Type
for our director.
"A Type is an example of any class, for instance a species of a genus,
which is considered as eminently possessing the character of the class. All
the species which have a greater afiinity with this type-species than with
any others, form the genus, and are arranged about it, deviating from it
in various directions and different degrees. Thus a genus may consist of
several species which approach very near the type, and of which the claim
to a place with it is obvious; while there may be other species which
straggle farther from this centi'al knot, and which yet are clearly more
connected with it than with any other. And even if there should be some
species of which the place is dubious, and which appear to be equally
bound to two generic types, it is easily seen that this would not destroy
the reality of the generic groups, any more than the scattered trees of the
intervening plain prevent our speaking intelligibly of the distinct forests
of two separate hills.
"The type-species of every genus, the type-genus of every family, is then,
one which possesses all the characters and properties of the genus in a
marked and prominent manner. The type of the Rose family has alter-
nate stipulate leaves, wants the albumen, has the ovules not erect, has the
stigmata simple, and besides these features, which distinguish it from the
exceptions or varieties of its class, it has the features which make it promi-
nent in its class. It is one of those which possess clearly several leading
attributes ; and thus, though we can not say of any one genus that it must
be the type of the family, or of any one species that it must be the type of
the genus, we are still not wholly to seek ; the type must be connected by
many aflinities with most of the others of its group ; it must be near the
centre of the crowd, and not one of the stragglers."
In this passage (the latter part of which especially I can not help no-
ticing as an admirable example of philosophic style) Dr. Whewell has
stated very clearly and forcibly, but (I think) without making all necessary
distinctions, one of the principles of a Natural Classification. "What this
principle is, what are its limits, and in what manner he seems to me to
have overstepped them, will appear when we have laid down another rule
of Natural Arrangement, which appears to me still more fundamental.
§ 4. The reader is by this time familiar with the general truth (which I
restate so often on account of the great confusion in which it is common-
ly involved), that there are in nature distinctions of Kind; distinctions
not consisting in a given number of definite properties plus the effects
which follow from those properties, but running through the whole nature,
through the attributes generally, of the things so distinguished. Our
knowledge of the properties of a Kind is never complete. We are always
discovering, and expecting to discover, new ones. Where the distinction
between two classes of things is not one of Kind, we expect to find their
properties alike, except where there is some reason for their being differ-
ent. On the contrary, when the distinction is in Kind, we expect to find
the properties different unless there be sotne cause for their being the
same. All knowledge of a Kind must be obtained by observation and
CLASSU7CATI0N. 503
experiment upon the Kind itself; no inference respecting its properties
fi-ora the properties of things not connected with it by Kind, goes for
more than the sort of presumption usually characterized as an analogy,
aud generally in one of its fainter degrees.
Since the common properties of a true Kind, and consequently the gen-
eral assertions which can be made respecting it, or which are certain to
be made hereafter as our knowledge extends, are indefinite and inexhausti-
ble ; and since the very first principle of natural classification is that of
forming the classes so that the objects composing each may have the great-
est number of properties in common; this principle prescribes that every
:such classification shall recognize and adopt into itself all distinctions of
Kind, which exist among the objects it professes to classify. To pass over
any distinctions of Kind, and substitute definite distinctions, which, how-
ever considerable they may be, do not p'oint to ulterior unknown difEer-
•euces, would be to replace classes with more by classes with fewer attri-
butes in common; and would be subversive of the Natural Method of
Classification.
Accordingly all natural arrangements, whether the reality of the distinc-
tion of Kinds was felt or not by their framers, have been led, by the mere
pursuit of their own proper end, to conform themselves to the distinctions
of Kind, so far as these have been ascertained at the time. The species
of Plants are not only real Kinds, but are probably, all of them, real lowest.
Kinds, Infimse Species; which, if we were to subdivide, as of course it is
■open to us to do, into sub-classes, the subdivision would necessarily be
founded on definite distinctions, not pointing (apart from what may be
known of their causes or effects) to any difference beyond themselves.
In so far as a natural classification is grounded on real Kinds, its groups
Jire certainly not conventional : it is perfectly true that they do not depend
upon an arbitrary choice of the naturalist. But it does not follow, nor, I
conceive, is it true, that these classes are determined by a type, and not by
characters. To determine them by a type would be as sure a way of miss-
ing the Kind, as if we were to select a set of characters arbitrarily. They
are determined by characters, but these are not arbitrary. The problem
is, to find a few definite characters which point to the multitude of indefi-
nite ones. Kinds are Classes between which there is an impassable bar-
rier; and what we have to seek is, marks whereby we may determine on
which side of the barrier an object takes its place. The characters which
will best do this should be chosen : if they are also important in them-
selves, so much the better. When we have selected the characters, we
parcel out the objects according to those characters, and not, I conceive,
according to resemblance to a type. We do not compose the species Ra-
nunculus acris, of all plants which bear a satisfactory degree of resemblance
to a model buttercup, but of those which possess certain characters select-
ed as marks by which we might recognize the possibility of a common
parentage ; and the enumeration of those characters is the definition of the
species.
The question next arises, whether, as all Kinds must have a place among
the classes, so all the classes in a natural arrangement must be Kinds?
And to this I answer, certainly not. The distinctions of Kinds are not
numerous enough to make up the whole of a classification. Very few of
the genera of plants, or even of the families, can be pronounced with cer-
tainty to be Kinds. The great distinctions of Vascular and Cellular, Di-
cotyledonous or Exogenous and Monocotyledonous or Endogenous plants,
504 OPERATIONS SUBSIDIARY TO INDUCTION.
are perhaps differences of kind ; the lines of demarkation which divide
those classes seem (though even on this I would not pronounce positively)
to go through the whole nature of the plants. But the different species
of a genus, or genera of a family, usually have in common only a limited
number of characters. A Rose does not seem to differ from a Rubus, or
the Umbelliferse from the Ranunculaeese, in much else than the characters
botanically assigned to those genera or those families. Unenumerated dif-
ferences certainly do exist in some cases; there are families of plants
which have peculiarities of chemical composition, or yield products having
peculiar effects on the animal economy. The Cruciferse and Fungi contain
an unusual proportion of nitrogen ; the Labiatse are the chief sources of
essential oils, the Solanese are very commonly narcotic, etc. In these and
similar cases there are possibly distinctions of Kind ; but it is by no means
indispensable that there should he. Genera and Families may be eminent-
ly natural, though marked out from one another by properties limited in
number; provided those properties are important, and the objects con-
tained in each genus or family resemble each other more than they resemj
ble any thing which is excluded from the genus or family.
After the recognition and definition, then, of the inJimoB species, the next
step is to arrange those infimae species into larger groups : making these
groups correspond to Kinds wherever it is possible, but in most cases with-
out any such guidance. And in doing this it is true that we are naturally
and properly guided, in most cases at least, by resemblance to a type. We
form our groups round certain selected Kinds, each of which serves as a
sort of exemplar of its group. But though the groups are suggested by
types, I can not think that a group when formed is determined by the type j
that in deciding whether a species belongs to the group, a reference is made
to the type, and not to the characters; that the characters "can not be ex-
pressed in words." This assertion is inconsistent with Dr.Whewell's own
statement of the fundamental principle of classification, namely, that "gen-
eral assertions shall be possible." If the class did not possess any charac-
ters in common, what general assertions would be possible respecting it?
Except that they all resemble each other more than they resemble any thing
else, nothing whatever could be predicated of the class.
The truth is, on the contrary, that every genus or family is framed with
distinct reference to certain characters, and is composed, first and princi-
pally, of species which agree in possessing all those characters. To these
are added, as a sort of appendix, such other species, generally in small num-
ber, as possess nearly all the properties selected ; wanting some of them
one property, some another, and which, while they agree with the rest al-
most as much as these agree with one another, do not resemble in an equal
degree any other group. Our conception of the class continues to be
grounded on the characters ; and the class might be defined, those things
which either possess that set of characters, or resemble the things that do
so, more than they resemble any thing else.
And this resemblance itself is not, like resemblance between simple sen-
sations, an ultimate fact, unsusceptible of analysis. Even the inferior de-
gree of resemblance is created by the possession of common characters.
Whatever resembles the genus Rose more than it resembles any other ge-
nus, does so because it possesses a greater number of the characters of that
genus than of the characters of any other genus. Nor can there be any
real difiiculty in representing, by an enumeration of characters, the nature
and degree of the resemblance which is strictly sufficient to include any ob*
CLASSIFICATION. 505
ject in the class. There are always some properties common to all things
which are included. Others there often are, to which some things, which
are nevertheless included, are exceptions. But the objects which are ex-
ceptions to one character are not exceptions to another; the resemblance
which fails in some particulars must be made up for in others. The class,
therefore, is constituted by the possession of all the characters which are
imiversal, and most of those which admit of exceptions. If a plant had the
ovules erect, the stigmata divided, possessed the albumen, and was without
stipules, it possibly would not be classed among the Rosacese. But it may
want any one, or more than one of these characters, and not be excluded.
The ends of a scientific classification are better answered by including it.
Since it agrees so nearly, in its known properties, with the sum of the char-
acters of the class, it is likely to resemble that class more than any other in
those of its properties which are still undiscovered.
Not only, therefore, are natural groups, no less than any artificial classes,
determined by characters ; they are constituted in contemplation of, and by
reason of, characters. But it is in contemplation not of those characters
only which are rigorously common to all the objects included in the group,
but of the entire body of characters, all of which are found in most of those
objects, and most of them in all. And hence our conception of the class,
the image in our minds which is representative of it, is that of a specimen
complete in all the characters ; most naturally a specimen which, by pos-
sessing them all in the greatest degree in which they are ever found, is the
best fitted to exhibit clearly, and in a marked manner, what they are. It is
by a mental reference to this standard, not instead of, but in illustration of,
the definition of the class, that we usually and advantageously determine
whether any individual or species belongs to the class or not. And this, as
it seems to me, is the amount of truth contained in the doctrine of Types.
We shall see presently that where the classification is made for the ex-
press purpose of a special inductive inquiry, it is not optional, but necessary
for fulfilling the conditions of a correct Inductive Method, that we should
establish a type-species or genus, namely, the one which exhibits in the most
eminent degree the particular phenomenon under investigation. But of this
hereafter. It remains, for completing the theory of natural groups, that a
few words should be said on the principles of the nomenclature adapted to
them.
§ 6. A Nomenclature in science is, as we have said, a system of the
names of Kinds. These names, like other class-names, are defined by the
enumeration of the characters distinctive of the class. The only merit
which a set of names can have beyond this, is to convey, by the mode of
their construction, as much information as possible : so that a person who
knows the thing, may receive all the assistance which the name can give in
remembering what he knows ; while he who knows it not, may receive as
much knowledge respecting it as the case admits of, by merely being told
its name.
There are two modes of giving to the name of a Kind this sort of signifi-
cance. The best, but which unfortunately is seldom practicable, is when the
word can be made to indicate, by its formation, the very properties which
it is designed to connote. The name of a Kind does not, of course, connote
all the properties of the Kind, since these are inexhaustible, but such of
them as are sufficient to distinguish it; such as are sure marks of all the
rest. Now, it is very rarely that one propeity, or even any two or three
506 OPERATIONS SUBSIDIARY TO INDUCTION.
properties, can answer this purpose. To distinguish the common daisy
from all other species of plants would require the specification of many
characters. And a name can not, without being too cumbrous for use, give-
indication, by its etymology or mode of construction, of more than a very
small number of these. The possibility, therefore, of an ideally perfect
Nomenclature, is probably confined to the one case in which we are hap-
pily in possession of something approaching to it — the Noiuenclature of
elementary Chemistry. The substances, whether simple or compound,with
which chemistry is conversant, are Kinds, and, as such, the properties which
distinguish each of them from the rest are innumerable; but in the case of
compound substances (the simple ones are not numerous enough to require
a systematic nomenclature), there is one property, the chemical composi-
tion, which is of itself sufficient to distinguish the Kind ; and is (with cer-
tain reservations not yet thoroughly understood) a sure mark of all the
other properties of the compound. All that was needful, therefore, was to
make the name of every compound express, on the first hearing, its chem-
ical composition ; that is, to form the name of the compound, in some uni-
form mannei', from the names of the simple substances which enter into it
as elements. This was done, most skillfully and successfully, by the Frencb
chemists, though their nomenclature has become inadequate to the conven-
ient expression of the very complicated compounds now known to chemists.
The only thing left unexpressed by them was the exact proportion in which
the elements were combined ; and even this, since the establishment of the-
atomic theory, it has been found possible to express by a simple adaptation-
of their phraseology.
But where the characters which must be taken into consideration, in
order sufficiently to designate the Kind, are too numerous to be all signified
in the derivation of the name, and where no one of them is of such prepon-
derant importance as to justify its being singled out to be so indicated, we
may avail ourselves of a subsidiary resource. Though we can not indicate
the distinctive properties of the Kind, we may indicate its nearest natural
aflinities, by incorporating into its name the name of the proximate natural
group of which it is one of the species. On this principle is founded the
admirable binary nomenclature of botany and zoology. In this nomen-
clature the name of every species consists of the name of the genus, or
natural group next above it, with a word added to distinguish the particu-
lar species. The last portion of the compound name is sometimes taken
from some one of the peculiarities in which that species differs from others
of the genus ; as Clematis integrifolia, Potentilla alba, Viola palustris,
Artemisia vulgaris; sometimes from a circumstance of an historical na-
ture, as Narcissus joo6<zcMS, Potentilla tormentilla (indicating that the plant
is that which was formerly known by the latter name), Exacum Gandollii
(from the fact that De Candolle was its first discoverer) ; and sometimes
the word is purely conventional, as Thlaspi bursapastoris, Ranunculus
thora; it is of little consequence which ; since the second, or, as it is usually
called, the specific name, could at most express, independently of conven-
tion, no more than a very small portion of the connotation of the term.
But by adding to this the name of the superior genus, we may make the
best amends we can for the impossibility of so contriving the name as to
express all the distinctive characters of the Kind. We make it, at all
events, express as many of those characters as are common to the proxi-
mate natural group in which the Kind is included. If even those common,
characters are so numerous or so little familiar as to require a further ex-
CLASSIFICATION BY SEEIES. 50V
tension of the same resource, we might, instead of a binary, adopt a ternary
nomenclature, employing not only the name of the genus, but that of tlie
next natural group in order of generality above the genus, commonly call-
ed the Family. This was done in the mineralogical nomenclature proposed
by Professor Mohs. " The names framed by him were not composed of
two, but of three elements, designating respectively the Species; the Genus,
and the Order; thus he has such species as Rhombohedral Lime Saloide,
Octohedral Fluor Haloide, Prismatic Sal BaryteH''* The binary con-
8ti-nction, however, has been found sufficient in botany and zoology, the
only sciences in which this general principle has hitherto been successfully
adopted in the construction of a nomenclature.
Besides the advantage which this principle of nomenclature possesses, in
giving to the names of species the greatest quantity of independent signifi-
cance which the circumstances of the case admit of, it answers the further
end of immensely economizing the use of names, and preventing an other-
wise intolerable burden on the memory. When the names of species be-
come extremely numerous, some artifice (as Dr. Whewellf observes) be-
comes absolutely necessary to make it possible to recollect or apply them.
" The known species of plants, for example, were ten thousand in the time
of Linnaeus, and are now probably sixty thousand. It would be useless to
endeavor to frame and employ separate names for each of these species.
The division of the objects into a subordinated system of classification en-
ables us to introduce a Nomenclature which does not require this enor-
mous number of names. Each of the genera has its name, and the species
are marked by the addition of some epithet to the name of the genus. In this
manner about seventeen hundred generic names, with a moderate number
of specific names, were found by Linnaeus sufficient to designate with pre-
cision all the species of vegetables known at his time." And though the
number of generic names has since greatly increased, it has not increased
in any thing like the proportion of the multiplication of known species.
CHAPTER VIII.
OP CLASSIFICATION BY SERIES.
§ 1. Thus far, we have considei-ed the principles of scientific classification
80 far only as relates to the formation of natural groups ; and at this point
most of those who have attempted a theory of natural arrangement, in-
cluding, among the rest, Dr. Whewell, have stopped. There remains, how-
ever, another, and a not less important portion of the theory, which has
not yet, as far as I am aware, been systematically treated of by any writer
except M. Corate. This is, the arrangement of the natural groups into a
natural series.J
* Nov. Org. Senov., p. 274. t Hist. Sc. Id., i. 133.
t Dr. Whewell, in his reply (Philosophy of Discovery, p. 270) says that he " stopped short
of, or rather passed by, the doctrine of a series of organized beings," because he "thought it
bad and narrow philosophy." If he did, it was evidently without understanding this form of
the doctrine; for he proceeds to quote a passage from his "History," in which the doctrine
he condemns is designated as that of " a mere linear progression in nature, which would place
each genus in contact only with the preceding and succeeding ones." Now the series treat-
ed of in the text agrees with this linear progression in nothing whatever but in being a pro-
gression.
508 OPERATIONS SUBSIDIARY TO INDUCTION.
The end of- Classification, as an instrument for the investigation of nature,
is (as before stated) to make us think of those objects together which have
the greatest number of important common properties ; and which, there-
fore, we have oftenest occasion, in the course of our inductions, for taking
into joint consideration. Our ideas of objects are thus brought into the
order most -conducive to the successful prosecution of inductive inquiries
generally. But when the purpose is to facilitate some particular inductive
inquiry, more is required. To be instrumental to that purpose, the classifi-
cation must bring those objects together, the simultaneous contemplation
of which is likely to throw most light upon the particular subject. That
subject being the laws of some phenomenon or some set of connected phe-
nomena ; the very phenomenon or set of phenomena in question must be
chosen as the groundwork of the classification.
The requisites of a classification intended to facilitate the study of a par-
tioular phenomenon, are, first to bring into one class all Kinds of things
which exhibit that phenomenon, in whatever variety of forms or degrees ;
and, secondly, to arrange those Kinds in a series according to the degree in
which they exhibit it, beginning with those which exhibit most of it, and
terminating with those which exhibit least. The principal example, as yet,
of such a classification, is afforded by comparative anatomy and physiology,
from which, therefore, our illustrations shall be taken.
§ 2. The object being supposed to be, the investigation of the laws of
animal life ; the first step, after forming the most distinct conception of
the phenomenon itself, possible in the existing state of our knowledge, is to
erect into one great class (that of animals) all the known Kinds of beings
where that phenomenon presents itself; in however various combinations
with other properties, and iff however different degrees. As some of these
Kinds manifest the general phenomenon of animal life in a very high de-
gree, and others in an insignificant degree, barely suflicient for recognition ;
we must, in the next place, arrange the various Kinds in a series, following
one another according to the degrees in which they severally exhibit the
phenomenon ; beginning thei'efore with man, and ending with the most im-
perfect kinds of zoophytes.
This is merely saying that we should put the instances, from which the
law is to be inductively collected, into the order which is implied in one of
the four Methods of Experimental Inquiry discussed in the preceding Book ;
the fourth Method, that of Concomitant Variations. As formerly remarked,
this is often the only method to which recourse can be had, with assurance
of a true conclusion, in cases in which we have but limited means of effecting,
by artificial experiments, a separation of circumstances usually conjoined.
The principle of the method is, that facts which increase or diminish to-
gether, and disappear together, are either cause and effect, or effects of a
common cause. When it has been ascertained that this relation really sub
sists between the variations, a connection between the facts themselves may
be confidently laid down, either as a law of nature or only as an empirical
law, according to circumstances.
That the application of this Method must be preceded by the formation
of such a series as we have described, is too obvious to need being pointed
out; and the mere arrangement of a set of objects in a series, according to
It would surely be possible to arrange all places (for example) in the order of their distance
from the North Pole, though there would be not merely a plurality, but a whole circle of places
at every single gradation in the scale.
CLASSIFICATION BY SERIES. 509
tlie degrees in which they exhibit some fact of which we are seeking the
law, is too naturally suggested by the necessities of our inductive opera-
tions, to require any lengthened illustration here. But there are cases in
which the arrangement required for the special purpose becomes the de-
termining principle of the classification of the same objects for general
purposes. This will naturally and properly happen, when those laws of the
objects which are sought in the special inquiry enact so principal a part in
the general character and history of those objects — exercise so much influ-
ence in determining all the phenomena of which they are either the agents
or the theatre — that all other differences existing among the objects are fit-
tingly regarded as mere modifications of the one phenomenon sought ; ef-
fects determined by the co-operation of some incidental circumstance with
the laws of that phenomenon. Thus in the case of animated beings, the
differences between one class of animals and another may reasonably be
considered as mere modifications of the general phenomenon, animal life ;
modifications arising either from the different degrees in which that phe-
nomenon is manifested in different animals, or from the intermixture of the
effects of incidental causes peculiar to the nature of each, with the effects
produced by the general laws of life ; those laws still exercising a predom-
inant influence over the result. Such being the case, no other inductive
inquiry respecting animals can be successfully carried on, except in sub-
ordination to the great inquiry into the universal laws of animal life ; and
the classification of animals best suited to that one purpose, is the most suit-
able to all the other purposes of zoological science.
§ 3. To establish a classification of this sort, or even to apprehend it
when established, requires the power of recognizing the essential similarity
of a phenomenon, in its minuter degrees and obscurer forms, with what is
called the same phenomenon in the greatest perfection of its development ;
that is, of identifying with each other all phenomena which differ only in
degree, and in properties which we suppose to be caused by difference of
degree. In order to recognize this identity, or, in other words, this exact
similarity of quality, the assumption of a type-species is indispensable. We
must consider as the type of the class, that among the Kinds included in
it, which exhibits the properties constitutive of the class, in the highest
degree; conceiving the other varieties as instances of degeneracy, as it
were, from that type ; deviations from it by inferior intensity of the char-
acteristic property or properties. For every phenomenon is best studied
{coBteris paribus) where it exists in the greatest intensity. It is there that
yie effects which either depend on it, or depend on the same causes with
it, will also exist in the greatest degree. It is there, consequently, and only
there, that those effects of it, or joint effects with it, can become fully
known to us, so that we may learn to recognize their smaller degrees, or
even their mere rudiments, in cases in which the direct study would have
been diflBcult or even impossible. Not to mention that the phenomenon in
its higher degrees may be attended by effects or collateral circumstances
w,hich in its smaller degrees do not occur at all, requiring for their produc-
tion in any sensible amount a greater degree of intensity of the cause than
is there met with. In man, for example (the species in which both the
phenomenon of animal and that of organic life exist in the highest degree),
many subordinate phenomena develop themselves in the course of his ani-
mated existence, which the inferior varieties of animals do not show. The
knowledge of these properties may nevertheless be of great avail toward
510 OPERATIONS SUBSIDIARY TO INDUCTION.
the discovery of the conditions and laws of the general phenomenon of life,
which is common to man with those inferior animals. And they are, even,
rightly considered as properties of animated nature itself; because they
may evidently be affiliated to the general laws of animated nature; be-
cause we may fairly presume that some rudiments or feeble degrees of
those properties would be recognized in all animals by more perfect or-
gans, or even by more perfect instruments, than ours ; and because those
may be correctly termed properties of a class, which a thing exhibits
exactly in proportion as it belongs to the class, that is, in proportion as it
possesses the main attributes constitutive of the class.
1 § 4. It remains to consider how the internal distribution of the series
may most properly take place; in what manner it should be divided into
Orders, Families, and Genera.
The main principle of division must of course be natural affinity; the
classes formed must be natural groups ; and the formation of these has al-
ready been sufficiently treated of. But the principles of natural grouping
must be applied in subordination to the principle of a natural series. The
groups must not be so constituted as to place in the same group things
which ought to occupy different points of the general scale. The precau-
tion necessary to be observed for this purpose is, that the primary divis-
ions must be grounded not on all distinctions indiscriminately, but on
those which correspond to variations in the degree of the main phenome-
non. The series of Animated Nature should be broken into parts at the
points where the variation in the degree of intensity of the main phenome-
non (as marked by its principal characters. Sensation, Thought, Voluntary
Motion, etc.) begins to be attended by conspicuous changes in the miscel-
laneous properties of the animal. Such well-marked changes take place,
for example, where the class Mammalia ends ; at the points where Fishes
are separated from Insects, Insects from MoUusca, etc. When so formed,
the primary natural groups will compose the series by mere juxtaposition,
without redistribution ; each of them corresponding to a definite portion
of the scale. In like manner each family should, if possible, be so subdi-
vided, that one portion of it shall stand higher and the other lower, though
of course contiguous, in the general scale; and only when this is impossi-
ble is it allowable to ground the remaining subdivisions on characters hav-
ing no determinable connection with the main phenomenon. 4i^
Where the principal phenomenon so far transcends in importance all
other properties on which a classification could be grounded, as it does in
the case of animated existence, any considerable deviation from the rule
last laid down is in general sufficiently guarded against by the first princi-
ple of a natural arrangement, that of forming the groups according to the
most important characters. All attempts at a scientific classification of
animals, since first their anatomy and physiology were successfully studied,
have been framed with a certain degree of instinctive reference to a natu-
ral series, and have accorded in many more points than they have difEei'ed,
with the classification which would most naturally have been grounded on
such a series. But the accordance has not always been complete; and it
still is often a matter of discussion, which of several classifications best ac-
cords with the true scale of intensity of the main phenomenon. Cuvier,
for example, has been justly criticised for having formed his natural
groups, with an undue degree of reference to the mode of alimentation, a
circumstance directly connected only with organic life, and not leading to
CLASSIFICATION BY SERIES. 511
the arrangement most appropriate for the purposes of an investigation of
the laws of animal life, since both carnivorous and herbivorous or frugivo-
Tous animals are found at almost every degree in the scale of animal per-
fection. Blainville's classification has been considered by high authorities
to be free from this defect ; as representing correctly, by the mere order
of the principal groups, the successive degeneracy of animal nature from
its highest to its most imperfect exemplification.
§ 5. A classification of any large portion of the field of nature in con-
formity to the foregoing principles, has hitherto been found practicable
only in one great instance, that of animals. In the case even of vegetables,
the natural arrangement has not been carried beyond the formation of nat-
ural groups. Naturalists have found, and probably will continue to find it
impossible to form those groups into any series, the terms of which corre-
spond to real gradations in the phenomenon of vegetative or organic life.
Such a difference of degree may be traced between the class of Vascular
Plants and that of Cellular, which includes lichens, algse, and other sub-
stances whose organization is simpler and more rudimentary than that of
the higher order of vegetables, and which therefore approach nearer to
mere inorganic nature. But when we rise much above this point, we do
not find any sufficieqt difference in the degree in which different plants
possess the properties of organization and life. The dicotyledons are of
more complex structure, and somewhat more perfect organization, than the
monocotyledons ; and some dicotyledonous families, such as the Compositae,
are rather more complex in their organization than the rest. But the dif-
ferences are not of a marked character, and do not promise to throw any
particular light upon the conditions and laws of vegetable life and develop-
ment. If they did, the classification of vegetables would have to be made,
like that of animals, with reference to the scale or series indicated.
Although the scientific arrangements of organic nature afford as yet the
only complete example of the true principles of rational classification,
whether as to the formation of groups or of series, those principles are ap-
plicable to all cases in which mankind are called upon to bring the various
parts of any extensive subject into mental co-ordination. They are as
much to the point when objects are to be classed for purposes of art or
business, as for those of science. The proper arrangement, for example, of
a code of laws, depends on the same scientific conditions as the classifica-
tions in natural history ; nor could there be a better preparatory discipline
for that important function, than the study of the principles of a natural
arrangement, not only in the abstract, but in their actual application to the
class of phenomena for which they were first elaborated, and which are still
the best school for learning their use. Of this the great authority on codi-
fication, Bentham, was perfectly aware ; and his early Fragment on Gov-
ernment, the admirable introduction to a series of wi'itings unequaled in
their department, contains clear and just views (as far as they go) on the
meaning of a natural arrangement, such as could scarcely have occurred to
•any one who lived anterior to the age of Linnaeus and Bernard de Jussieu.
BOOK Y.
ON FALLACIES.
" Errare non modo afiBrmando et negando, sed etiam sentiendo, et in tacit^ bominum cogi-
tatione contingit." — Hoebes, Computatio sive Logica, chap. v.
" II leur semble qu'il n'y a qu'a douter par fantaisie, et qu'il n'y a qu'i dire en general que
notre nature est infirme ; que notre esprit est plein d'aveuglement ; qu'il faut avoir un grand
Boin de se ddfaire de ses prejuges, et autres choses serablables. lis pensent que cela suffit
pour ne plus se laisser s^duire k ses sens, et pour ne plus se tromper du tout. II ne suffit pas
de dire que I'esprit est foible, il faut lui faire sentir ses foiblesses. Ce n'est pas assez de dire
qu'il est sujet k. I'erreur, il faut lui deeouvrir en quoi consistent ses erreurs." — MALEBSAifOHE,
Recherche de la V£rit€.
CHAPTER I.
OF FALLACIES IN GENBEAL.
§ 1. It is a maxim of the school-men, that " contrariorum eadem est sci-
entia ;" we never really know what a thing is, unless we are also able to
give a suflScient account of its opposite. Conformably to this maxim, one
considerable section, in most treatises on Logic, is devoted to the subject of
Fallacies ; and the practice is too well worthy of observance, to allow of
our departing from it. The philosophy of reasoning, to be complete, ought
to comprise the theory of bad as well as of good reasoning.
We have endeavored to ascertain the principles by which the suflSciency
of any proof can be tested, and by which the nature and amount of evi-
dence needful to prove any given conclusion can be determined beforehand.
If these principles were adhered to, then although the number and value
of the truths ascertained would be limited by the opportunities, or by the
industry, ingenuity, and patience, of the individual inquirer, at least error
would not be embraced instead of truth. But the general consent of man-
kind, founded on their experience, vouches for their being far indeed from
even this negative kind of perfection in the employment of their reasoning
powers.
In the conduct of life — in the practical business of mankind — wrong infer-
ences, incorrect interpretations of experience, unless after much culture of the
thinking faculty, are absolutely inevitable ; and with most people, after th&
highest degree of culture they ever attain, such erroneous inferences, produ-
cing corresponding errors in conduct, are lamentably frequent. Even in the
speculations to which eminent intellects have systematically devoted them-
selves, and in reference to which the collective mind of the scientific world is
always at hand to aid the efforts and correct the aberrations of individuals,
it is only from the more perfect sciences, from those of which the subject-
matter is the least complicated, that opinions not resting on a correct in-
duction have at length, generally speaking, been expelled. In the depart-
FALLACIES IN GENERAL. 513
ments of inquiry relating to the more complex phenomena of nature, and
especially those of which the subject is man, whether as a moral and intel-
lectual, a social, or even as a physical being ; the diversity of opinions still
prevalent among instructed persons, and the equal confidence with which
those of the most contrary ways of thinking cling to their respective ten-
ets, are proof not only that right modes of philosophizing are not yet gen-
erally adopted on those subjects, but that wrong ones are; that inquirers
have not only in general missed the. truth, but have often embraced error ;,
that even the most cultivated portion of our species have not yet learned
to abstain from drawing conclusions which the evidence does not warrant.
The only complete safeguard against reasoning ill, is the habit of reason-
ing well; familiarity with the principles of correct reasoning, and practice
in applying those principles. It is, however, not unimportant to consider
what are the most common modes of bad reasoning; by what appearances-
the mind is most likely to be seduced from the observance of true princi-
ples of induction ; what, in short, are the most common and most danger-
ous varieties of Apparent Evidence, whereby persons are misled into opin-
ions for which there does not exist evidence really conclusive.
A catalogue of the varieties of apparent evidence which are not real evi-
dence, is an enumeration of Fallacies. Without such an enumeration, there-
fore, the present work would be wanting in an essential point. And while
writers who included in their theory of reasoning nothing more than rati-
ocination, have in consistency with this limitation, confined their remarks to
the fallacies which have their seat in that portion of the process of investi-
gation ; we, who profess to treat of the whole process, must add to our di-
rections for performing it rightly, warnings against performing it wrongly
in any of its parts : whether the ratiocinative or the experimental portion
of it be in fault, or the fault lie in dispensing with ratiocination and induc-
tion altogether.
§ 2. In considering the sources of unfounded inference, it is unnecessa-
ry to reckon the errors which arise, not from a wrong method, nor even
from ignorance of the right one, but from a casual lapse, through hurry or
inattention, in the application of the true principles of induction. Such
errors, like the accidental mistakes in casting up a sum, do not call for
philosophical analysis or classification ; theoretical considerations can throw
no light upon the means of avoiding them. In the present treatise our at-
tention is required, not to mere inexpertness in performing the operation
in the right way (the only remedies for which are increased attention and
more sedulous practice), but to the modes of performing it in a way fun-
damentally wrong; the conditions under which the human mind persuades
itself that it has sufficient grounds for a conclusion which it has not ar-
rived at by any of the legitimate methods of induction — which it has not,
even carelessly or overhastily, endeavored to test by those legitimate
methods.
§ 3. There is another branch of what may be called the Philosophy of
Error, which must be mentioned here, though only to be excluded from
our subject. The sources of erroneous opinions are twofold, moral and in-
tellectual. Of these, the moral do not fall within the compass of this work.
They may be classed under two general heads : Indifference to the attain-
ment of truth, and Bias ; of which last the most common case is that in
which we are biased by our wishes ; but the liability is almost as great to
33
514 FALLACIES.
the undue adoption of a conclusion which is disagreeable to us, as of one
which is agreeable, if it be of a nature to bring into action any of the
stronger passions. Persons of timid character are the more predisposed
to believe any statement, the more it is calculated to alarm them. Indeed
it is a psychological law, deducible from the most general laws of the men-
tal constitution of man, that any strong passion renders us credulous as to
the existence of objects suitable to excite it.
But the moral causes of opinions, though with most persons the most
powerful of all, are but remote causes ; they do not act directly, but by
means of the intellectual causes ; to which they bear the same relation that
the circumstances called, in the theory of medicine, predisposing causes,
bear to exciting causes. Indifference to truth can not, in and by itself,
produce erroneous belief ; it operates by preventing the mind from collect-
ing the proper evidences, or from applying to them the test of a legitimate
and rigid induction ; by which omission it is exposed unprotected to the
influence of any species of apparent evidence which offers itself sponta-
neously, or which is elicited by that smaller quantity of trouble which the
mind may be willing to take. As little is Bias a direct source of wrong
conclusions. "We can not believe a proposition only by wishing, or only
by dreading, to believe it. The most violent inclination to find a set of
propositions true, will not enable the weakest of mankind to believe them
without a vestige of intellectual grounds — without any, even apparent, evi-
dence. It acts indirectly, by placing the intellectual grounds of belief in
an incomplete or distorted shape before his eyes. It makes him shrink
from the irksome labor of a rigorous induction, when he has a misgiving
that its result may be disagreeable; and in such examination as he does
institute, it makes him exert that which is in a certain measure voluntary,
his attention, unfairly, giving a larger share of it to the evidence which
seems favorable to the desired conclusion, a smaller to that which seems
unfavorable. It operates, too, by making him look out eagerly for reasons,
or apparent reasons, to support opinions which are conformable, or resist
those which are repugnant, to his interests or feelings ; and when the in-
tei'ests or feelings are common to great numbers of persons, reasons are
accepted and pass current, which would not for a moment be listened to in
that character if the conclusion had nothing more powerful than its reasons
to speak in its behalf. The natural or acquired partialities of mankind are
continually throwing up philosophical theories, the sole recommendation of
which consists in the premises they afford for proving cherished doctrines,
or justifying favorite feelings; and when any one of these theories has
been so thoroughly discredited as no longer to serve the purpose, another
is always ready to takes its place. This propensity, when exercised in fa-
vor of any widely-spread persuasion or sentiment, is often decorated with
complimentary epithets; and the contrary habit of keeping the judgment
in complete subordination to evidence, is stigmatized by various hard names,
as skepticism, immorality, coldness, hard-heartedness, and similar expres-
sions according to the nature of the case. But though the opinions of the
generality of mankind, when not dependent on mere habit and inculcation,
have their root much more in the inclinations than in the intellect, it is a
necessary condition to the triumph of the moral bias that it should first
pervert the understanding. Every erroneous inference, though originating
in moral causes, involves the intellectual operation of admitting insufficient
evidence as sufficient ; and whoever was on his guard against all kinds of
inconclusive evidence which can be mistaken for conclusive, would be in
CLASSIFICATION OF FALLACIES. 513
mo danger of being led into error even by the strongest bias. There are
minds so strongly fortified on the intellectual side, that they could not
blind themselves to the light of truth, however really desirous of doing so ;
they could not, with all the inclination in the world, pass ofE upon them-
selves bad arguments for good ones. If the sophistry of the intellect could
be rendered impossible, that of the feelings, having no instrument to work
with, would be powerless. A comprehensive classification of all those
things which, not being evidence, are liable to appear such to the under-
standing, will, therefore, of itself include all errors of judgment arising
from moral causes, to the exclusion only of errors of practice committed
against better knowledge.
To examine, then, the various kinds of apparent evidence which are not
evidence at all, and of apparently conclusive evidence which do not really
amount to conclusiveness, is the object of that part of our inquiry into
which we are about to enter.
The subject is not beyond the compass of classification and comprehen-
fiive survey. The things, indeed, which are not evidence of any given con-
clusion, are manifestly endless, and this negative property, having no de-
pendence on any positive ones, can not be made the groundwork of a real
classification. But the things which, not being evidence, are susceptible
of being mistaken for it, are capable of a classification having reference to
the positive property which they possess of appearing to be evidence. We
may arrange them, at our choice, on either of two principles ; according
to the cause which makes them appear to be evidence, not being so ; or
according to the particular kind of evidence which they simulate. The
Classification of Fallacies which will be attempted in the ensuing chapter,
is founded on these considerations jointly.
CHAPTER II.
CLASSIFICATION OF FALLACIES.
§ 1. In attempting to establish certain general distinctions which shall
mark out from one another the various kinds of Fallacious Evidence, we
propose to ourselves an altogether different aim from that of several emi-
nent thinkers, who have given, under the name of Political or other Falla-
cies, a mere enumeration of a certain number of erroneous opinions ; false
general propositions which happen to be often met with ; loci communes
of bad arguments on some particular subject. Logic is not concerned with
the false opinions which people happen to entertain, but with the manner
in which they come to entertain them. The question is not, what facts
have at any time been erroneously supposed to be proof of certain other
facts, but what property in the facts it was which led any one to this mis-
taken supposition.
When a fact is supposed, though incorrectly, to be evidentiary of, or
a mark of, some other fact, there must be a cause of the error; the sup-
posed evidentiary fact must be connected in some particular manner with
the fact of which it is deemed evidentiary — must stand in some partienlai-
relation to it, without which relation it would not be regarded in that light.
The relation may either be one resulting front the simple contemplation of
the two facts side by side with one another, or it may depend on some
516 FALLACIES.
process of mind, by which a previous association has been established be-
tween them. Some peculiarity of relation, however, there must be ; the
fact which can, even by the wildest aberration, be supposed to prove an-
other fact, must stand in some special position with regard to it ; and if
we could ascertain and define that special position, we should perceive the
origin of the error.
We can not regard one fact as evidentiary of another, unless we believe
that the two are always, or in the majority of cases, conjoined. If we be-
lieve A to be evidentiary of B, if when we see A we are inclined to infer
B from it, the reason is because we believe that wherever A is, B also ei-
ther always or for the most part exists, either as an antecedent, a conse-
quent, or a concomitant. If when we see A we are inclined not to expect
B — if we believe A to be evidentiary of the absence of B — it is because we
believe that where A is, B either is never, or at least seldom, found. Er-
roneous conclusions, in short, no less than correct conclusions, have an in-
variable relation to a general formula, either expressed or tacitly implied.
"When we infer some fact from some other fact which does not really prove
it, we either have admitted, or, if we maintained consistency, ought to ad-
mit, some groundless general proposition respecting the conjunction of the
two phenomena.
For every property, therefore, in facts, or in our mode of considering
facts, which leads us to believe that they are habitually conjoined when
they are not, or that they are not when in reality they are, there is a cor-
responding kind of Fallacy ; and an enumeration of fallacies would consist
in a specification of those properties in facts, and those peculiarities in our
mode of considering them, which give rise to this erroneous opinion.
§ 2. To begin, then ; the supposed connection, or repugnance, between
the two facts, may either be a conclusion from evidence (that is, from some
other proposition or propositions), or may be admitted without any such
ground ; admitted, as the phrase is, on its own evidence ; embraced as self-
evident, as an axiomatic truth. This gives rise to the first great distinc-
tion, that between Fallacies of Inference and Fallacies of Simple Inspec-
tion. In the latter division must be included not only all cases in which
a proposition is believed and held for true, literally without any extrinsic
evidence, either of specific experience or general reasoning; but those
more frequent cases in which simple inspection creates a presump^on in
favor of a proposition ; not sufficient for belief, but sufficient to cause the
strict principles of a regular induction to be dispensed with, and creating
a predisposition to believe it on evidence which would be seen to be in-
sufficient if no such presumption existed. This class, comprehending the
whole of what may be termed Natural Prejudices, and which I shall call
indiscriminately Fallacies of Simple Inspection or Fallacies a priori, shall
be placed at the head of our list.
Fallacies of Inference, or erroneous conclusions from supposed evidence,
must be subdivided according to the nature of the apparent evidence from
which the conclusions are drawn ; or (what is the same thing) according
to the particular kind of sound argument which the fallacy in question
simulates. But there is a distinction to be first drawn, which does not
answer to any of the divisions of sound arguments, but arises out of the
nature of bad ones. We may know exactly what our evidence is, and yet
draw a false conclusion from it; we may conceive precisely what our
premises are, what alleged matters of fact, or general principles, are the
CLASSIFICATION OF FALLACIES. 617
foundation of our inference ; and yet, because the premises are false, or
because we have inferred from them what they will not support, our con-
•clasion may be erroneous. But a case, perhaps even more frequent, is that
in which the error arises from not conceiving our premises with due clear-
ness, that is (as shown in the preceding Book*), with due fixity : form-
ing one conception of our evidence when we collect or receive it, and an-
other when we make use of it ; or unadvisedly, and in general unconscious-
ly, substituting, as we proceed, difEerent premises in the place of those
with which we set out, or a different conclusion for that which we under-
took to prove. This gives existence to a class of fallacies which may be
justly termed (in a phrase borrowed from Bentham) Fallacies of Confu-
sion; comprehending, among others, all those which have their source in
language, whether arising from the vagueness or ambiguity of our terms,
or from casual associations with them.
When the fallacy is not one of Confusion, that is, when the proposition
believed, and the evidence on which it is believed, are steadily apprehended
and unambiguously expressed, there remain to be made two cross divisions.
The Apparent Evidence may be either particular facts, or foregone general-
izations ; that is, the process may simulate either simple Induction or De-
duction ; and again, the evidence, whether consisting of supposed facts or
of general propositions, may be false in itself, or, being true, may fail to
bear out the conclusion attempted to be founded on it. This gives us first.
Fallacies of Induction and Fallacies of Deduction, and then a subdivision
of each of these, according as the supposed evidence is false, or true but in-
conclusive.
Fallacies of Induction, where the facts on which the induction proceeds
are erroneous, may be termed Fallacies of Observation. The term is not
strictly accurate, or, rather, not accurately co-extensive with the class of fal-
lacies which I pi'opose to designate by it. Induction is not always ground-
ed on facts immediately observed, but sometimes on facts inferred ; and
when these last are erroneous, the error may not be, in the literal sense of
the term, an instance of bad observation, but of bad inference. It will be
eonvenient, however, to make only one class of all the inductions of which
the error lies in not sufficiently ascertaining the facts on which the theory
is grounded ; whether the cause of failure be malobservation, or simple non-
observation, and whether the malobservation be direct, or by means of in-
termediate marks which do not prove what they are supposed to prove.
And in the absence of any comprehensive term to denote the ascertainment,
by whatever means, of the facts on which an induction is grounded, I will
venture to retain for this class of fallacies, under the explanation now given,
the title of Fallacies of Observation.
The other class of inductive fallacies, in which the facts are correct, but
the conclusion not warranted by them, are properly denominated Fallacies
of Generalization ; and these, again, fall into various subordinate classes or
natural groups, some of which will be enumerated in their proper place.
When we now turn to Fallacies of Deduction, namely those modes of in-
correct argumentation in which the premises, or some of them, are general
propositions, and the argument a ratiocination ; we may of course subdi-
vide these also into two species similar to the two preceding, namely, those
which proceed on false premises, and those of which the premises, though
true, do not support the conclusion. But of these species, the first must
* Supra, p. 137.
618 FALLACIES.
necessarily fall under some one of the heads already enumerated. For the-
error must be either in those premises which are general propositions, or in.
those which assert individual facts. In the former case it is an Inductive
Fallacy, of one or the other class ; in the latter it is a Fallacy of Observa-
tion ; unless, in either case, the erroneous premise has been assumed on-
simple inspection, in which case the fallacy is a priori. Or, finally, the prem--
ises, of whichever kind they are, may never have been conceived in so dis-
tinct a manner as to produce any clear consciousness by what means they
were arrived at; as in the case of what is called . reasoning in a circle; and
then the fallacy is one of Confusion.
There remain, therefore, as the only class of fallacies having properly
their seat in deduction, those in which the premises of the ratiocination do'
not bear out its conclusion ; the various cases, in short, of vicious argu-
mentation, provided against by the rules of the syllogism. We shall call
these, Fallacies of Ratiocination.
We have thus five distinguishable classes of fallacy, which may be ex-
pressed in the following synoptic table :
of Simple Inspection 1. Fallacies a priori.
{Inductive f 2. Fallacies of Observation.
Fallacies ( 3. Fallacies of Generalization.
D^^=J^«l 4. Fallacies of Ratiocination.
FaIiLACIES
"-of Inference
from evidence indis- '
,. H, L'°fq^'!- 5. Fallacies of Confusion.
tmctly conceived.. )
§ 3. We must not, however, expect to find that men's actual errors al-
ways, or even commonly, fall so unmistakably under some one of these
classes, as to be incapable of being referred to any other. Erroneous ar-
guments do not admit of such a sharply cut division as valid arguments
do. An argument fully stated, with all its steps distinctly set out, in lan-
guage not susceptible of misunderstanding, must, if it be erroneous, be so-
in some one of these five modes unequivocally ; or indeed of the first four,
since the fifth, on such a supposition, would vanish. But it is not in the
nature of bad reasoning to express itself thus unambiguously. When a
sophist, whether he is imposing on himself or attempting to impose on oth-
ers, can be constrained to throw his sophistry into so distinct a form, it
needs, in a large proportion of cases, no further exposure.
In all arguments, evei-ywhere but in the schools, some of the links are
suppressed ; a fortiori when the arguer either intends to deceive, or is a
lame and inexpert thinker, little accustomed to bring his reasoning proc-
esses to any test; and it is in those steps of the reasoning which are made
in this tacit and half-conscious, or even wholly unconscious manner, that
the error oftenest lurks. In order to detect the fallacy, the proposition,
thus silently assumed must be supplied ; but the reasoner, most likely, has
never really asked himself what he was assuming; his confuter, unless per-
mitted to extort it from him by the Socratic mode of interrogation, must
himself judge what the suppressed premise ought to be in order to support
the conclusion. And hence, in the words of Archbishop Whately, " it must
be often a matter of doubt, or, rather, of arbitrary choice, not only to which
genus each kind of fallacy should be referred, but even to which kind to
refer any one individual fallacy; for since, in any course of argument, one
premise is usually suppressed, it frequently happens in the case of a fallacy,
that the hearers are left to the alternative of supplying either a premise
CLASSIFICATION OF FALLACIES. 51 9,
■which is not true, or else, one which does not prove the conclusion ; e. g., if
a man expatiates on the distress of the country, and thence argues that the
government is tyrannical, we must suppose hira to assume either that 'ev-
ery distressed country is under a tyranny,' which is a manifest falsehood,
or merely that ' every country under a tyranny is distressed,' which, how-
ever true, proves nothing, the middle term being undistributed." The for-
mer would be ranked, in our distribution, among fallacies of generalization,
the latter among those of ratiocination. " Which are we to suppose the
speaker meant us to understand ? Surely " (if he understood himself) " just
whichever each of his hearers might happen to prefer : some might assent
to the false premise; others allow the unsound syllogism."
Almost all fallacies, therefore, might in strictness be brought under our
fifth class, Fallacies of Confusion. A fallacy can seldom be absolutely re-
ferred to any of the other classes ; we can only say, that if all the links
were filled up which should be capable of being supplied in a valid argu-
ment, it would either stand thus (forming a fallacy of one class), or thus (a
fallacy of another) ; or at furthest we may say, that the conclusion is most.
likely to have originated in a fallacy of such and such a class. Thus, in
the illustration just quoted, the error committed may be traced with most
probability to a fallacy of generalization ; that of mistaking an uncertain
mark, or piece of evidence, for a certain one ; concluding from an effect to
some one of its possible causes, when there are others which would have-
been equally capable of producing it.
Yet, though the five classes run into each other, and a particular error
often seems to be arbitrarily assigned to one of them rather than to any
of the rest, there is considerable use in so distinguishing them. We shall
find it convenient to set apart, as Fallacies of Confusion, those of which
confusion is the most obvious characteristic ; in which no other cause can
be assigned for the mistake committed, than neglect or inability to state-
the question properly, and to apprehend the evidence with definiteness and.
precision. In the remaining four classes I shall place not only the cases in
which the evidence is clearly seen to be what it is, and yet a wrong conclu-
sion drawn from it, but also those in which, although there be confusion,
the confusion is not the sole cause of the error, but there is some shadow
of a ground for it in the nature of the evidence itself. And in distribu-
ting these cases of partial confusion among the four classes, I shall, when
there can be any hesitation as to the precise seat of the fallacy, suppose it
to be in that part of the process in which, from the nature of the case, and
the tendencies of the human mind, an error would in the particular circum-
stances be the most probable.
After these observations we shall proceed, without further preamble, ta
consider the five classes in their order.
520 FALLACIES.
CHAPTER III.
FALLACIES OF SIMPLE INSPECTION; OE A. PRIORI FALLACIES.
§ 1. The tribe of errors of which we are to treat in the first instance,
are those in which no actual inference takes place at all ; the proposition
(it can not in such cases be called a conclusion) being embraced, not as
proved, but as requiring no proof ; as a self-evident truth ; or else as hav-
ing such intrinsic verisimilitude, that external evidence not in itself amount-
ing to proof, is sufficient in aid of the antecedent presumption.
An attempt to treat this subject comprehensively would be a trans-
gression of the bounds prescribed to this work, since it would necessitate
the inquiry which, more than any other, is the grand question of what is
called metaphysics, viz.. What are the propositions which may reasonably
be received without proof? That there must be some such propositions
all are agreed, since there can not be an infinite series of proof, a chain sus-
pended from nothing. But to determine what these propositions are, is
the opus magnum, of the more recondite mental philosophy. Two prin-
cipal divisions of opinion on the subject have divided the schools of phi-
losophy from its first dawn. The one recognizes no ultimate premises but
the facts of our subjective consciousness ; our sensations, emotions, intellect-
ual states of mind, and volitions. These, and whatever by strict rules of
induction can be derived from these, it is possible, according to this theory,
for us to know ; of all else we must remain in ignorance. The opposite
school hold that there are other existences, suggested indeed to our minds
by these subjective phenomena, but not inferable from them, by any proc-
ess either of deduction or of induction ; which, however, we must, by the
constitution of our mental nature, recognize as realities ; and realities, too,
•of a higher order than the phenomena of our consciousness, being the ef-
ficient causes and necessary substrata of all Phenomena. Among these
entities they reckon Substances, whether matter or spirit ; from the dust
under o"ur feet to the soul, and from that to Deity. All these, according to
them, are preternatural or supernatural beings, having no likeness in expe-
rience, though experience is entirely a manifestation of their agency. Their
existence, together with more or less of the laws to which they conform in
their operations, are, on this theory, apprehended and recognized as real by
the mind itself intuitively ; experience (whether in the form of sensation
or of mental feeling) having no other part in the matter than as afEording
facts which are consistent with these necessary postulates of reason, and
which are explained and accounted for by them.
As it is foreign to the purpose of the present treatise to decide between
these conflicting theories, we are precluded from inquiring into the exist-
ence, or defining the extent and limits, of knowledge a priori, and from
characterizing the kind of correct assumption which the fallacy of incorrect
assumption, now under consideration, simulates. Yet since it is allowed
on both sides that such assumptions are often made improperly, we may
find it practicable, without entering into the ultimate metaphysical grounds
•of the discussion, to state some speculative propositions, and suggest some
FALLACIES OF SIMPLE INSPECTION. 521
practical cautions, respecting the forms in which such unwarranted assump-
tions are most likely to be made.
§ 2. In the cases in which, according to the thinkers of the ontological
school, the mind apprehends, by intuition, things, and the laws of things^
not cognizable by our sensitive faculty ; those intuitive, or supposed intui-
live, perceptions are undistinguishable from what the opposite school are
accustomed to call ideas of the mind. When they themselves say that they
perceive the things by an immediate act of a faculty given for that purpose
by their Creator, it would be said of them by their opponents that they
find an idea or conception in their own minds, and from the idea or concep-
tion, infer the existence of a corresponding objective reality. Nor would
this be an unfair statement, but a mere version into other words of the ac-
count given by many of themselves ; and one to which the more clear-
sighted of them might, and generally do, without hesitation, subscribe.
Since, therefore, in the cases which lay the strongest claims to be examples
of knowledge a priori, the mind proceeds from the idea of a thing to th&
reality of the thing itself, we can not be surprised by finding that illicit
assumptions a priori consist in doing the same thing erroneously; in mis-
taking subjective facts for objective, laws of the percipient mind for laws-
of the perceived object, properties of the ideas or conceptions for proper-
ties of the things conceived.
Accordingly, a large proportion of the erroneous thinking which exists,
in the world proceeds on a tacit assumption, that the same order must ob-
tain among the objects in nature which obtains among our ideas of them.
That if we always think of two things together, the two things must al-
ways exist together. That if one thing makes us think of another as pre-
ceding or following it, that other must precede it or follow it in actual
fact. And conversely, that when we can not conceive two things together
they can not exist together, and that their combination may, without fur-
ther evidence, be rejected from the list of possible occurrences.
Few persons, I am inclined to think, have reflected on the great extent
to which this fallacy has prevailed, and prevails, in the actual beliefs and
actions of mankind. For a first illustration of it we may refer to a large-
class of popular superstitions. If any one will examine in what circum-
stances most of those things agree, which in different ages and by differ-
ent portions of the human race have been considered as omens or prognos-
tics of some interesting event, whether calamitous or fortunate ; they will
be found very generally characterized by this peculiarity, that they cause-
the mind to think of that, of which they are therefore supposed to forbode
the actual occurrence. " Talk of the devil and he will appear," has passed,
into a proverb. Talk of the devil, that is, raise the idea, and the reality
will follow. In times when the appearance of that personage in a visible
form was thought to be no unfrequent occurrence, it has doubtless often
happened to persons of vivid imagination and susceptible nerves, that talk-
ing of the devil has caused them to fancy they saw him ; as, even in our
more incredulous days, listening to ghost stories predisposes us to see
ghosts; and thus, as a prop to the a priori fallacy, there might come to be
added an auxiliary fallacy of malobservation, with one of false generaliza-
tion grounded on it. Fallacies of different orders often herd or cluster to-
gether in this fashion, one smoothing the way for another. But the origia
of the superstition is evidently that which we have assigned. In like man-
ner, it has been universally considered unlucky to speak of misfortune.
522 FALLACIES.
The day on which any calamity liappened has been considered an unfor-
tunate day, and there has been a feeling eveiywhere, and in some nations
u religious obligation, against transacting any important business on that
^ay. For on such a day our thoughts are likely to be of misfortune. For
a similar reason, any untoward occurrence in commencing an undertaking
has been considered ominous of failure ; and often, doubtless, has really
■contributed to it by putting the persons engaged in the enterprise more or
less out of spirits ; but the belief has equally prevailed where the disagree-
able circumstance was, independently of superstition, too insignificant to
•depress the spirits by any influence of its own. All know the story of
■Csesar's accidentally stumbling in the act of landing on the African coast;
and the presence of mind with which he converted the direful pi'esage into
■a favorable one by exclaiming, "Africa, I embrace thee." Such omens, it
is true, were often conceived as warnings of the future, given by a friendly
or a hostile deity ; but this very superstition grew out of a pre-existing
tendency; the god was supposed to send, as an indication of what was to
«ome, something which people were already disposed to consider in that
■light. So in the case of lucky or unlucky names. Herodotus tells us how
the Greeks, on the way to Mycale, were encouraged in their enterprise by
the arrival of a deputation from Samos, one of the members of which was
named Hegesistratus, the leader of armies.
Cases may be pointed out in which something which could have no real
•effect but to make Yieraons'think of misfortune, was regarded not merely
as a prognostic, but as something approaching to an actual cause of it.
The Eu0)7;ufi of the Greeks, and favete Unguis, or bona verba qumso, of the
Romans, evince the care with which they endeavored to repress the utter-
ance of any word expressive or suggestive of ill fortune ; not from notions
of delicate politeness, to which their general mode of conduct and feeling
had very little reference, but from bona fide alarm lest the event so sug-
-gested to the imagination should in fact occur. Some vestige of a similar
superstition has been known to exist among uneducated persons even in
our own day : it is thought an unchristian thing to talk of, or suppose, the
death of any person while he is alive. It is known how careful the Ro-
mans were to avoid, by an indirect mode of speech, the utterance of any
word directly expressive of death or other calamity ; how instead of mor-
4ints est they said vixit; and "be the event fortunate or otherwise" instead
of adverse. The name Maleventum, of which Salmasius so sagaciously de-
tected the Thessalian origin (MaXdtic, MaXotVroc), they changed into the
highly propitious denomination, Beneventum ; Egesta into Segesta; and
Epidamnus, a name so interesting in its associations to the reader of Thu-
•cydides, they exchanged for Dyrrhachium, to escape the perils of a word
suggestive .of damnum or detriment.
"If a hare cross the highway," says Sir Thomas Browne,* "there are
few above threescore that are not perplexed thereat; which notwithstand-
ing is b>it an augurial terror, according to that received expression, Jnau-
■spicatum dat iter oblatus lepus. And the ground of the conceit was prob-
ably no greater than this, that a fearful animal passing by us portended
unro us someinmg to S>e feared ; as upon the like consideration the meet-
ing of a fox presaged some future imposture." Such sunerstitions as these
l&.st must be the resuk of stud/ ; they are too reconaue lor natural or spon-
taneous growth. But when the attempt was once made to construct a
* Vulnar Errors, book v.. chaD. 21.
FALLACIES OF SIMPLE INSPECTION. 523
science of predictions, any association, though ever so faint or remote, by
which an object could be connected in however far-fetched a manner with
ideas either of prosperity or of danger and misfortune, w^as enough to de-
termine its being classed among good or evil omens.
An example of i-ather a different kind from any of these, but falling un-
der the same principle, is the famous attempt on which so much labor and
ingenuity were expended by the alchemists, to make gold potable. The
motive to this was a conceit that potable gold could be no other than the
universal medicine; and why gold ? Because it was so precious. It must
have all marvelous properties as a physical substance, because the mind
was already accustomed to marvel at it.
From a similar feeling, " every substance," says Dr. Paris,* " whose ori-
gin is involved in mystery, has at different times been eagerly applied to
the purposes of medicine. Not long since, one of those showers which are
now known to consist of the excrements of insects, fell in the north of
Italy; the inhabitants regarded it as manna, or some supernatural panacea,
and they swallowed it with such avidity, that it was only by extreme ad-
dress that a small quantity was obtained for a chemical examination."
The superstition, in this instance, though doubtless partly of a religious
character, probably in part also arose from the prejudice that a wonderful
thing must of course have wonderful properties.
§ 3. The instances of a priori fallacy which we have hitherto cited be-
long to the class of vulgar errors, and do not now, nor in any but a rude
age ever could, impose upon minds of any considerable attainments. But
those to which we are about to proceed, have been, and still are, all but
universally prevalent among thinkers. The same disposition to give ob-
jectivity to a law of the mind — to suppose that what is true of our ideas
of things must be true of the things themselves — exhibits itself in many of
the most acci-edited modes of philosophical investigation, both on physical
and on metaphysical subjects. In one of its most undisguised manifesta-
tions, it embodies itself in two maxims, which lay claim to axiomatic truth :
Things which we can not think of together, can not co-exist ; and Things
which we can not help thin] \ng of together, must co-exist. I am not sure
that the maxims were ever expressed in these precise words, but the his-
tory both of philosophy and of popular opinions abounds with exemplifica-
tions of both forms of the doctrine.
To begin with the latter of them: Things which we can not think of
except together, must exist together. This is assumed in the generally
received and accredited mode of reasoning which concludes that A must
accompany B in point of fact, because " it is involved in the idea." Such
thinkers do not reflect that the idea, being a result of abstraction, ought to
conform to the facts, and can not make the facts conform to it. The ar-
gument is at most admissible as an appeal to authority ; a surmise, that
what is now part of the idea, must, before it became so, have been found
by previous inquirers in the facts. Nevertheless, the philosopher who
more than all others made professions of rejecting authority, Descartes,
constructed his system on this very basis. His favorite device for arriving
at truth, even in regard to outward things, was by looking into his own
mind for it. " Credidi me," says his celebrated maxim, " pro reguli. ge-
nerali suraere posse, omne id quod vald6 dilucid5 et distinct^ concipiebam,
* Pharmacologia, Historical Introduction, p. 16.
524 FALLACIES.
verum esse ;" whatever can be very clearly conceived must certainly exist ;.
that is, as he afterward explains it, if the idea includes existence. And on
this gi-ound he infers that geometrical figures really exist, because they
can be distinctly conceived. Whenever existence is " involved in an idea,'*'
a thing conformable to the idea must really exist ; which is as much as to^
say, whatever the idea contains must have its equivalent in the thing ; and
what we are not able to leave out of the idea can not be absent from the
reality.* This assumption pervades the philosophy not only of Descartes,,
but of all the thinkers who received their impulse mainly from him, in par-
ticular the two most remarkable among them, Spinoza and Leibnitz, from
whom the modern German metaphysical philosophy is essentially an ema-
nation. I am indeed disposed to think that the fallacy now under consid-
eration has been the cause of two-thirds of the bad philosophy, and espe-
cially of the bad metaphysics, which the human mind has never ceased t&
produce. Our general ideas contain nothing but what has been put into
tlfem, either by our passive experience, or by our active habits of thought;
and the metaphysicians in all ages, who have attempted to construct the
laws of the universe by reasoning from our supposed necessities of thought,
have always proceeded, and only could proceed, by laboriously finding in
their own minds what they themselves had formerly put there, and evolv-
ing from their ideas of things what they had first involved in those ideas.
In this way all deeply-rooted opinions and feelings are enabled to create
apparent demonstrations of their truth and reasonableness, as it were, out
of their own substance.
The other form of the fallacy: Things which we can not think of to-
gether can not exist together — including as one of its branches, that what
we can not think of as existing can not exist at all — may thus be briefly
expressed: Whatever is inconceivable must be false.
Against this prevalent doctrine I have sufliciently argued in a former
Book,f and nothing is required in this place but examples. It was long
held that Antipodes were impossible because of the diflSculty which was-
found in conceiving persons with their heads in the same direction as our
feet. And it was one. of the received arguments against the Copernican
system, that we can not conceive so great a void space as that system sup-
poses to exist in the celestial regions. When men's imaginations had al-
ways been used to conceive the stars as firmly set in solid spheres, they
naturally found much difficulty in imagining them in so different, and, as
it doubtless appeared to them, so precarious a situation. But they had no
right to mistake the limitation (whether natural, or, as it in fact proved,,
only artificial) of their own faculties, for an inherent limitation of the pos-
sible modes of existence in the universe.
It may be said in objection, that the error in these cases was in the'
minor premise, not the major; an error of fact, not of principle; that it
did not consist in supposing that what is inconceivable can not be true, but
* The author of one of the Bridgewater Treatises has fallen, as it seems to me, into a simi-
lar fallacy when, after arguing in rather a curious way to prove that matter may exist with-
out any of the known properties of matter, and may therefore be changeable, he concludes:
that it can not be eternal, because "eternal (passive) existence necessarily involves incapa-
bility of change." I believe it would be difficult to point out any other connection between,
the facts of eternity and unchangeableness, than a strong association between the two ideas.
Most of the a priori arguments, both religious and anti-religious, on the origin of things, are
fallacies drawn from the same source.
t Supra, book ii., chap, v., § 6, and chap, vii., § 1, 2, 3, i. See also Examination of Sit
William Hamilton's Philosophy, chap. vi. and elsewhere.
FALLACIES OF SIMPLE INSPECTION. 525
in supposing antipodes to be inconceivable, when present experience proves
that they can be conceived. Even if this objection were allowed, and the
proposition that what is inconceivable can not be true were suffered to
remain unquestioned as a speculative truth, it would be a truth on which
no practical consequence could ever be founded, since, on this showing,
it is impossible to affirm of any proposition, not being a contradiction in
terms, that it is inconceivable. Antipodes were really, not fictitiously, in-
conceivable to our ancestors : they are indeed conceivable to us ; and as
the limits of our power of conception have been so largly extended, by the
€xtension of our experience and the more varied exercise of our imagina-
tion, so may postei'ity find many combinations perfectly conceivable to
them which are inconceivable to us. But, as beings of limited experience,
-we must always and necessarily have limited conceptive powers ; while it
does not by any means follow that the same limitation obtains in the pos-
sibilities of Nature, nor even in her actual manifestations.
Rather more than a century and a half ago it was a scientific maxim,
■disputed by no one, and which no one deemed to require any proof, that
*' a thing can not act where it is not."* With this weapon the Cartesians
waged a formidable war against the theory of gravitation, which, accord-
ing to them, involving so obvious an absurdity, mast be rejected in limine :
the sun could not possibly act upon the earth, not being there. It was not
surprising that the adherents of the old systems of astronomy should urge
this objection against the new ; but the false assumption imposed equally
on Newton himself, who, in order to turn the edge of the objection, im-
agined a subtle ether which filled up the space between the sun and the
earth, and by its intermediate agency was the proximate cause of the phe-
nomena of gravitation. " It is inconceivable," said Newton, in one of his
letters to Dr. Bentley,f " that inanimate brute matter should, without the
mediation of something else, which is not material, operate upon and affect
other matter without mutual contact That gravity should be innate,
inherent, and essential to matter, so that one body may act on another, at
a distance, through a vacuum, without the mediation of any thing else, by
and through which their action and force may be conveyed from one to
another, is to me so great an absurdity, that I believe no man, who in phil-
osophical matters has a competent faculty of thinking, can ever fall into
it." This passage should be hung up in the cabinet of every cultivator of
science who is ever tempted to pronounce a fact impossible because it
appears to him inconceivable. In our own day one would be more tempt-
ed, though with equal injustice, to reverse the concluding observation, and
consider the seeing any absurdity at all in a thing so simple and natural,
to be what really marks the absence of " a competent faculty of thinking."
No one now feels any difficulty in conceiving gi-avity to be, as much as
any other property is, " inherent and essential to matter," nor finds the
comprehension of it facilitated in the smallest degree by the supposition
of an ether (though some recent inquirers do give this as an explanation
of it) ; nor thinks it at all incredible that the celestial bodies can and do
act where they, in actual bodily presence, are not. To us it is not more
wonderful that bodies should act upon one another " without mutual con-
tact," than that they should do so when in contact ; we are familiar with
* It seems that this doctrine was, before the time I have mentioned, disputed by some
thinkers. Dr. Ward mentions Scotos, Vasquez, Biel, Francis Lugo, and Valentia.
1 1 quote this passage from Playfair's celebrated Dissertation on the Progress of Mathemat-
ical and Physical Science.
526 FALLACIES.
both these facts, and we find them equally inexplicable, but equally easy to
believe. To Newton, the one, because his imagination was familiar with it,
appeared natural and a matter of course, while the other, for the contrary
reason, seemed too absurd to be credited.
It is strange that any one, after such a warning, should rely impUcitly
on the evidence a priori of such propositions as these, that matter can not
think; that space, or extension, is infinite; that nothing can be made out
of nothing (ex nihilo nihil fit). Whether these propositions are true or
not this is not the place to determine, nor even whether the questions are
soluble by the human faculties. But such doctrines are no more self-evi-
dent truths, than the ancient maxim that a thing can not act where it is
not, which probably is not now believed by any educated person in Eu-
rope.* . Matter can not think ; why ? because we can not conceive thought
to be annexed to any arrangement of material particles. Space is infinite,
because having never known any part of it. which had not other parts be-
yond it, we can not conceive an absolute termination. £lx nihilo nihil fit^
because having never known any physical product without a pre-existing
physical material, we can not, or think we can not, imagine a creation out
of nothing. But these things may in themselves be as conceivable as
gravitation without an intervening medium, which Newton thought too
great an absurdity for any person of a competent faculty of philosophical
thinking to admit : and even supposing them not conceivable, this, for
aught we know, may be merely one of the limitations of our very limited
minds, and not in nature at all.
No writer has more directly identified himself with the fallacy now un-
der consideration, or has embodied it in more distinct terms, than Leibnitz.
In his view, unless a thing was not merely conceivable, but even explaina-
ble, it could not exist in nature. All natural phenomena, according to him,
must be susceptible of being accounted for a priori. The only facts of
which no explanation could be given but the will of God, were miracles
properly so called. " Je reconnais," says he,f " qu'il n'est pas permis de
nier ce qu'on n'entend pas ; mais j'ajoute qu'on a droit de nier (au moins
dans I'ordre naturel) ce que absolument n'est point intelligible ni explicable.
Je soutiens aussi .... qu'enfin la conception des creatures n'est pas la me-
sure du poavoir de Dieu, mais que leur conceptivit^, ou force de concevoir,
est la raesure du pouvoir de la nature, tout ce qui est conforme h, I'ordre
naturel pouvant Stre congu ou entendu par quelque creature."
Not content with assuming that nothing can be true which we are unable
to conceive, scientific inquirers have frequently given a still further exten-
sion to the doctrine, and held that, even of things not altogether inconceiv-
able, that which we can conceive with the greatest ease is likeliest to be
true. It was long an admitted axiom, and is not yet entirely discredited,
that " nature always acts by the simplest means," i. e., by those which are
most easily conceivable.J A large proportion of all the errors ever commit-
ted in the investigation of the laws of nature, have arisen from the assump-
tion that the most familiar explanation or hypothesis must be the truest.
* This statement I must now correct, as too unqualified. The maxim in question was
maintained with full conviction by no less an authority than Sir William Hamilton. See my
Examination, chap. xxiy.
t Nouveattx Essais sur VEntendement Humain — Avant-propos. (CEuvres, Paris ed., 1842,
vol. i., p. 19.)
X This doctrine also was accepted as true, and conclusions weie giounded on it, by Sir
William Hamilton. See Examination, chap. xxiv.
FALLACIES OF SIMPLE INSPECTION. 527
One of the most instructive facts in scientific history is the pertinacity with
which the human mind clung to the belief that the heavenly bodies must
move in circles, or be carried round by the revolution of spheres ; merely
because those were in themselves the simplest suppositions : though, to
make them accord with the facts which were ever contradicting them more
and more, it became necessary to add sphere to sphere and circle to circle,
until the original simplicity was converted into almost inextricable compli-
cation.
§ 4. We pass to another a priori fallacy or natural prejudice, allied to
the former, and originating, as that does, in the tendency to presume an ex-
act correspondence between the laws of the mind and those of things ex-
ternal to it. The fallacy may be enunciated in this general form — What-
ever can be thought of apart exists apart: and its most remarkable mani-
festation consists in the personification of abstractions. Mankind in all
ages have had a strong propensity to conclude that wherever there is a
name, there must be a distinguishable separate entity corresponding to the
name ; and every complex idea which the mind has formed for itself by
operating upon its conceptions of individual things, was considered to have
an outward objective reality answering to it. Fate, Chance, Nature, Time,
Space, were real beings, nay, even gods. If the analysis of qualities in the
earlier part of this work be correct, names of qualities and names of sub-
stances stand for the very same sets of facts or phenomena ; whiteness and
a white thing are only different phrases, required by convenience for speak-
ing of the same external fact under different relations. Not such, how-
ever, was the notion which this verbal distinction suggested of old, either
to the vulgar or to the scientific. Whiteness was an entity, inhering or
sticking in the white substance : and so of all other qualities. So far was
this carried, that even concrete general terms were supposed to be, not
names of indefinite numbers of individual substances, but names of a pe-
culiar kind of entities termed Universal Substances. Because we can think
and speak of man in general, that is, of all persons in so far as possessing
the common attributes of the species, without fastening oui- thoughts per-
manently on some one individual person; therefore man in general was
supposed to be, not an aggregate of individual persons, but an abstract or
universal man, distinct from these.
It may be imagined what havoc metaphysicians trained in these habits
made with philosophy, when they came to the largest generalizations of all.
SuhstanticB Secundm of any kind were bad enough, but such Substantiae Se-
cundsB as to 6v, for example, and ro av, standing for peculiar entities supposed
to be inherent in all things which exist, or in all which are said to be one,
were enough to put an end to all intelligible discussion ; especially since,
with a just perception that the truths which philosophy pursues are gener-
al truths, it was soon laid down that these general substances were the only
subjects of science, being immutable, while individual substances cogniza^
ble by the senses, being in a perpetual flux, could not be the subject of real
knowledge. This misapprehension of the import of general language con-
stitutes Mysticism, a word so much oftener written and spoken than under-
stood. Whether in the Vedas, in the Platonists, or in the Hegelians, mysti-
cism is neither more nor less than ascribing objective existence to the sub-
jective creations of our own faculties, to ideas or feelings of the mind ;
and believing that by watching and contemplating these ideas of its own
making, it can read in them what takes place in the world without.
628 FALLACIES.
§ 5. Proceeding with the enumeration of a priori fallacies, and endeav-
oring to arrange them with as much reference as possible to their natural
affinities, we come to another, which is also nearly allied to the fallacy pre-
ceding the last, standing in the same relation to one variety of it as the
fallacy last mentioned does to the other. This, too, represents nature as
under incapacities corresponding to those of our intellect; but instead of
only asserting that nature can not do a thing because we can not oonceive
it done, goes the still greater length of averring that nature does a particu-
lar thing, on the sole ground that we can see no reason why she should not.
Absurd as this seems when so plainly stated, it is a received principle
among scientific authorities for demonstrating a priori the laws of physical
phenomena. A phenomenon must follow a certain law, because we see no
reason why it should deviate from that law in one way rather than in an-
other. This is called the Principle of the SuflScient Reason;* and by
means of it philosophers often flatter themselves that they are able to es-
tablish, without any appeal to experience, the most general truths of ex-
perimental physics.
Take, for example, two of the most elementary of all laws, the law of in-
ertia and the first law of motion. A body at rest can not, it is affirmed,
begin to move unless acted upon by some external force ; because, if it
did, it must either move up or down, forward or backward, and so forth ;
but if no outward force acts upon it, there can be no reason for its mov-
ing up rather than down, or down rather than up, etc., ergo, it will not
move at all.
This reasoning I conceive to be entirely fallacious, as indeed Dr. Brown,
in his treatise on Cause and Effect, has shown with great acuteness and
justness of thought. We have before remarked, that almost every fallacy
may be referred to different genera by different modes of filling up the
suppressed steps ; and this particular one may, at our option, be brought
under petitio principii. It supposes that nothing can be a " sufficient rea-
son " for a body's moving in one particular direction, except some external
force. But this is the very thing to be proved. Why not some internal
force ? Why not the law of the thing's own nature ? Since these philoso-
phers think it necessary to prove the law of inertia, they of course do not
suppose it to be self-evident ; they must, therefore, be of opinion that pre-
viously to all proof, the supposition of a body's moving by internal impulse
is an admissible hypothesis ; but if so, why is not the hypothesis also ad-
missible, that the internal impulse acts naturally in some one particular di-
rection, not in another? If spontaneous motion might have been the law
of matter, why not spontaneous motion toward the sun, toward the earth,
or toward the zenith? Why not, as the ancients supposed, toward a par-
ticular place in the universe, appropriated to each pai-ticular kind of sub-
stance? Surely it is not allowable to say that spontaneity of motion is
credible in. itself, but not credible if supposed to take place in any deter-
minate direction.
Indeed, if any one chose to assert that all bodies when uncontrolled set
out in a direct line toward the North Pole, he might equally prove his point
by the principle of the Sufficient Reason. By what right is it assumed
that a state of rest is the particular state which can not be deviated from
without special cause ? Why not a state of motion, and of some particular
sort of motion ? Why may we not say that the natural state of a horse
♦ Not that of Leibnitz, but the principle commonly appealed to under that name by mathe-
maticians.
FALLACIES OF SIMPLE INSPECTION. 529
left to himself is to amble, because otherwise he must either trot, gallop, or
stand still, and because we know no reason why he should do one of these
rather than another ? If this is to be called an unfair use of the " suflBcient
reason," and the other a fair one, there must be a tacit assumption that a
state of rest is more natural to a horse than a state of ambling. If this
means that it is the state which the animal will assume when left to him--
self, that is the very point to be proved ; and if it does not mean this, it
can only mean that a state of rest is the simplest state, and therefore the
most likely to prevail in nature, which is one of the fallacies or natural
prejudices we have already examined.
So again of the First Law of Motion ; that a body once moving will, if
left to itself, continue to move uniformly in a straight line. An attempt
is made to prove this law by saying, that if not, the body must deviate
either to the right or to the left, and that there is no reason why it should
do one more than the other. But who could know, antecedently to experi-
ence, whether there was a reason or not ? Might it not be the nature of
bodies, or of some particular bodies, to deviate towai-d the right? or if the
supposition is preferred, toward the east, or south ? It was long thought
that bodies, terrestrial ones at least, had a natural tendency to deflect down-
ward ; and there is no shadow of any thing objectionable in the supposition,
except that it is not true. The pretended proof of the law of motion is even
more manifestly untenable than that of the law of inertia, for it is flagrantly'
inconsistent; it assumes that the continuance of motion in the direction first
taken is more natural than deviation either to the right or to the left, but
•denies that one of these can possibly be more natural than the other. All
these fancies of the possibility of knowing what is natural or not natural
by any other means than experience, are, in truth, entirely futile. The real
and only proof of the laws of motion, or of any other law of the universe, is
experience ; it is simply that no other suppositions explain or are consistent
with the facts of universal nature.
Geometers have, in all ages, been open to the imputation of endeavoring
to prove the most general facts of the outward world by sophistical reason-
ing, in order to avoid appeals to the senses. Archimedes, says Professor
Playfair,* established some of the elementary propositions of statics by a
process in which he " borrows no principle from experiment, but establish-
es his conclusion entirely by reasoning a priori. He assumes, indeed, that
equal bodies, at the ends of the equal arms of a lever, will balance one an-
other; and also that a cylinder or parallelopiped of homogeneous matter,
will be balanced about its centre of magnitude. These, however, are not in-
ferences from experience ; they are, properly speaking, conclusions deduced
fi'om the principle of the Sufiicient Reason." And to this day there are
few geometers who would not think it far more scientific to establish these
or any other premises in this way, than to rest their evidence on that fa-
miliar experience which in the case in question might have been so safely
•appealed to.
§ 6. Another natural prejudice, of most extensive prevalence, and which
had a great share in producing the errors fallen into by the ancients in
their physical inquiries, was this : That the differences in nature must cor-
respond to our received distinctions : that effects which we are accustom-
ed, in popular language, to call by different names, and arrange in different
* Dissertation, p. 27.
34
530 FALLACIES.
classes, must be of different natures, and have different causes. This prej-
udice, so evidently of the same origin with those already treated of, marks
more especially the earliest stage of science, when it has not yet broken
loose from the trammels of every -day phraseology. The extraordinary
prevalence of the fallacy among the Greek philosophers may be accounted
for by their generally knowing no other language than their own ; from
which it was a consequence that their ideas followed the accidental or ar-
bitrary combinations of that language, more completely than can happea
among the moderns to any but illiterate persons. They had great difficulty
in distinguishing between things which their language confounded, or in
putting mentally together things which it distinguished; and could hardly
combine the objects in nature, into any classes but those which were made
for them by the popular phrases of their own country ; or at least could
not help fancying those classes to be natural and all others arbitrary and
artificial. Accordingly, scientific investigation among the Greek schools
of speculation and their followers in the Middle Ages, was little moi-e than
a mere sifting and analyzing of the notions attached to common language.
They thought that by determining the meaning of words, they could be-
come acquainted with facts. "They took for granted," says Dr.Whewell,*
" that philosophy must result from the relations of those notions which are
involved in the common use of language, and they proceeded to seek it by
studying such notions." In his next chapter, Dr. Whewell has so well
illustrated and exemplified this error, that I shall take the liberty of quot-
ing him at some length.
"The propensity to seek for principles in the common usages of lan-
guage may be discerned at a very eai'ly pei'iod. Thus we have an example
of it in a saying which is reported of Thales, the founder of Greek philoso-
phy. When he was asked, ' What is the greatest thing ?' he replied ^Place;
for all other things are in the world, but the world is in it.' In Aristotle
we have the consummation of this mode of speculation. The usual point
from which he starts in his inquiries is, that we say thus or thus in common
language. Thus, when he has to discuss the question whether there be, in
any part of the universe, a void, or space in which there is nothing, he in-
quires first in how many senses we say that one thing is in another. He
enumerates many of these ; we say the part is in the whole, as the finger is
in the hand ; again we say, the species is in the genus, as man is included
in animal; again, the government of Greece is in the king; and various
other senses are described and exemplified, but of all these itAe most proper
is when we say a thing is in a vessel, and generally in place. He next ex-
amines wh'dt place is, and comes to this conclusion, that 'if about a body
there be another body including it, it is in place, and if not, not.' A body
moves when it changes its place ; but he adds, that if water be in a vessel,
the vessel being at rest, the parts of the water may still move, for they are
included by each other ; so that while the whole does not change its place,
the parts may change their place in a circular order. Proceeding then to
the question of a void, he as usual examines the different senses in which
the term is used, and adopts as the most proper, place without matter,
with no useful result.
"Again, in a question concerning mechanical action, he says, 'When a
man moves a stone by pushing it with a stick, we say both that the man
moves the stone, and that the stick moves the stone, but the latter "nore
properly.''
* Mist. Ind. Sc, Book i., chap. i.
FALLACIES OF SIMPLE INSPECTION. 531
"Again, we find the Greek philosophers applying themselves to extract
their dogmas from the most general and abstract notions which they could
detect; for example, from the conception of the Universe as One or as
Many things. They tried to determine how far we may, or must, combine
with these conceptions that of a whole, of parts, of number, of limits, of
place, of beginning or end, of full or void, of rest or motion, of cause and
effect, and the like. The analysis of such conceptions with such a view,
occupies, for instance, almost the whole of Aristotle's Treatise on the
Heavens."
The following paragraph merits particular attention : " Another mode
of reasoning, very widely applied in these attempts, was the doctrine of
contrarieties, in which it was assumed that adjectives or substances which
are in common language, or in some abstract mode of conception, opposed
to each other, must point at some fundamental antithesis in nature, which
it is important to study. Thus Aristotle says that the Pythagoreans, from
the contrasts which number suggests, collected ten principles — Limited
and Unlimited, Odd and Even, One and Many, Right and Left, Male and
Female, Rest and Motion, Straight and Curved, Light and Darkness, Good
and Evil, Square and Oblong Aristotle himself deduced the doctrine
of four elements and other dogmas by oppositions of the same kind."
Of the manner in which, from premises obtained in this way, the ancients
attempted to deduce laws of nature, an example is given in the same work
a few pages further on. "Aristotle decides that there is no void on such
arguments as this. In a void there could be no difference of up and down ;
for as in nothing there are no differences, so there are none in a privation
or negation ; but a void is merely a privation or negation of matter ; there-
fore, in a void, bodies could not move up and down, which it is in their
nature to do. It is easily seen " (Dr. Wbewell very justly adds) " that
such a mode of reasoning elevates the familiar forms of language, and
■ the intellectual connections of terms, to a supremacy over facts; making
truth depend upon whether terms are or are not privati^•e, and whether we
say that bodies fall naturally."
The propensity to assume that the same relations obtain between ob-
jects themselves, which obtain between our ideas of them, is here seen in
the extreme stage of its development. For the mode of philosophizing,
exemplified in the foregoing instances, assumes no less than that the prop-
er way of arriving at knowledge of nature, is to study nature itself sub-
jectively ; to apply our observation and analysis not to the facts, but to
the common notions entertained of the facts.
Many other equally striking examples may be given of the tendency to
assume that things which for the convenience of common life are placed in
different classes, must differ in every respect. Of this nature was the uni-
versal and deeply-rooted prejudice of antiquity and the Middle Ages, that
celestial and terrestrial phenomena must be essentially different, and could
in no manner or degree depend on the same laws. Of the same kind, also,
was the prejudice against which Bacon contended, that nothing produced
by nature could be successfully imitated by man : " Calorem solis et ignis
toto genere differre ; ne scilicet homines putent se per opera ignis, aliquid
simile iis quiE in Natura finnt, educere et formare posse ;" and again, " Com-
positionem tantum opus Hominis, Mistionem vero opus solius Naturae esse :
ne scilicet homines sperent aliquam ex arte Corporum naturalium genera-
tionem aut transformationem."* The grand distinction in the ancient sci-
* Novum Organum, Aph. 75.
532 FALLACIES.
entific speculations, between natui-al and violent motions, though not with-
out a plausible foundation in the appearances themselves, was doubtless
greatly recommended to adoption by its conformity to this pi-ejudice.
§ 7. From the fundamental error of the scientific inquirers of antiquity,
we pass, by a natural association, to a scarcely less fundamental one of
their great rival and successor, Bacon. It has excited the surprise of phi-
losophers that the detailed system of inductive logic, which this extraor-
dinary man labored to construct, has been turned to so little direct use by
subsequent inquirers, having neither continued, except in a few of its gen-
eralities, to be recognized as a theory, nor having conducted in practice to
any great scientific results. But this, though not unfrequently remarked,
has scarcely received any plausible explanation ; and some, indeed, have
preferred to assert that all rules of induction are useless, rather than sup-
pose that Bacon's rules are grounded on an insufficient analysis of the in-
ductive process. Such, however, will be seen to be the fact, as soon as it
is considered, that Bacon entirely overlooked Plurality of Causes. All his
rules tacitly imply the assumption, so contrary to all we now know of na-
ture, that a phenomenon can not have more than one cause.
"When he is inquiring into what he terms the forma calidi aut frigidi,
gravis aut levis, sicci aut humidi, and the like, he never for an instant
doubts that there is some one thing, some invariable condition or set of
conditions, which is present in all cases of heat, or cold, or whatever other
phenomenon he is considering ; the only difficulty being to find what it is ;
which accordingly he tries to do by a process of elimination, rejecting or
excluding, by negative instances, whatever is not the forma or cause, in or-
der to arrive at what is. But, that this forma or cause is one thing, and
that it is the same in all hot objects, he has no more doubt of, than anoth-
er person has that there is always some cause or other. In the present
state of knowledge it could not be necessary, even if we had not already
treated so fully of the question, to point out how widely this supposition
is at variance with the truth. It is particularly unfortunate for Bacon
that, falling into this error, he should have fixed almost exclusively upon a
class of inquiries in which it was especially fatal ; namely, inquiries into
the causes of the sensible qualities of objects. For his assumption, ground-
less in every case, is false in a peculiar degree with respect to those sensi-
ble qualities. In regard to scarcely any of them has it been found possible
to trace any unity of cause, any set of conditions invariably accompanying
the quality. The conjunctions of such qualities with one another consti-
tute the variety of Kinds, in which, as already remarked, it has not been
found possible to trace any law. Bacon was seeking for what did not ex-
ist. The phenomenon of which he sought for the one cause has oftenest no
cause at all, and when it has, depends (as far as hitherto ascertained) on
an unassignable vai-iety of distinct causes.
And on this rock every one must split, who represents to himself as the
first and fundamental problem of science to ascertain what is the cause of
a given effect, rather than what are the effects of a given cause. It was
shown, in an early stage of our inquiry into the nature of Induction,* how
much more ample are the resources which science commands for the latter
than for the former inquiry, since it is upon the latter only that we can
throw any direct light hj means of experiment ; the power of artificially
* Supra, book iii., chap, vii., § i.
FALLACIES OF SIMI^LE INSPECTION. 533
prodncing an effect, implying a previous knowledge of at least one of its
causes. If we discover the causes of effects, it is generally by having pre-
viously discovered the effects of causes ; the greatest skill in devising cru-
cial instances for the former purpose may only end, as Bacon's physical in-
quiries did, in no result at all. "Was it that his eagerness to acquire the
power of producing for man's benefit effects of practical importance to hu-
man life, rendering him impatient of pursuing that end by a circuitous
route, made even him, the champion of experiment, prefer the direct mode,
though one of mere observation, to the indirect, in which alone experiment
was possible? Or had even Bacon not entirely cleared his mind from the
notion of the ancients, that " rerum cognoscere causas " was the sole ob-
ject of philosophy, and that to inquire into the effects of things belonged
to servile and mechanical arts ?
It is worth remarking that, while the only eflBcient mode of cultivating
speculative science was missed from an undue contempt of manual opera-
tions, the false speculative views thus engendered gave in their turn a false
direction to such practical and mechanical aims as were suffered to exist.
The assumption universal among the ancients and in the Middle Ages, that
there were principles of heat and cold, dryness and moisture, etc., led di-
rectly to a belief in alchemy ; in a transmutation of substances, a change
from one Kind into another. Why should it not be possible to make
gold? Each of the characteristic properties of gold has its forma, its
essence, its set of conditions, which if we could discover, and learn how to
realize, we could superinduce that particular property upon any other sub-
stance, upon wood, or iron, or lime, or clay. If, then, we could effect this
with respect to every one of the essential properties of the precious metal,
we should have converted the other substance into gold. Nor did this, if
once the premises were granted, appear to transcend the real powers of
mankind. F'or daily experience showed that almost every one of the dis-
tinctive sensible properties of any object, its consistence, its color, its taste,
its smell, its shape, admitted of being totally changed by fire, or water, or
some other chemical agent. The formce of all those qualities seeming,
therefore, to be within human power either to produce or to annihilate,
not only did the transmutation of substances appear abstractedly possible,
but the employment of the power, at our choice, for practical ends, seemed
by no means hopeless.*
A prejudice, universal in the ancient world, and from which Bacon was
so far from being free, that it pervaded and vitiated the whole practical
part of his system of logic, may with good reason be ranked high in the
order of Fallacies of which we are now treating.
§ 8. There remains one a priori fallacy or natural prejudice, the most
deeply-rooted, perhaps, of all which we have enumerated ; one which not
only reigned supreme in the ancient world, but still possesses almost undis-
puted dominion over many of the most cultivated minds ; and some of the
most remarkable of the numerous instances by which I shall think it neces-
sary to exemplify it, will be taken from recent thinkers. This is, that the
conditions of a phenomenon must, or at least probably will, resemble the
phenomenon itself.
* It is hardly needful to remark that nothing is here intended to be said against the possi-
bility at some future period of making gold — by first discovering it to be a compound, and
putting together its different elements or ingredients. But this is a totally different idea from
that of the seekers of the grand arcanum.
534 FALLACIES.
Conformably to what we have before remarked to be of frequent oocur
rence, this fallacy might without much impropriety have been placed in a
different class, among Fallacies of Generalization ; for experience does af-
ford a certain degree of countenance to the assumption. The cause does,
in very many cases, resemble its effect; like produces like. Many phe-
nomena have a direct tendency to perpetuate their own existence, or to
give rise to other phenomena similar to themselves. Not to mention
forms actually moulded on one another, as impressions on wax and the
like, in which the closest resemblance between the effect and its cause is
the very law of the phenomenon ; all motion tends to continue itself, with
its own velocity, and in its own original direction ; and the motion of one
body tends to set others in motion, which is indeed the most common of
the modes in which the motions of bodies originate. We need scarcely
refer to contagion, fermentation, and the like ; or to the production of ef-
fects by the growth or expansion of a germ or rudiment resembling on a
smaller scale the completed phenomenon, as in the growth of a plant or
animal from an embryo, that embryo itself deriving its origin from another
plant or animal of the same kind. Again, the thoughts or reminiscences,
which are effects of our past sensations, resemble those sensations; feel-
ings produce similar feelings by way of sympathy ; acts produce similar
acts by involuntary or voluntary imitation. With so many appearances in
its favor, no wonder if a presumption naturally grew up, that causes must
necessarily resemble their effects, and that like could only be produced by
like.
This principle of fallacy has usually presided over the fantastical at-
tempts to influepce the course of nature by conjectural means, the choice
of which was not directed by previous observation and experiment. The
guess almost always fixed upon some means which possessed features of
real or apparent resemblance to the end in view. If a charm was wanted,
as by Ovid's Medea, to prolong life, all long-lived animals, or what were
esteemed such, were collected and brewed into a broth :
nee defuit illic
Sqaamea Cinyphii tenuis membrana chelydri
Vivacisque jecur cei-vi : quibus insupei- addit
Oia caputque novem cornicis ssecula passse.
A similar notion was embodied in the celebrated medical theory called
the "Doctrine of Signatures," " which is no less," says Dr. Paris,* " than
a belief that every natural substance which possesses any medicinal virtue
indicates by an obvious and well-marked external character the disease for
which it is a remedy, or the object for which it should be employed."
This outward character wsts generally some feature of resemblance, real or
fantastical, either to the effect it was supposed to produce, or to the phe-
nomenon over which its power was thought to be exercised. " Thus the
lungs of a fox must be a specific for asthma, because that animal is re-
markable for its strong powers of respiration. Turmeric has a brilliant
yellow color, which indicates that it has the power of curing the jaundice; •
for the same reason, poppies must relieve diseases of the head ; Agaricus
those of the bladder; Cassia fistula the affections of the intestines, and
Aristolochia the disorders of the uterus: the polished surface and stony
hardness which so eminently characterize the seeds of the Lithosperraum
officinale (common gromwell) were deemed a certain indication of their
* Pharmacologia, pp. 43-45.
FALLACIES OF SIMPLE INSPECTION. 533
efficacy in calculous and gravelly disorders ; for a similar reason, the roots
•of the Saxifi-aga granulata (white saxifrage) gained reputation in the cure
of the same disease; and the Euphrasia (eye-bright) acquired fame, as an
application in complaints of the eye, because it exhibits a black spot in its
corolla resembling the pupil. The blood-stone, the Heliotropium of the
ancients, from the occasional small specks or points of a blood-red color
exhibited on its green surface, is even at this very day employed in many
parts of England and Scotland to stop a bleeding from the nose ; and net-
tle tea continues a popular remedy for the cure of Urticaria. It is also
asserted that some substances bear the signatures of the humors, as the
petals of the red rose that of the blood, and the roots of rhubarb and the
iiowers of saffron that of the bile."
The early speculations respecting the chemical composition of bodies
were rendered abortive by no circumstance more than by their invariably
taking for granted that the properties of the elements must resemble those
of the compounds which were formed from them.
To descend to more modern instances ; it was long thought, and was
«toutly maintained by the Cartesians and even by Leibnitz against the
Newtonian system (nor did Newton himself, as we have seen, contest the
assumption, but eluded it by an arbitrai-y hypothesis), that nothing (of a
physical nature at least) could account for motion, except previous motion ;
the impulse or impact of some other body. It was very long before the
scientific world could prevail upon itself to admit attraction and repulsion
{i. e., spontaneous tendencies of particles to approach or recede from one
another) as ultimate laws, no more requiring to be accounted for than
impulse itself, if indeed the latter were not, in truth, resolvable into the
former. From the same source arose the innumerable hypotheses devised
to explain those classes of motion which appeared more mysterious than
others because there was no obvious mode of attributing them to impulse,
as for example the voluntary motions of the human body. Such were the
interminable systems of vibrations propagated along the nerves, or animal
spirits rushing up and down between the muscles and the brain ; which, if
the facts could have been proved, would have been an important addition
to our knowledge of physiological laws ; but the mere invention, or arbi-
trary supposition of them, could not unless by the strongest delusion be
supposed to render the phenomena of animal life more comprehensible, or
less mysterious. Nothing, however, seemed satisfactory, but to make out
that motion was caused by motion ; by something like itself. If it was
not one kind of motion, it must be another. In like manner it was sup-
posed that the physical qualities of objects must arise from some similar
■quality, or perhaps only some quality bearing the same name, in the parti-
cles or atoms of which the objects were composed ; that a sharp taste, for
example, must arise from sharp particles. And reversing the inference, the
•effects produced by a phenomenon must, it was supposed, resemble in their
physical attributes the phenomenon itself. The influences of the planets
were supposed to be analogous to their visible peculiarities : Mars, being of
a red color, portended fire and slaughter ; and the like.
Passing from physics to metaphysics, we may notice among the most re-
markable fruits of this a priori fallacy two closely analogous theories, em-
ployed in ancient and modern times to bridge over the chasm between the
world of mind and that of matter ; the species sensibiles of the Epicureans,
and the modern doctrine of perception by means of ideas. These theories
^re indeed, probably, indebted for their existence not solely to the fallacy in
536 ' FALLACIES.
question, but to that fallacy combined with another natural prejudice already
adverted to, that a thing can not act where it is not. In both doctrine*
it is assumed that the phenomenon which takes place in us when we see
or touch an object, and which we regard as an effect of that object, or rath-
er of its presence to our organs, must of necessity resemble very closely the
outward object itself. To fulfill this condition, the Epicureans supposed
that objects were constantly projecting in all directions impalpable image*
of themselves, which entered at the eyes and penetrated to the mind ; while
modern metaphysicians, though they rejected this hypothesis, agreed in
deeming it necessary to suppose that not the thing itself, but a mental im-
age or representation of it, was the direct object of perception. Dr. Reid
had to employ a world of argument and illustration to familiarize people
with the truth, that the sensations or impressions on our minds need not
necessarily be copies of, or bear any resemblance to, the causes which pro-
duce them; in opposition to the natural prejudice which led people to as-
similate the action of bodies upon our senses, and through them upon our
minds, to the transfer of a given form from one object to another by actual
moulding. The works of Dr. Reid are even now the most effectual course of
Btudy for detaching the mind from the prejudice of which this was an exam-
ple. And the value of the service which he thus rendered to popular philos-
ophy is not much diminished, although we may hold, with Brown, that he
went too far in imputing the "ideal theory" as an actual tenet, to the gen-
erality of the philosophers who preceded him, and especially to Locke and
Hume ; for if they did not themselves consciously fall into the error, unques-
tionably they often led their readers into it.
The prejudice, that the conditions of a phenomenon must resemble the
phenomenon, is occasionally exaggerated, at least verbally, into a still more
palpable absurdity ; the conditions of the thing are spoken of as if they
were the very thing itself. In Bacon's model inquiry, which occupies so
great a space in the Novum Organum, the inquisitio informam calidi, the
conclusion which he favors is that heat is a kind of motion ; meaning of
course not the feeling of heat, but the conditions of the feeling ; meaning,
therefore, only that wherever there is heat, there must first be a particu-
lar kind of motion ; but he makes no distinction in his language between
these two ideas, expressing himself as if heat, and the conditions of heat,
were one and the same thing. So the elder Darwin, in the beginning of
his Zoonomia, says, " The word idea has various meanings in the writers of
metaphysics ; it is here used simply for those notions of external things
which our organs of sense bring us acquainted with originally" (thus far
the proposition, though vague, is unexceptionable in meaning), "and is de-
fined a contraction, a motion, or configuration, of the fibres which constitute
the immediate organ of sense." Our notions, a configuration of the fibres I
What kind of logician must he be who thinks that a phenomenon is defined
to be the condition on which he supposes it to depend ? Accordingly he
says soon after, not that our ideas are caused by, or consequent on, certain
organic phenomena, but " our ideas are animal motions of the organs of
sense." And this confusion runs through the four volumes of the Zoono-
mia; the reader never knows whether the writer is speaking of the effect,
or of its supposed cause ; of the idea, a state of mental consciousness, or of
the state of the nerves and brain which he considers it to presuppose.
I have given a variety of instances in which the natural jftejudice, that
causes and their effects must resemble one another, has operated in practice
so as to give rise to serious errors. I shall now go further, and produce
FALLACIES OF SIMPLE INSPECTION. 537
from writings even of tlie present or very recent times, instances in which
this prejudice is laid down as an established principle. M. Victor Cousin,
in the last of his celebrated lectures on Locke, enunciates the maxim in the
following unqualified terms : " Tout ce qui est vrai de I'effet, est vrai de la
cause." A doctrine to which, unless in some peculiar and technical mean-
ing of the words cause and effect, it is not to be imagined that any person
would literally adhere ; but he who could so write must be far enough from
seeing that the very reverse might be the effect ; that thei-e is nothing im-
possible in the supposition that no one property which is true of the effect
might be true of the cause. Without going quite so far in point of ex-
pression, Coleridge, in his Biographia Ziiteraria* affirms as an " evident
truth," that " the law of causality holds only between homogeneous things,
•i.e., things having some common property," and therefore "can not extend
from one world into another, its opposite ;" hence, as mind and matter
have no common property, mind can not act upon matter, nor matter
upon mind. What is this but the a priori fallacy of which we are speak-
ing? The doctrine, like many others of Coleridge, is taken from Spinoza,
in the first book of whose Ethica {De Deo) it stands as the Third Pi-opo-
sition, " Quse res nihil commune inter se habent, earum una alterius causa
*sse non potest," and is there proved from two so-called axioms, equally
gratuitous with itself ; but Spinoza ever systematically consistent, pursued
the doctrine to its inevitable consequence, the materiality of God.
The same conception of impossibility led the ingenious and subtle mind
of Leibnitz to his celebrated doctrine of a pre-established harmony. He,
too, thought that mind could not act upon matter, nor matter upon mind,
and that the two, therefore, must have been arranged by their Maker like
two clocks, which, though unconnected with one another, strike simultane-
ously, and always point to the same hour. Malebranche's equally famous
theory of Occasional Causes was another form of the same conception ; in-
stead of supposing the clocks originally arranged to strike together, he held
that when the one strikes, God interposes, and makes the other strike in
oorrespondence with it.
Descartes, in like manner, whose works are a rich mine of almost every
<Jescription of a priori fallacy, says that the Efficient Cause must at least
have all the perfections of the effect, and for this singular reason : " Sienim
ponamus aliquid in idea repe'riri quod non fuerit in ejus causa, hoc igitur
habet a nihilo ;" of which it is scarcely a parody to say, that if there be
pepper in the soup there must be pepper in the cook who made it, since
otherwise the pepper would be without a cause. A similar fallacy is com-
mitted by Cicero, in his second book De Finibus, where, speaking in his
own person against the Epicureans, he charges them with inconsistency in
saying that the pleasures of the mind had their origin from those of the
body, and yet that the former were more valuable, as if the effect could sur-
pass the cause. "Animi voluptas oritur propter voluptatera corporis, et
major est animi voluptas quam corporis ? ita fit ut gratulator, laetior sit
quam is cui gratulatur." Even that, surely, is not an impossibility ; a per-
son's good fortune has often given more pleasure to others than it gave to
the person himself.
Descartes, with no less readiness, applies the same principle the converse
way, and infers the nature of the effects from the assumption that they
mast, in this or that property or in all their properties, resemble their
* Vol. i., chap. 8. *
538 FALLACIES.
cause. To this class belong his speculations, and those of so many others
after him, tending to infer the order of the universe, not from observation^
but by a priori reasoning from supposed qualities of the Godhead. This
sort of inference was probably never carried to a greater length than it
was in one particular instance by Descartes, when, as a proof of one of his
physical principles, that the quantity of niotion in the universe is invaria-
ble, he had recourse to the immutability of the Divine Nature. Reason-
ing of a very similai- character is, however, nearly as common now as it
was in his time, and does duty largely as a means of fencing off disagree-
able conclusions. Writers have not yet ceased to oppose the theory of
divine benevolence to the evidence of physical facts, to the principle of
population for example. And people seem in general to think that they
have used a very powerful argument, when they have said, that to suppose
some proposition true, would be a reflection on the goodness or wisdom of
the Deity. Put into the simplest possible terms, their argument is, ''If it
had depended on me, I would not have made the proposition true, there-
fore it is not true." Put into other words, it stands thus: " God is perfect,,
therefore (what I think) perfection must obtain in nature." But since in
reality every one feels that nature is very far from perfect, the doctrine is-
never applied consistently. It furnishes an argument which (like many
others of a similar character) people like to appeal to when it makes for
their own side. Nobody is convinced by it, but each appears to think
that it puts religion on his side of the question, and that it is a useful
weapon of offense for wounding an adversary.
Although several other varieties of a priori fallacy might probably be
added to those here specified, these are all against which it seems neces-
sary to give any special caution. Our object is to open, without attempt-
ing or affecting to exhaust, the subject. Having illustrated, therefore, this,
first class of Fallacies at sufficient length, 1 shall proceed to the second.
CHAPTER IV.
FALLACIES OF OBSERVATION.
§ 1. Fkom the Fallacies which are properly Prejudices, or presumptions
antecedent to, and superseding, proof, we pass to those which lie in the in-
correct performance of the proving process. And as Proof, in its widest
extent, embraces one or more, or all, of three processes. Observation, Gen-
eralization, and Deduction, we shall consider in their order the errors ca-
pable of being committed in these three operations. And first, of the first
mentioned.
A fallacy of misobservation may be either negative or positive ; either
Non- observation or Mai -observation. It is non-observation, when all the-
error consists in overlooking, or neglecting, facts or particulars which
ought to have been observed. It is mal- observation, when something is
not simply unseen, but seen wrong; when the fact or phenomenon, instead
of being recognized for what it is in reality, is mistaken for something else.
§ 2. Non-observation may either take place by overlooking instances, or
by overlooking some of the circumstances of a given instance. If we were
to conclude that a fortune-teller was a true prophet, from not adverting^
to the cases in which his predictions had been falsified by the event, this
FALLACIES OF OBSERVATION. 539
■would be non-observation of instances ; but if we overlooked or remained
ignorant of the fact that in cases where the predictions had been fulfilled,
he had been in collusion with some one who had given him the informa-
tion on which they were grounded, this would be non-observation of cir-
cumstances.
The former case, in so far as the act of induction from insufficient evi-
dence is concerned, does not fall under this second class of Fallacies, but
under the third. Fallacies of Generalization. In every such case, however
there are two defects or errors instead of one ; there is the error of treat-
ing the insufiicient evidence as if it were sufficient, which is a Fallacy of
the third class ; and there is the insuificiency itself ; the not having better
evidence ; which, when such evidence, or, in other words, when other in-
stances, were to be had, is Non-observation ; and the erroneous inference,
so far as it is to be attributed to this cause, is a Fallacy of the second
class.
It belongs not to our purpose to treat of non-observation as arising from
casual inattention, from general slovenliness of mental habits, want of due
practice in the use of the observing faculties, or insufficient interest in
the subject. The question pertinent to logic is — Granting the want of
complete competency in the observer, on what point is that insufficiency
on his part likely to lead him wrong ? or rather, what sorts of instances,
or of circumstances in any given instance, are most likely to escape the
notice of observers generally ; of mankind at large.
§ 3. First, then, it is evident that when the instances on one side of a
question are more likely to be remembered and recorded than those on
the other ; especially if there be any strong motive to preserve the memory
of the first, but not of the latter ; these last are likely to be overlooked,
and escape the observation of the mass of mankind. This is the recog-
nized explanation of the credit given, in spite of reason and evidence, to
many classes of impostors; to quack-doctors, and fortune-tellers in all
ages; to the "cunning man " of modern times, and the oracles of old.
Few have considered the extent to which this fallacy operates in practice,
even in the teeth of the most palpable negative evidence. A striking ex-
ample of it is the faith which the uneducated portion of the agricultural
classes, in this and other countries, continue to repose in the prophecies as
to weather supplied by almanac-makers ; though every season aiffords to
them numerous cases of completely erroneous prediction ; but as every
season also furnishes some cases in which the prediction is fulfilled, this is
enough to keep up the credit of the prophet, with people who do not re-
flect on the number of instances requisite for what we have called, in our
inductive terminology, the Elimination of Chance ; since a certain number
of casual coincidences not only may bat will happen, between any two un-
connected events.
Coleridge, in one of the essays in the Friend, has illustrated the matter
we are now considering, in discussing the origin of a proverb, " which, dif-
ferently worded, is to be found in all the languages of Europe," viz., " For-
tune favors fools." He ascribes it partly to the " tendency to exaggerate
all effects that seem disproportionate to their visible cause, and all circum-
stances that are in any way strongly contrasted with our notions of the
persons under them." Omitting some explanations which would refer the
error to mal-observation, or to the other species of non-observation (that
of circumstances), I take up the quotation further on. " Unforeseen coinci-
540 FALLACIES.
dences may have greatly helped a man, yet if they have done for him only
what possibly from his own abilities he might have effected for himself,
his good luck will excite less attention, and the instances be less remem-
bered. That clever men should attain their objects seems natural, and we
neglect the circumstances that perhaps produced that success of themselves
without the intervention of skill or foresight; but we dwell on the fact and
remember it, as something strange, when the same happens to a weak or
ignorant man. So too, though the latter should fail in his undertakings
from concurrences that might have happened to the wisest man, yet his
failure being no more than might have been expected -and accounted for
from his folly, it lays no hold on our attention, but fleets away among the
other undistinguished waves in which the stream of ordinary life murmurs
by us, and is forgotten. Had it been as true as it was notoriously false,
that those all-embracing discoveries, which have shed a dawn of science
on the art of chemistry, and give no obscure promise of some one great
constitutive law, in the light of which dwell dominion and the power of
prophecy ; if these discoveries, instead of having been, as they really were,
preconcerted by meditation, and evolved out of his own intellect, had oc-
curred by a set of lucky accidents to the illustrious father and founder of
philosophic alchemy; if they had presented themselves to Professor Davy
exclusively in consequence of his luck in possessing a particular galvanic
battery ; if this battery, as far as Davy was concerned, had itself been an
accident, and not (as in point of fact it was) desired and obtained by him
for the purpose of insuring the testimpny of experience to his principles,
and in order to bind down material nature under the inquisition of reason,
and force from her, as by torture, unequivocal answers to prepared and
preconceived questions — yet still they would not have been talked> of or
described as instances of luck, but as the natural results of his admitted
genius and known skill. But should an accident have disclosed similar
discoveries to a mechanic at Birmingham or Sheffield, and if the man
should grow rich in consequence, and partly by the envy of his neighbors
and partly with good reason, be considered by them as a man below par in
the general powers of his understanding; then, 'Oh, what a lucky fellow!
Well, Fortune does favor fools — that's for certain ! It is always so !' And
forthwith the exclaimer relates half a dozen similar instances. Thus ac-
cumulating the one sort of facts and never collecting the other, we do, as
poets in their diction, and quacks of all denominations do in their reason-
ing, put a part for the whole."
This passage very happily sets forth the manner in which, under the
loose mode of induction which proceeds per enumerationem simpUcem,
not seeking for instances of such a kind as to be decisive of the question,
but generalizing from any which occur, or rather which are remembered,
opinions grow up with the apparent sanction of experience, which have no
foundation in the laws of nature at all. " Itaque recte respondit ille " (we
may say with Bacon*), " qui cum suspensa tabula in templo ei monstrare-
tur eorum, qui vota solverant, quod naufragii periculo elapsi sint, atque
interrogando premeretur, anne tum quidem Deorum numen agnosceret,
quxsivitdenno, At ubi sunt illi depicti qui post vota nuncupata perienint?
Eadem ratio est fere omnis superstitionis, ut in Astrologicis, in Somniis,
Ominibus, Nemesibus, et hujusmodi; in quibus, homines delectati hujus-
inodi vanitatibus, advertunt eventus, ubi implentur; ast ubi fallunt, licet
* Nov. Org., Aph. 46.
FALLACIES OF OBSERVATION. 541
multo frequentius, tameu negligunt, et preetereunt." And he proceeds to
Bay that, independently of the love of the marvelous, or any other bias in
the inclinations, there is a natural" tendency in the intellect itself to this
kind of fallacy ; since the mind is more moved by affirmative instances,
though negative ones are of most use in philosophy : " Is tamen humano
intellectui error est proprius et perpetuus, ut magis moveatur et excitetur
Affirmativis quam Negativis; cum rite et ordine isquum se utrique prse-
bere debeat; quin contra, in omni Axiomate vero constituendo, major vis
est instantise negativse."
But the greatest of all causes oT non-observation is a preconceived opin-
ion. This it is which, in all ages, has made the whole race of mankind,
and every separate section of it, for the most part unobservant of all facts,
however abundant, even when passing under their own eyes, which are con-
tradictory to any first appearance, or any received tenet. It is worth
while to recall occasionally to the oblivious memory of mankind some of
the striking instances in which opinions that the simplest experiment
would have shown to be erroneous, continued to be entertained because
nobody ever thought of trying that experiment. One of the most remark-
able of these was exhibited in the Copernican controversy. The opponents
of Copernicus argued that the earth did not move, because if it did, a
stone let fall from the top of a high tower would not reach the ground at
the foot of the tower, but at a little distance from it, in a contrary direc-
tion to the earth's course ; in the same manner (said they) as, if a ball is
let drop from the mast-head while the ship is in full sail, it does not fall
exactly at the foot of the mast, but nearer to the stern of the vessel. The
Copernicans would have silenced these objectors at once if they had tried
dropping a ball from the mast-head, since they would have found that it
does fall exactly at the foot, as the theory requires ; but no ; they admitted
the spurious fact, and struggled vainly to make out a difference between
the two cases. " The ball was no part of the ship — and the motion for-
ward was not natural, either to the ship or to the ball. The stone, on the
other hand, let fall from the top of the tower, was a part of the earth ; and
therefore, the diurnal and annular revolutions which were natural to the
earth, were ^Iso natural to the stone ; the stone would, therefore, retain
the same motion with the tower, and strike the ground precisely at the
bottom of it."*
Other examples, scarcely less striking, are recorded by Dr. Whewell,!
where imaginary laws of nature have continued to be received as real,
merely because no person had steadily looked at facts which almost every
one had the opportunity of observing. "A vague and loose mode of look-
ing at facts very easily observable, left men for a long time under the be^
lief that a body ten times as heavy as another falls ten times as fast ; that
objects immersed in water are always magnified, without regard to the
form of the surface ; that the magnet exerts an irresistible force ; that crys-
tal is always found associated with ice ; and the like. These and many
others are examples how blind and careless man can be even in observation
of the plainest and commonest appearances; and they show us that the
mere faculties of perception, although constantly exercised upon innumer-
able objects, may long fail in leading to any exact knowledge."
If even on physical facts, and these of the most obvious character, the
observing faculties of mankind can be to this degree the passive slaves of
* Playfair's Dissertation, sect. 4. t ^ov. Org. Renov., p. 61.
542 FALLACIES.
their preconcdved impressions, we need not be surprised that this should
be so lamentably true as all experience attests it to be, on_ things more
nearly connected with their stronger feelings — on moral, social, and relig-
ious subjects. The information which an ordinary traveler brings back
from a foreign country, as the result of the evidence of his senses, is almost
always such as exactly confirms the opinions with which he set out. He
has had eyes and ears for such things only as he expected to see. Men read
the sacred books of their religion, and pass unobserved therein multitudes
of things utterly irreconcilable with even their own notions of moral ex-
cellence. With the same authorities before them, different historians, alike
innocent of intentional misrepresentation, see only what is favorable to
Protestants or Catholics, royalists or republicans, Charles I. or Cromwell;
while others, having set out with the preconception that extremes must
be in the wrong, are incapable of seeing truth and justice when these are
wholly on one side.
The influence of a preconceived theory is well exemplified in the super-
stitions of barbarians respecting the virtues of medicaments and charms.
The negroes, among whom coral, as of old among ourselves, is worn as an
amulet, aflirm, according to Dr. Paris,* that its color " is always affected
by the state of health of the wearer, it becoming paler in disease." On a
matter open to universal observation, a general proposition which has not
the smallest vestige of truth is received as a result of experience ; the pre-
conceived opinion preventing, it would seem, any observation whatever on
the subject.
§ 4. For illustration of the first species of non-observation, that of In-
stances, what has now been stated may suffice. But there may also be
non-observation of some material circumstances, in instances which have
not been altogether overlooked — nay, which may be the very instances on
which the whole superstructure of a theory has been founded. As, in the
cases hitherto examined, a general proposition was too rashly adopted, on
the evidence of particulars, true indeed, but insufficient to support it ; so
in the cases to which we now turn, the particulars themselves have been
imperfe'ctly observed, and the singular propositions on which the generali-
zation is grounded, or some at least of those singular projfositions, are
false.
Such, for instance, was one of the mistakes committed in the celebrated
phlogistic theory ; a doctrine which accounted for combustion by the ex-
trication of a substance called phlogiston, supposed to be contained in all
combustible matter. The hypothesis accorded tolerably well with super-
ficial appearances ; the ascent of flame naturally suggests the escape of a
substance ; and the visible residuum of ashes, in bulk and weight, generally
falls extremely short of the combustible material. The error was, non-ob-
servation of an important portion of the actual residue, namely, the gaseous
products of combustion. When these were at last noticed and brought
into account, it appeared to be a universal law, that all substances gain in-
stead of losing weight by undergoing combustion ; and after the usual at-
tempt to accommodate the old theory to the new fact by means of an ar-
bitrary hypothesis (that phlogiston had the quality of positive levity in-
stead of gravity), chemists were conducted to the true explanation, namely,
that instead of a substance separated, there was, on the contrary, a substance
absorbed.
* Pharmacohgia, p. 21.
FALLACIES OF OBSERVATION. 543
Many of the absurd practices which have been deemed to possess medic-
inal efficacy, have been indebted for their reputation to non-observance of
gome accompanying circumstance which was the real agent in the cures
ascribed to them. Thus, of the sympathetic powder of Sir Kenelm Digby :
« Whenever any wound had been inflicted, this powder was applied to the
weapon that had inflicted it, which was, moreover, covered with ointment,
and dressed two or three times a day. The wound itself, in the mean time,
was directed to be brought together, and carefully bound up with clean
linen rags, but, above all, to be let alone for seven days, at the end of which
period the bandages were removed, when the wound was generally found
perfectly united. The triumph of the cure was decreed to the mysterious
agency of the sympathetic powder which had been so assiduously applied
to the weapon, whereas it is hardly necessary to observe that the prompt-
ness of the cure depended on the total exclusion of air from the wound,
and upon the sanative operations of nature not having received any dis-
turbance from the officious interference of art. . The result, beyond all
doubt, furnished the first hint which led surgeons to the improved practice
of healing wounds by what is technically called the first intention."* " In
all records," adds Dr. Paris, of " extraordinary cures performed by mysteri-
ous agents, there is a great desire to conceal the remedies and other curative
means which were simultaneously administered with them ; thus Oribasius
commends in high terms a necklace of Paeony root for the cure of epilepsy ;
but we learn that he always took care to accompany its use with copious
evacuations, although he assigns to them no share of credit in the cure.
In later times we have a good specimen of this species of deception, pre-
sented to us in a work on scrofula by Mr. Morley, written, as we are in-
formed, for the sole purpose of restoring the much-injured character and
use of the Vervain ; in which the author directs the root of this plant to
be tied with a yard of white satin ribbon around the neck, where it is to
remain until the patient is cured ; but mark — during this interval he calls
to his aid the most active medicines in the materia medica."f
In other cases, the cures really produced by rest, regimen, and amuse-
ment have been ascribed to the medicinal, or occasionally to the supernatu-
ral, means which were put in requisition. " The celebrated John Wesley,
while he commemorates the triumph of sulphur and supplication over his
bodily infirmity, forgets to appreciate the resuscitating influence of four
months' repose from his apostolic labors ; and such is the disposition of
the human mind to place confidence in the operation of mysterious agents,
that we find him more disposed to atti-ibute his cure to a brown paper
plaster of egg and brimstone, than to Dr. Fothergill's salutary prescription
of country air, rest, asses' milk, and horse exercise."J
In the following example, the circumstance overlooked was of a some-
what difEerent character. " When the yellow fever raged in America, the
practitioners trusted exclusively to the copious use of mercury; at first
this plan was deemed so universally efficacious, that, in the enthusiasm of the
moment, it was triumphantly proclaimed that death never took place after
the mercury had evinced its effect upon the system : all this was very true,
but it furnished no proof of the efficacy of that metal, since the disease in its
■aggravated form was so rapid in its career, that it swept away its victims
long before the system could be brought under mercurial influence, while in
Us milder shape it passed off equally well without any assistance from art."§
♦ Pharmacologia, pp. 23, 24. t Ibid., p. 28. t Ibid., p. 62. § Ibid., pp. 61, 62.
544 FALLACIES.
In these, examples the circurastanoe overlooked was cognizable by the
senses. In other cases, it is one the knowledge of which could only be ar-
rived at by reasoning ; but the fallacy may still be classed under the head
to which, for want of a more appropriate name, we have given the appel-
lation Fallacies of Non-observation. It is not the nature of the facul-
ties which ought to have been employed, but the non-employment of them,
which constitutes this Natural Order of Fallacies. Wherever the error is
negative, not positive; wherever it consists especially in overlooking, in
being ignorant or unmindful of some fact which, if known and attended to,
would have made a difference in the conclusion arrived at; the error is
properly placed in the Class which we are considering. In this Class, there
is not, as in all other fallacies there is, a positive misestimate of evidence
actually had. The conclusion would be just, if the portion which is seen
of the case were the whole of it ; but there is another portion overlooked,
which vitiates the result.
For instance, there is a remarkable doctrine which has occasionally found
a vent in the public speeches of unwise legislators, but which only in one
instance that I am aware of has received the sanction of a philosophical
writer, namely, M. Cousin, who in his preface to the Gorgias of Plato, con-
tending that punishment must have some other and higher justification
than the prevention of crime, makes use of this argument — that if punish-
ment were only for the sake of example, it would be indiffei-ent whether
we punished the innocent or the guilty, since the punishment, considered as
an example, is equally efficacious in either case. Now we must, in order
to go along with this reasoning, suppose, that the person who feels himself
under temptation, observing somebody punished, concludes himself to be
in danger of being punished likewise, and is terrified accordingly. But it
is forgotten that if the person punished is supposed to be innocent, or even
if there be any doubt of his guilt, the spectator will reflect that his own
danger, whatever it may be, is not contingent on his guiltiness, but threat-
ens him equally if he remains innocent, and how, therefore, is he deterred
from guilt by the apprehension of such punishment? M. Cousin supposes-
that people will be dissuaded from guilt by whatever renders the condi-
tion of the guilty more perilous, forgetting that the condition of the inno-
cent (also one of the elements in the calculation) is, in the case supposed,
made pei-ilous in precisely an equal degree. This is a fallacy of overlook-
ing; or of non-observation, within the intent of our classification.
Fallacies of this description are the great stumbling-block to correct
thinking in political economy. The economical workings of society afford
numerous cases in which the effects of a cause consist of two sets of phe-
nomena : the one immediate, concentrated, obvious to all eyes, and passing,
in common apprehension, for the whole effect ; the other widely diffused,
or lying deeper under the surface, and which is exactly contrary to the
former. Take, for instance, the common notion so plausible at the first
glance, of the encouragement given to industi'y by lavish expenditure. A^
who spends his whole income, and even his capital, in expensive living, is
supposed to give great employment to labor. B, who lives on a small por-
tion, and invests the remainder in the funds, is thought to give little or
no employment. _ For every body sees the gains which are made by A's
tradesmen, servants, and others, while his money is spending. B's sav-
ings, on the contrary, pass into the hands of the person whose stock he
purchased, who with it pays a debt he owed to some banker, who lends it
again to some merchant or manufacturer; and the capital being laid out
FALLACIES OF OBSEBVATION. 545
in hiring spinners and weavers, or carriers and the crews of merchant ves-
sels, not only gives immediate employment to at least as much industry as
A employs during the whole of his career, but coming back with increase
by the sale of the goods which have been manufactured or imported, forms
a fund for the employment of the same and perhaps a greater quantity of
labor in perpetuity. But the observer does not see, and therefore does
not consider, what becomes of B's money ; he does see what is done with
A's ; he observes the amount of industry which A's profusion feeds ; he
observes not the far greater quantity which it prevents from being fed j
and thence the prejudice, universal to the time of Adam Smith, that prodi-
gality encourages industry, and parsimony is a discouragement to it.
The common argument against free trade was a fallacy of the same na-^
tare. The pui-chaser of British silk encourages British industry ; the pur-
chaser of Lyons silk encourages only French ; the former conduct is patri-
otic, the latter ought to be prevented by law. The circumstance is over-
looked, that the purchaser of any foreign commodity necessarily causes, di
rectly or indirectly, the export of an equivalent value of some article of
home production (beyond what would otherwise be exported), either to
the same foreign countiy or to some other ; which fact, though from the
complication of the circumstances it can not always be verified by specific
observation, no observation can possibly be brought to contradict, while the
evidence of reasoning on which it rests is irrefragable. The fallacy is,
therefore, the same as in the preceding case, that of seeing a part only of
the phenomena, and imagining that part to be the whole ; and may be
ranked among Fallacies of Non-observation.
§ 5. To complete the examination of the second of our five classes, we
have now to speak of Mal-observation ; in which the error does not lie in
the fact that something is unseen, but that something seen is seen wrong.
Perception being infallible evidence of wh.atever is really perceived, the
error now under consideration can be committed no otherwise than by
mistaking for conception what is, in fact, inference. We have formerly
shown how intimately the two are blended in almost every thing which i&
called observation, and still more in every Description.* What is actually
on any occasion perceived by our senses being so minute in amount, and
generally so unimportant a portion of the state of facts which we wish to
ascertain or to communicate ; it would be absurd to say that either in our
observations, or in conveying their result to others, we ought not to mingle
inference with fact ; all that can be said is, that when we do so we ought
to be aware of what we are doing, and to know what part of the assertion
rests on consciousness, and is therefore indisputable, what part on inference,,
and is therefore questionable.
One of the most celebrated examples of a universal error produced by
mistaking an inference for the direct evidence of the senses, was the resist-
ance made, on the ground of common sense, to the Copernican system.
People fancied they saw the. sun rise and set, the stars revolve in circles
round the pole. We now know that they saw no such thing; what they
really saw was a set of appearances, equally reconcilable with the theory
they held and with a totally difEerent one. It seems strange that such an
instance as this of the testimony of the senses pleaded with the most en-
tire conviction iu favor of something which was a mere inference of the
* Suvra, p. 450.
35
546 FALLACIES.
judgment, and, as it turned out, a false inference, should not have opened
the eyes of the bigots of common sense, and inspired them with a more
modest distrust of the competency of mere ignorance to judge the conclu-
flions of cultivated thought.
In proportion to any person's deficiency of knowledge and mental culti-
vation is, generally, his inability to discriminate between his inferences and
the perceptions on which they were grounded. Many a marvelous tale,
many a scandalous anecdote, owes its origin to this incapacity. The nar-
rator relates, not what he saw or heard, but the impression which he de-
rived from what he saw or heard, and of which perhaps the greater part
consisted of inference, though the whole is related not as inference but as
matter of fact. The difficulty of inducing witnesses to restrain within any
moderate limits the intermixture of their inferences with the narrative of
their perceptions, is well known to experienced cross-examiners ; and still
more is this the case when ignorant persons attempt to describe any natu-
ral phenomenon. " The simplest narrative," says Dugald Stewart,* " of
the most illitei-ate observer involves more or less of hypothesis ; nay, in
general, it will be found that, in proportion to his ignorance, the greater is
the number of conjectural principles involved in his statements. A village
apothecary (and, if possible, in a still greater degree, an experienced nurse)
is seldom able to describe the plainest case, without employing a phraseol-
ogy of which every word is a theory : whereas a simple and genuine speci-
fication of the phenomena which mark a particular disease ; a specification
unsophisticated by fancy, or by preconceived opinions, may be regarded as
unequivocal evidence of a mind trained by long and successful study to the
most difficult of all arts, that of the faithful interpretation of nature."
The universality of the confusion between perceptions and the inferences
drawn from them, and the rarity of the power to discriminate the one from
the other, ceases to surprise us when we consider that in the far greater
number of instances the actual perceptions of our senses are of no impor-
tance or interest to us except as marks from which we infer something be-
yond them. It is not the color and superficial extension perceived by the
eye that are important to us, but the object, of which those visible appear-
ances testify the presence ; and where the sensation itself is indifferent, as
it generally is, we have no motive to attend particularly to it, but acquire a
habit of passing it over without distinct consciousness, and going on at
once to the inference. So that to know what the sensation actually was, is
a study in itself, to which painters, for example, have to train themselves
by special and long-continued discipline and application. In things farther
removed from the dominion of the outward senses, no one who has not
great experience in pyschologioal analysis is competent to break this in-
tense association ; and when such analytic habits do not exist in the requi-
site degree, it is hardly possible to mention any of the habitual judgments
of mankind on subjects of a high degree of abstraction, from the being of
a God and the immortality of the soul down to the multiplication table,
which are not, or have not been, considered as matter of direct intuition.
So strong is the tendency to ascribe an intuitive character to judgments
which are mere inferences, and often false ones. No one can doubt that
many a deluded visionary has actually believed that he was directly in-
spired from Heaven, and that the Almighty had conversed with him face
to face ; which yet was only, on his part, a conclusion drawn from appear-
* Elements of the Philosophy of the Mind, vol. ii., chap. 4, sect. 6.
FALLACIES OF GENERALIZATION. 547
ances to his senses, or feelings in his internal consciousness, which afforded
no warrant for any such belief. A caution, therefore, against this class of
errors, is not only needful but indispensable ; though to determine wheth-
er, on any of the great questions of metaphysics, such errors are actually
committed, belongs not to this place, but, as I have so often said, to a dif-
ferent science.
CHAPTER V.
FALLACIES OF GBNBEALIZATION.
§ 1. The class of Fallacies of which we are now to speak, is the most
■extensive of all ; embracing a greater number and variety of unfounded
inferences than any of the other classes, and which it is even more difficult
to reduce to sub-classes or species. If the attempt made in the preceding
books to define the principles of well-grounded generalization has been
successful, all generalizations not conformable to those principles might,
in a certain sense, be brought under the present class ; when, however, the
rules are known and kept in view, but a casual lapse committed in the ap-
plication of them, this is a blunder, not a fallacy. To entitle an error of
generalization to the latter epithet, it must be committed on principle ;
there must lie in it some erroneous general conception of the inductive
process ; the legitimate mode of drawing conclusions from observation and
■experiment must be fundamentally misconceived.
Without attempting any thing so chimerical as an exhaustive classifica-
tion of all the misconceptions which can exist on the subject, let us con-
tent ourselves with noting, among the cautions which might be suggested,
a few of the most useful and needful.
§ 2. In the first place, there are certain kinds of generalization which,
if the principles already laid down be correct, must be groundless ; expe-
rience can not afford the necessary conditions for establishing them by a
correct induction. Such, for instance, are all inferences from the order of
nature existing on the earth, or in the solar system, to that which may
exist in remote parts of the universe ; where the phenomena, for aught we
know, may be entirely different, or may succeed one another according to
different laws, or even according to no fixed law at all. Such, again, in
matters dependent on causation, are all universal negatives, all propositions
that assert impossibility. The non-existence of any given phenomenon,
however uniformly experience may as yet have testified to the fact, proves
at most that no cause, adequate to its production, has yet manifested itself ;
but that no such causes exist in nature can only be inferred if we are so
foolish as to suppose that we know all the forces in nature. The supposi-
tion would at least be premature while our acquaintance with some even
of those which we do know is so extremely recent. And however much
our knowledge of nature may hereafter be extended, it is not easy to see
how that knowledge could ever be complete, or how, if it were, we could
■ever be assured of its being so.
The only laws of nature which afford sufficient warrant for attributing
impossibility (even with reference to the existing order of nature, and to
our own region of the universe) are, first, those of number and extension,
which are paramount to the laws of the succession of phenomena, and not
exposed to the agency of counteracting causes ; and, secondly, the universal
548 FALLACIES.
law of causality itself. That no variation in any effect or consequent will
take place while the whole of the antecedents remain tlie same, may be
affirmed with full assurance. But, that the addition of some new anteced-
ent might not entirely alter and subvert the accustomed consequent, or that
antecedents competent to do this do not exist in nature, we are in no case
empowered positively to conclude.
§ 3. It is next to be remarked that all generalizations which profess,
like the theories of Thales, Democritus, and others of the early Greek
speculators, to resolve all things into some one element, or like many mod-
ern theories, to resolve phenomena radically different into the same, are
necessarily false. By radically different phenomena I mean impressions
on our senses which differ in quality, and not merely in degree. On this
subject what appeared necessary was said in the chapter on the Limits to
the Explanation of Laws of Nature ; but as the fallacy is even in our own
times a common one, I shall touch on it somewhat further in this place.
When we say that the force which retains the planets in their orbits is
I'esolved into gravity, or that the force which makes substances combine
chemically is resolved into electricity, we assert in the one case what is,
and in the other case what might, and probably will ultimately, be a legiti-
mate result of induction. In both these cases motion is resolved into mo-
tion. The assertion is, that a case of motion, which was supposed to be
special, and to follow a distinct law of its own, confoi'ms to and is included
in the general law which regulates another class of motions. But, from
these and similar generalizations, countenance and currency have been
given to attempts to resolve, not motion into motion, but heat into motion,,
light into motion, sensation itself into motion ; states of consciousness intO'
states of the nervous system, as in the ruder forms of the materialist phi-
losophy; vital phenomena into mechanical or chemical processes, as in
some schools of physiology.
Now I am far from pretending that it may not be capable of proof, or
that it is not an important addition to our knowledge if proved, that cer-
tain motions in the particles of bodies are the conditions of the production
of heat or light; that certain assignable physical modifications of the nerves
may be the conditions not only of our sensations or emotions, but even of
our thoughts ; that certain mechanical and chemical conditions may, in the
order of nature, be sufficient to determine to action the physiological laws
of life. All I insist upon, in common with every thinker who entertains
any clear idea of the logic of science, is, that it shall not be supposed that
by proving these things one step would be made toward a real explanation
of heat, light, or sensation ; or that the generic peculiarity of those phe-
nomena can be in the least degree evaded by any such discoveries, how-
ever well established. Let it be shown, for instance, that the most com-
plex series of physical causes and effects succeed one another in the eye
and in the brain to produce a sensation of color; rays falling on the eye,,
refracted, converging, crossing one another, making an inverted image on
the retina, and after this a motion — let it be a vibration, or a rush of nerv-
ous fluid, or whatever else you are pleased to suppose, along the optic
nerve — a propagation of this motion to the brain itself, and as many more
different motions as you choose ; still, at the end of these motions, there is
something which is not motion, there is a feeling or sensation of color.
Whatever number of motions we may be able to interpolate, and whether
they be real or imaginary, we shall still find, at the end of the series, a mo-
FALLACIES OF GENERALIZATION. 549
tion antecedent and a color consequent. The mode in which any one of
the motions produces the next, may possibly be susceptible of explanation
by some general law of motion : but the mode in which the last motion
produces the sensation of color, can not be explained by any law of mo-
tion ; it is the la\t.of color : which is, and must always remain, a peculiar
thing. Where our consciousness recognizes between two phenomena an
inherent distinction; where we are sensible of a difference which is not
merely of degree, and feel that no adding one of the phenomena to itself
would produce the other ; any theory which attempts to bring either un-
der the laws of the other must be false; though a theory which merely
treats the one as a cause or condition of the other, may possibly be true.
§ 4. Among the remaining forms of erroneous generalization, several of
those most worthy of and most requiring notice have fallen under our ex-
amination in former places, where, in investigating the rules of correct in-
duction, we have had occasion to advert to the distinction between it and
some common mode of the incorrect. In this number is what I have for-
merly called the natural Induction of uninquiring minds, the induction of
the ancients, which proceeds ^er enumerationem simplicem: "This, that,
and the other A are B, I can not think of any A which is not B, therefore
every A is B." As a final condemnation of this rude and slovenly mode
of generalization, I will quote Bacon's emphatic denunciation of it ; the
most important part, as I have more than once ventui'ed to assert, of the
permanent service rendered by him to philosophy. " Inductio quae pro-
cedit per enumerationem simplicem, res puerilis est, et precario concludit "
(concludes only by your leave, or provisionally), " et periculo exponitur ab
instantia contradictoria, et plerumque secundum pauciora quam par est, et
ex his tantummodo quce prcesto sunt pronunciat. At Inductio quae ad in-
ventionem et demonstrationern Scientiarum et Artium erit utilis, Naturam
separare debet, per rejectiones et exclusiones debitas ; ac delude post nega-
tivas tot quot sufEciunt, super affirmativas concludere."
I have already said that the mode of Simple Enumeration is still the
common and received method of Induction in whatever relates to man and
society. Of this a very few instances, more by way of memento than of
instruction, may suffice. "What, for example, is to be thought of all the
"common-sense" maxims for which the following may serve as the uni-
versal formula, "Whatsoever has never been, will never be." As for ex-
ample: negroes have never been as civilized as whites sometimes are,
therefore it is impossible they should be so. Women, as a class, are sup-
posed not to have hitherto been equal in intellect to men, therefore they
are necessarily inferior. Society can not prosper without this or the other
institution ; e. g., in Aristotle's time, without slavery ; in later times, with-
out an established priesthood, without artificial distinctions of rank, etc.
One poor person in a thousand, educated, while the nine hundred and nine-
ty-nine remain uneducated, has usually aimed at raising himself out of his
class, therefore education makes people dissatisfied with the condition of a
laborer. Bookish men, taken from speculative pursuits and set to work
on something they know nothing about, have generally been found or
thought to do it ill; therefore philosophers are unfit for business, etc.,
etc. All these are inductions by simple enumeration. Reasons having
some reference to the canons of scientific investigation have been attempt-
ed to be given, however unsuccessfully, for some of these propositions ;
but to the multitude of those who parrot them, the enumeratio simplex, ex
550 FALLACIES.
his tantummodo qumproesto sunt pronuncians, is the sole evidence. Their
fallacy consists in this, that they are inductions without elimination : theve-
has been no real comparison of instances, nor even ascertainment of the
material facts in any given instance. There is also the further error, of
forgetting that such generalizations, even if well established, could not be;
ultimate truths, but must be results of laws much more elementary ; and.
therefore, until deduced from such, could at most be admitted as empirical
laws, holding good within the limits of space and time by which the partic-
ular observations that suggested the generalization were bounded.
This error, of placing mere empirical laws, and laws in which there is no-
direct evidence of causation, on the same footing of certainty as laws of
cause and effect, an error which is at the root of perhaps the greater num-
ber of bad inductions, is exemplified only in its grossest form in the kind
of generalizations to which we have now referred. These, indeed, do not
possess even the degree of evidence which pertains to a well-ascertained,
empirical law; but admit of refutation on the empirical ground itself, with-
out ascending to casual laws. A little reflection, indeed, will show that
mere negations can only form the ground of the lowest and least valuable
kind of empirical law. A phenomenon has never been noticed ; this only
proves that the conditions of that phenomenon have not yet occurred in ex-
perience, but does not prove that they may not occur hereafter. There ia
a better kind of empirical law than this, namely, when a phenomenon which
is observed presents within the limits of observation a series of gradations^
in which a regularity, or something like a mathematical law, is perceptible;
from which, therefore, something may be rationally presumed as to those-
terms of the series which are beyond the limits of observation. But in ne-
gation there are no gradations, and no series ; the generalizations, therefore,,
which deny the possibility of any given condition of man and society merely
because it has never yet been witnessed, can not possess this higher degree
of validity even as empirical laws. What is more, the minuter examinatiort
which that higher order of empirical laws presupposes, being applied to-
the subject-matter of these, not only does not confirm but actually refutes
them. For in reality the past history of Man and Society, instead of ex-
hibiting them as immovable, unchangeable, incapable of ever presenting
new phenomena, shows them, on the contrary, to be, in many most impor-
tant particulars, not only changeable, but actually undergoing a progressive
change. The empirical law, therefore, best expressive, m most cases, of the
genuine result of observation, would be, not that such and such a phenom-
enon will continue unchanged, but that it will continue to change in some
particular manner.
Accordingly, while almost all generalizations relating to Man and Society,
antecedent to the last fifty or sixty years, have erred in the gross way which
we have attempted to characterize, namely, by implicitly assuming that na-
ture and society will forever revolve in the same orbit, and exhibit essential-
ly the same phenomena ; which is also the vulgar error of the ostentatiously
practical, the votaries of so-called common sense, in our day, especially in
Great Britain ; the more thinking minds of the present age, having applied
a more minute analysis to the past records of our race, have for the most
part adopted a contrary opinion, that the human species is in a state of neces-
sary progression, and that from the terms of the series which are past we
may infer positively those which are yet to come. Of this doctrine, consid-
ered as a philosophical tenet, we shall have occasion to speak more fully in
the concluding Book. If not, in all its forms, free from error, it is at least
FALLACIES OF GENERALIZATION. 55 1
free from the gross and stupid error which we previously exemplified. But,
in all except the most eminently philosophical minds, it is infected with pre-
cisely the same kind of fallacy as that is. For we must remember that even
this other and better generalization, the progi-essive change in the condition
of the human species, is, after all, but an empirical law ; to which, too, it is
not difficult to point out exceedingly large exceptions ; and even if these
could be got rid of, either by disputing the facts or by explaining and lim-
iting the theory, the general objection remains valid against the supposed
law, as applicable to any other than what, in our third book, were termed
Adjacent Cases. For not only is it no ultimate, but not even a causal law.
Changes do indeed take place in human affairs, but every one of those
changes depends on determinate causes; the " progressiveness of the spe-
cies" is not a cause, but a summary expression for the general result of all the
causes. So soon as, by a quite different sort of induction, it shall be ascer-
tained what causes have produced these successive changes, from the begin-
ning of history, in so far as they have really taken place, and by what causes
of a contrary tendency they have been occasionally checked or entirely
counteracted, we may then be prepared to predict the future with reason-
able foresight; we may be in possession of the real law of the future; and
may be able to declare on what cii-cumstances the continuance of the same
onward movement will eventually depend. But this it is the error of many
of the more advanced thinkers, in the present age, to overlook ; and to im-
agine that the empirical law collected from a mere comparison of the con-
dition of our species at different past times, is a real law, is the law of its
changes, not only past but also to come. The truth is, that the causes on
which the phenomena of the moral world depend, are in every age, and al-
most in every country, combined in some different proportion ; so that it is
Bcai-cely to be expected that the general result of them all should conform,
very closely, in its details at least, to any uniformly progressive series. And
all generalizations which affirm that mankind have a tendency to grow bet-
ter or worse, richer or poorer, more cultivated or more barbarous, that pop-
ulation increases faster than subsistence, or subsistence than population,,
that inequality of fortune has a tendency to increase or to break down, and
the like, propositions of considerable value as empirical laws within certain
(but generally rather narrow) limits, are in reality true or false according
to times and circumstances.
What we have said of empirical generalizations from times past to times
still to come, holds equally true of similar generalizations from present
times to times past ; when persons whose acquaintance with moral and so-
cial facts is confined to their own age, take the men and the things of that
age for the type of men and things in general, and apply without scruple
to the interpretation of the events of history, the empirical laws which rep-
resent sufficiently for daily guidance the common phenomena of human
nature at that time and in that particular state of society. If examples-
are wanted, almost every historical work, until a very recent period, abound-
ed in them. The same may be said of those who generalize empirically
from the people of their own country to the people of other countries, as
if human beings felt, judged, and acted everywhere in the same manner.
§ 5. In the foregoing instances, the distinction is confounded between-
empirical laws, which express merely the customary order of the succession
of effects, and the laws of causation on which the effects depend. There-
may, however, be incorrect generalization when this mistake is not com-
552 FALLACIES.
mitted ; when the investigation takes its proper direction, that of causes,
and the result erroneously obtained purports to be a really causal law.
The most vulgar form of this fallacy is that which is commonly called
post hoc, ergo propter hoc, or, cum hoc, ergo propter hoc. As when it was
inferred that England owed her industrial pre-eminence to her restrictions
on commerce ; as when the old school of financiers, and some speculative
writers, maintained that the national debt was one of the causes of nation-
al prosperity ; as when the excellence of the Church, of the Houses of
Xords and Commons, of the procedure of the law courts, etc., were infer-
red from the mere fact that the country had prospered under them. In
fiuch cases as these, if it can be rendered probable by other evidence that
the supposed causes have some tendency to produce the effect ascribed to
them, the fact of its having been produced, though only in one instance, is
of some value as a verification by specific experience ; but in itself it goes
scarcely any way at all toward establishing such a tendency, since, admit-
ting the effect, a hundred other antecedents could show an equally strong
title of that kind to be considered as the cause.
In these examples we see bad generalization a posteriori, or empiricism
properly so called; causation inferred from casual conjunction, without ei-
ther due elimination, or any presumption arising from known properties
•of the supposed agent. But bad generalization a priori is fully as common ;
which is properly called false theory ; conclusions drawn, by way of deduc-
tion, from properties of some one agent which is known or supposed to be
present, all other co-existing agents being overlooked. As the former is
the error of sheer ignorance, so the latter is especially that of semi-instruct-
ed minds ; and is mainly committed in attempting to explain complicated
phenomena by a simpler theory than their nature admits of. As when one
school of physicians sought for the universal principle of all disease in
"lentor and morbid viscidity of the blood," and imputing most bodily
derangements to mechanical obstructions, thought to cure them by me-
chanical remedies ;* while another, the chemical school, " acknowledged no
source of disease but the presence of some hostile acid or alkali, or some
deranged condition in the chemical composition of the fluid or solid parts,"
and conceived, therefore, that " all remedies must act by producing chem-
ical changes in the body. We find Tournefoit busily engaged in testing
every vegetable juice, in order to discover in it some traces of an acid or
alkaline ingredient, which might confer upon it medicinal activity. The
fatal errors into which such an hypothesis was liable to betray the practi-
tioner, received an awful illustration in the history of the memorable fever
that raged at Ley den in the year 1699, and which consigned two-thirds of
the population of that city to an untimely grave ; an event which in a great
measure depended upon the Professor Sylvius de la Boe, who having just
embraced the chemical doctrines of Van Helmont, assigned the origin of
the distemper to a prevailing acid, and declared that its cure could alone
* "Thus roiircroy," says Dr. Paris, " explained the operation of mercury by its specific
gravity, and the advocates of this doctrine favored the general introduction of the preparations
of iron, especially in scirrhus of the spleen or liver, upon the same hypothetical principle ; for,
say they, whatever is most forcible in removing the obstruction must be the most proper in-
strument of cure ; such is steel, which, besides the attenuating power with which it is fur-
nished, has still a greater force in this case from the gravity of its particles, which, being sev-
en times specifically heavier than any vegetable, acts in proportion with a stronger impulse,
and therefore is a more powerful deobstruent. This may be taken as a specimen of the style
in which these mechanical physicians reasoned and practiced." — Pharmacologia, pp. 38, 39-
FALLACIES OF GENERALIZATION. 553
[only] be effected by the copious administration of absorbent and testa-
ceous medicines.*
These aberrations in medical theory have their exact parallels in politics.
All the doctrines which ascribe absolute goodness to particular forms of
government, particular social arrangements, and even to particular modes of
education, without reference to the state of civilization and the various dis-
tinguishing characters of the society for which they are intended, are open
to the same objection — that of assuming one class of influencing circum-
stances to be the paramount rulers of phenomena which depend in an equal
or greater degree on many others. But on these considerations it is the
less necessary that we should now dwell, as they will occupy our attention
more largely in the concluding Book.
§ 6. The last of the modes of erroneous generalization to which I shall
advert, is that to which we may give the name of False Analogies. This-
Fallacy stands distinguished from those already treated of by the peculiar-
ity that it does not even simulate a complete and conclusive induction, but
consists in the misapplication of an argument which is at best only admis-
sible as an inconclusive presumption, where real proof is unattainable.
An ai'gument from analogy, is an inference that what is true in a certain
case is true in a case known to be somewhat similar, but not known to be
exactly parallel, that is, to be similar in all the material circumstances. An
object has the property B: another object is not known to have that prop-
erty, but resembles the first in a property A, not known to be connected
with B; and the conclusion to which the analogy points, is that this object,
has the property B also. As, for example, that the planets are inhabited^
because the earth is so. The planets resemble the earth in describing
elliptical orbits round the sun, in being attracted by it and by one another,
in being nearly spherical, revolving on their axes, etc. ; and, as we havfr
now reason to believe from the revelations of the spectroscope, are com-
posed, in great part at least, of similar materials ; but it is not known that
any of these properties, or all of them together, are the conditions on which
the possession of inhabitants is dependent, or are marks of those conditions.
Nevertheless, so long as we do not know what the conditions are, they
may be connected by some law of nature with those common properties ;.
and to the extent of that possibility the planets are more likely to be in-
habited than if they did not resemble the earth at all. This non-assignable
and generally small increase of probability, beyond what would otherwise
exist, is all the evidence which a conclusion can derive from analogy. For
if we have the slightest reason to suppose any real connection between
the two properties A and B, the argument is no longer one of analogy. If
it had been ascertained (I purposely put an absurd supposition) that there
was a connection by causation between the fact of revolving on an axia
and the existence of animated beings, or if there were any reasonable
ground for even suspecting such a connection, a probability would arise-
of the existence of inhabitants in the planets, which might be of any de-
gree of strength, up to a complete induction ; but we should then infer the
fact from the ascertained or presumed law of causation, and not from the
analogy of the earth.
The name analogy, however, is sometimes employed by extension to
denote those arguments of an inductive character but not amounting ta
* Pharmacologia, pp. 39, 40.
554 FALLACIES.
a veal induction, which are employed to strengthen the argument drawn
from a simple resemblance. Though A, the property common to the two
•cases, can not be shown to be the cause or effect of B, the analogical rea-
soner will endeavor to show that there is some less close degree of connec-
tion between them ; that A is one of a set of conditions from which, when
all united, B would result; or is an occasional effect of some cause which
has been known also to produce B; and the like. Any of which things,
if shown, would render the existence of B by so much more probable,
than if there had not been even that amount of known connection be-
tween B and A.
Now an error or fallacy of analogy may occur in two ways. Sometimes
it consists in employing an argument of either of the above kinds with
■correctness indeed, but overrating its probative force. This very common
aberration is sometimes supposed to be particularly incident to persons
•distinguished for their imagination ; but in reality it is the characteristic
intellectual vice of those whose imaginations are barren, either from want
of exercise, natural defect, or the narrowness of their range of ideas. To
such minds objects present themselves clothed in but few properties; and
as, therefore, few analogies between one object and anothei- occur to them,
they almost invariably overrate the degree of importance of those few:
while one whose fancy takes a wider range, perceives and remembers so
many analogies tending to conflicting conclusions, that he is much less
likely to lay undue stress on any of them. We always find that those
are the greatest slaves to metaphorical language who have but one set
of metaphors.
But this is only one of the modes of error in the employment of argu-
ments of analogy. There is another, more properly deserving the name
■of fallacy ; namely, when resemblance in one point is inferred from resem-
blance in another point, though there is not only no evidence to connect
the two circumstances by way of causation, but the evidence tends posi-
tively to disconnect them. This is properly the Fallacy of False Analogies.
As a first instance, we may cite that favorite argument in defense of
absolute power, drawn from the analogy of paternal government in a fam-
ily, which government, however much in need of control, is not and can
not be controlled by the children themselves, while they remain children.
Paternal government, says the argument, works well ; therefore, despotic
-government in a state will work well. I waive, as not pertinent in this
place, all that could be said in qualification of the alleged excellence of
paternal government. However this might be, the argument from the
family to the state would not the less proceed on a false analogy ; imply-
ing that the beneficial working of parental government depends, in the
family, on the only point which it has in common with political despotism,
namely, irresponsibility. Whereas it depends, when real, not on that but
on two other circumstances of the case, the affection of the parent for the
children, and the superiority of the parent in wisdom and experience;
neither of which properties can be reckoned on, or are at all likely to exist,
between a political despot and his subjects ; and when either of these cir-
cumstances fails even in the family, and the influence of the irresponsibil-
ity is allowed to work uncorrected, the result is any thing but good govern-
ment. This, therefore, is a false analogy.
Another example is the not uncommon dictum that bodies politic have
youth, maturity, old age, and death, like bodies natural; that after a cer-
tain duration of prosperity, they tend spontaneously to decay. This also
FALLACIES OF GENERALIZATION. 555
is a false analogy, because the decay of the vital powers in an animated
body can be distinctly traced to the natural progress of those very changes
of structure which, in their earlier stages, constitutes its growth to maturi-
ty; while in the body politic the progress of those changes can not, gener-
ally speaking, have any effect but the still further continuance of growth :
it is the stoppage of that progress, and the commencement of retrogression,
that alone would constitute decay. Bodies politic die, but it is of disease,
or violent death ; they have no old age.
The following sentence from Hooker's Ecclesiastical Polity is an in-
stance of a false analogy fi-om physical bodies to what are called bodies
politic. "As there could be in natural bodies no motion of any thing un-
less there were some which moveth all things, and continueth immovable ;
even so in politic societies there must be some unpunishable, or else no
man shall suffer punishment." There is a double fallacy here, for not only
the analogy, but the premise from which it is drawn, is untenable. The
notion that there must be something immovable which moves all other
things, is the old scholastic error of aprinium mobile.
The following instance I quote from Archbishop Whately's JRhetoric:
"It would be admitted that a great and permanent diminution in the quan-
tity of some useful commodity, such as corn, or coal, or iron, throughout
the world, would be a serious and lasting loss ; and again, that if the fields
and coal-mines yielded regularly double quantities, with the same labor.
We should be so much the richer ; hence it might be inferred, that if the
quantity of gold and silver in the world were diminished one-half, or were
doubled, like results would follow ; the utility of these metals, for the pur-
poses of coin, being very great. Now there are many points of resem-
blance and many of difference, between the precious metals on the one
hand, and corn, coal, etc., on the other ; but the important circumstance to
the supposed argument is, that the utility of gold and silver (as coin,
which is far the chief) depends on their value, which is regulated by their
scarcity; or rather, to speak strictly, by the difficulty of obtaining them;
whereas, if corn and coal were ten times as abundant (i. e., moi'e easily ob-
tained), a bushel of either would still be as useful as now. But if it were
twice as easy to procure gold as it is, a sovereign would be twice as large ;
if only half as easy, it would be of the size of a half-sovereign, and this (be-
sides the trifling circumstance of the cheapness or dearness of gold orna-
ments) would be all the difference. The analogy, therefore, fails in the
point essential to the argument."
The same author notices, after Bishop Copleston, the case of False
Analogy which consists in inferring from the similarity in many respects
between the metropolis of a country and the heart of the animal body,
that the increased size of the metropolis is a disease.
Some of the false analogies on which systems of physics were confident-
ly grounded in the time of the Greek philosophers, are such as we now
call fanciful, not that the resemblances are not often real, but that it is
long since any one has been inclined to draw from them the inferences
"which were then drawn. Such, for instance, ai-e the curious speculations
of the Pythagoreans on the subject of numbers. Finding that the dis-
tances of the planets bore, or seemed to bear, to one another a proportion
not varying much from that of the divisions of the monochoi'd, they in-
ferred from it the existence of an inaudible music, that of the spheres ; as
if the music of a harp had depended solely on the numerical proportions,
and not on the material, nor even on the existence of any material, any
556 FALLACIES.
Strings at all. It has been similavly imagined that certain combinations;
of numbers, which were found to prevail in some natural phenomena, must
run through the whole of nature: as that there must be four elements,
because there are four possible combinations of hot and cold, wet and dry ;.
that there must be seven planets, because there were seven metals, and
even because there were seven days of the week. Kepler himself thought
that there could be only six planets, because there were only five regular
solids. With these we may class the reasonings, so common in the specu-
lations of the ancients, founded on a supposed perfection in nature ; mean-
ing by nature the customary order of events as they take place of them-
selves without human interference. This also is a rude guess at an analo-
gy supposed to pervade all phenomena, however dissimilar. Since what
was thoughf to be perfection appeared to obtain in some phenomena, it
was inferred (in opposition to the plainest evidence) to obtain in all.
" We always suppose that which is better to take place in nature, if it be-
possible," says Aristotle; and the vaguest and most heterogeneous quali-
ties being confounded together under the notion of being better, there was
no limit to the wildness of the inferences. Thus, because the heavenly
bodies were "perfect," they must move in circles and uniformly. For
" they " (the Pythagoreans) " would not allow," says Geminus,* " of any
such disorder among divine and eternal things, as that they should some-
times move quicker and sometimes slower, and sometimes stand still; for
no one would tolerate such anomaly in the movements even of a man, who-
was decent and orderly. The occasions of life, however, are often reasons
for men going quicker or slower; but in the incorruptible nature of the
stars, it is not possible that any cause can be alleged of quickness or slow-
ness." It is seeking an argument of analogy very far, to suppose that the
stars must observe the rules of decorum in gait and carriage prescribed
for themselves by the long-bearded philosophers satirized by Lucian.
As late as the Copernican controversy it was urged as an argument m
favor of the true theory of the -solar system, that it placed the fire, the no-
blest element, in the centre of the universe. This was a remnant of the no-
tion that the order of nature must be perfect, and that perfection consisted
in conformity to rules of precedency in dignity, either real or conventional.
Again, reverting to numbers : certain numbers were perfect, therefore those-
numbers must obtain in the great phenomena of nature. Six was a per-
fect number, that is, equal to the sum of all its factors ; an additional rea-
son why there must be exactly six planets. The Pythagoreans, on the oth-
er hand, attributed perfection to the number ten ; but agreed in thinking
that the perfect number must be somehow realized in the heavens ; and
knowing only of nine heavenly bodies, to make up the enumeration, they
asserted "that there was an antichthon, or connter-eai'th, on the other side
of the sun, invisible to us."f Even Huygens was persuaded that when the
number of the heavenly bodies had reached twelve, it could not admit of
any further increase. Creative power could not go beyond that sacred
number.
Some curious instances of false analogy are to be found in the arguments
of the Stoics to prove the equality of all crimes, and the equal wretchedness
of all who had not realized their idea of perfect virtue. Cicero, toward the
end of his Fourth Book, De Finibus, states some of these as follows : " Ut,
inquit, in fidibus plurimis, si nulla earum ita contenta numeris sit, ut concen-
* I quote from Dr. Whewell's Hist. Ind. Sc, 3d ed., i., 129. t Sist. Ind. Sc, i., 52.
FALLACIES OF GENERALIZATION. 557
turn sevvare possit, omnes seque incontentaa sunt ; sic peccata, quia discre-
pant, ssque disciepant; paria sunt igitur." To which Cicero himself aptly
answers, " seque contingit omnibus fidibus, ut incoiitent£e sint ; illud non con-
tinuo, ut seque iucontentse." The Stoic resumes : " Ut enim, inquit, guber-
nator seque peccat, si palearum navem evertit, et si auri ; item seque peccat
qui parentem, et qui servum, injuria verberat;" assuming, that because the
magnitude of the interest at stake makes no difference in the mere defect
•of skill, it can make none in the moral defects a false analogy. Again,
•" Quis ignorat, si plures ex alto emergere velint, propius fore eos quidem
ad respirandum, qui ad summam jam aquam appropinquant, sed nihilo
magis respirare posse, quam eos, qui sunt in profundo ? Nihil ergo adju-
-vat procedere, et progredi in virtute, quominus miserrimus sit, antequam
.ad eam pervenerit, quoniam in aqu^, nihil adjuvat: et quoniam catuli, qui
jam despecturi sunt, cseci seque, et ii qui modo nati ; Platonem quoque ne-
•cesse est, quoniam nondum videbat sapientiara, seque caecum animo, ao
Phalarim fuisse." Cicero, in his own person, combats these false analogies
by other analogies tending to an opposite conclusion. " Ista similia non
eunt, Cato Ilia sunt similia ; hebes acies est cuipiam ocnlorum : cor-
pore alius languescit: hi curatione adhibita levantur in dies: alter' valet
pins quotidie : alter videt. Hi similes sunt omnibus, qui virtuti student ;
levantur vitiis, levantur erroribus."
§ 7. In these and all other arguments drawn from remote analogies, and
from metaphors, which are cases of analogy, it is apparent (especially when
we consider the extreme facility of raising up contrary analogies and con-
flicting metaphors) that, so far from the metaphor or analogy proving any
thing, the applicability of the metaphor is the very thing to be made out.
It has to be shown that in the two cases asserted to be analogous, the same
law is really operating ; that between the known resemblance and the in-
ferred one there is some connection by means of causation. Cicero and
Cato might have bandied opposite analogies forever; it rested with each
of them to prove by just induction, or at least to render probable, that the
case resembled the one set of analogous cases and not the other, in the cir-
cumstances on which the disputed question i-eally hinged. Metaphors, for
the most part, therefore, assume the proposition which they are brought to
prove : their use is, to aid the apprehension of it ; to make clearly and viv-
idly comprehended what it is that the person who employs the metaphor is
proposing to make out ; and sometimes also, by what media he proposes to do
80. For an apt metaphor, though it can not prove, often suggests the proof.
For instance, when D'Alembert (I believe) remarked that in certain gov-
ernments only two creatures find their way to the highest places, the eagle
and the serpent, the metaphor not only conveys with great vividness the
assertion intended, but contributes toward substantiating it, by suggesting,
in a lively manner, the means by which the two opposite characters thus
typified effect their rise. When it is said that a certain person misunder-
stands another because the lesser of two objects can not comprehend the
greater, the application of what is true in the literal sense of the word com-
prehend, to its metaphorical sense, points to the fact which is the ground
and justification of the assertion, viz., that one mind can not thoroughly
understand another unless it can contain it in itself, that is, unless it pos-
sesses all that is contained in the other. When it is urged as an argument
for education, that if the soil i8..1eft uncultivated, weeds will spring up, the
metaphor, though no proof, but a statement of the thing to be proved.
558 FALLACIES.
states it in terms which, by suggesting a parallel case, put the mind upon
the track of the real proof. For, the reason why weeds grow in an uncul-
tivated soil, is that the seeds of worthless products exist everywhere, and
can germinate and gi-ow in almost all circumstances, while the reverse is
the case with those which are valuable; and this being equally true of
mental products, this mode of conveying an argument, independently of its
rhetorical advantages, has a logical value ; since it not only suggests the
grounds of the conclusion, but points to another case in which those grounds
have been found, or at least deemed to be, sufficient.
On the other hand, when Bacon, who is equally conspicuous in the use
and abuse of figurative illustration, says that the stream of time has brought
down to us only the least valuable part of the writings of the ancients, as a
river carries froth and straws floating on its surface, while more weighty
objects sink to the bottom ; this, even if the assertion illustrated by it were
true, would be no good illustration, there being no parity of cause. The
levity by which substances float on a stream, and the levity which is syn-
onymous with worthlessness, have nothing in common except the namej
and (to show how little value there is in the metaphoi') we need only
change the word into buoyancy, to turn the semblance of argument in-
volved in Bacon's illustration against himself.
A metaphor, then, is not to be considered as an argument, but as an
assertion that an argument exists ; that a parity subsists between the case
from which the metaphor is drawn and that to which it is applied. This
parity may exist though the two cases be apparently very remote from one
another; the only resemblance existing between them may be a resem-
blance of relations, an analogy in Ferguson's and Archbishop Whately's
sense : as in the preceding instance, in which an illustration from agricul-
ture was applied to mental cultivation.
§ 8. To terminate the subject of Fallacies of Generalization, it remains
to be said, that the most fertile source of them is bad classification : bring-
ing together in one group, and under one name, things which have no com-
mon properties, or none but such as are too unimportant to allow general
propositions of any considerable value to be made respecting the class.
The misleading effect is greatest, when a word which in common use ex-
presses some definite fact, is extended by slight links of connection to
cases in which that fact does not exist, but some other or others, only
slightly resembling it. Thus Bacon,* in speaking of the Idola or Fallacies
arising from notions temere et incBqualiter d rebus abstractce, exemplifies
them by the notion of Humidum or Wet, so familiar in the physics of an-
tiquity and of the Middle Ages. "Invenietur verbum istud, Humidum,.
nihil aliud quam nota confusa diversarum actionum, quse nuUam constanti-
am aut reductionem patiwntur. Significat enim, et quod circa aliud corpus
facile se circumfundit; et quod in se est indeterminabile, nee consistere
potest ; et quod facile cedit undique ; et quod facile se dividit et dispergit;
et quod facile se unit et colligit; et quod facile fluit, et in motu ponitur;.
et quod alteri corpori facile adhaeret, idque madefacit; et quod facile redu-
citur in liquidum, sive colliquatur, cum antea consisteret. Itaque qunni ad
hujus nominis prsedicationem et impositionem ventum sit; si alia accipias,
flamma humida est; si alia accipias, aer humidus non est; si alia, pulvis
minutus humidus est; si alia, vitrum humidum est: ut facile appareat,,
* Nov. Org., Aph. 60.
FALLACIES OF RATIOCINATION. 558
istam notionera ex aqua tantnm, et communibus et vulgaribus liquoribus,
absque uUS. debitS, verificatione, temere abstractam esse."
Bacon himself is not exempt from a similar accusation when inquiring
into the nature of heat : where he occasionally proceeds like one who, seek-
ing for the cause of hardness, after examining that quality in iron, flint, and
diamond, should expect to find that it is something which can be traced
also in hard water, a hard knot, and a hard heart.
The word Kivriaie in the Greek philosophy, and the words Generation and
Corruption, both then and long afterward, denoted such a multitude of
heterogeneous phenomena, that any attempt at philosophizing in which
those words were used was almost as necessarily abortive as if the word
hard had been taken to denote a class including all the things mentioned
above. Kivqaie, for instance, which properly signified motion, was taken to
denote not only all motion but even all change : aWoimaiQ being recognized
as one of the modes of Kivr\ais. The effect was, to connect with every form
of aXKoibiaie or change, ideas drawn from motion in the proper and literal
sense, and which had no real connection with any other kind of Kivriaig than
that. Aristotle and Plato labored under a continual embarrassment from
this misuse of terms. But if we proceed further in this direction we shall
encroach upon the Fallacy of Ambiguity, which belongs to a different class,
the last in order of our classification. Fallacies of Confusion.
CHAPTER VI.
FALLACIES OF EATIOCINATION.
8 1. We have now, in our progress through the classes of Fallacies, ar-
rived at those to which, in the common books of logic, the appellation is
in general exclusively appropriated; those which have their seat in the
ratiocinative or deductive part of the investigation of truth. Of these fal-
lacies it is the less necessary for us to insist at any length, as they have
been most satisfactorily treated in a work familiar to almost all, in this
country at least, who feel any interest in these speculations. Archbishop
Whately's Logic. Against the more obvious forms of this class of falla-
cies, the rules of the syllogism are a complete protection. Not (as we
have so often said) that ratiocination can not be good unless it be in the
form of a syllogism ; but that, by showing it in that form, we are sure to
discover if it be bad, or at least if it contain any fallacy of this class.
§ 2. Among Fallacies of Ratiocination, we ought perhaps to include the
errors committed in processes which have the appearance only, not the re-
ality, of an inference from premises ; the fallacies connected with the con-
version and aequipollency of propositions. I believe errors of this descrip-
c tion to be far more frequently committed than is generally supposed, or
than their extreme obviousness might seem to admit of. For example,
the simple conversion of a universal affirmative proposition. All A are B,
therefore all B are A, I take to be a very common form of error: though
committed, like many other fallacies, oftener in the silence of thought than
in express words, for it can scarcely be clearly enunciated without being
detected. And so with another form of fallacy, not substantially different
from the preceding : the erroneous conversion of an hypothetical propo-
sition. The proper converse of an hypothetical proposition is this : If the
560 FALLACIES.
consequent be false, the antecedent is false; but this, If the consequent be
true, the antecedent is true, by na means holds good, but is an error corre-
sponding to the simple conversion of a universal affirmative. Yet hardly
any thing is more common than for people, in their private thoughts, to
draw this inference. As when the conclusion is accepted, which it so oft-
en is, for proof of the premises. That the premis.es can not be true if
the conclusion is false, is the unexceptionable foundation of the legitimate
mode of reasoning called reductio ad absurdum. But people continually
think and express themselves, as if they also believed that the premises
can not be false if the conclusion is true. The truth, or supposed truth, of
the inferences which follow from a doctrine, often enables it to find accepts
ance in spite of gross absurdities in it. How many philosophical systems
which had scarcely any intrinsic recommendation, have been received by
thoughtful men because they were supposed talend additional support to
religion, morality, some favorite view of politics, or some other cherished
persuasion : not merely because their wishes were thereby enlisted on its
side, but because its leading to what they deemed sound conclusions ap-
peared to them a strong presumption in favor of its truth : though the
presumption, when viewed in its true light, amounted only to the absence
of that particular evidence of falsehood, which would have resulted from
its leading by correct inference to something already known to be false.
Again, the very frequent error in conduct, of mistaking reyerse of wrong
for right, is the practical form of a logical error with respect to the Oppo-
sition of Propositions. It is committed for want of the habit of distin-
guishing the contrary of a proposition from the contradictory of it, and
•of attending to the logical canon, that contrary propositions, though they
«an not both be true, may both be false. If the error were to express it-
self in words, it would run distinctly counter to this canon. It generally,
however, does not so express itself, and to compel it to do so is the most
■effectual method of detecting and exposing it.
§ 3. Among Fallacies of Ratiocination are to be ranked, in the first
place, all the cases of vicious syllogism laid down in the books. These
generally resolve themselves into having more than three terms to the syl-
logism, either avowedly, or in the covert mode of an undistributed middle
term, or an illicit process of one of the two extremes. It is not, indeed,
very easy fully to oonvict an argument of falling under any one of these
vicious cases in particular ; for the reason already more than once referred
to, that the premises are seldom formally set out : if they were, the fallacy
would impose upon nobody ; and while they are not, it is almost always to
a certain degree optional in what manner the suppressed link shall be filled
up. The rules of the syllogism are rules for compelling a person to be
aware of the whole of what he must undertake to defend if he persists in
maintaining his conclusion. He has it almost always in his power to make
his syllogism good by introducing a false premise; and hence it is scarcely
over possible decidedly to affirm that any argument involves a bad syllo-
gism : but this detracts nothing from the' value of the syllogistic rules,
since it is by them that a reasoner is compelled distinctly to make his elec-
tion what premises he is prepared to maintain. The election made, there
is generally so little difficulty in seeing whether the conclusion follows,
from the premises set out, that we might without much logical improprie-
ty have merged this fourth class of fallacies in the fifth, or Fallacies of
Confusion.
FALLACIES OF KATIOCINATIOK 561
§ 4. Perhaps, however, the commonest, and certainly the most danger-
ous fallacies of this class, are those which do not lie in a single syllogism,
but slip in between one syllogism and another in a chain of argument, and
are committed by changing the premises. A proposition is proved, or an
acknowledged truth laid down, in the first part of an argumentation, and
in the second a further argument is founded not on the same proposition,
hut on some other, resembling it sufficiently to be mistaken for it. In-
stances of this fallacy will be found in almost all the argumentative dis-
courses of unprecise thinkers ; and we need only here advert to one of the
obscurer forms of it, i-ecognized by the school-men as the fallacy d dicto
■secundum quid ad dictum, simpliciter. This is committed when, in the
premises, a proposition is asserted with a qualification, and the qualifica-
tion lost sight of in the conclusion; or oftener, when a limitation or con-
dition, though not asserted, is necessary to the truth of the proposition,
but is forgotten when that proposition comes to be employed as a premise.
Many of the bad arguments in vogue belong to this class of error. The
premise is some admitted truth, some common maxim, the reasons or evi-
dence for which have been forgotten, or are not thought of at the time,
but if they had been thought of would have shown the necessity of so lim-
iting the premise that it would no longer have supported the conclusion
drawn from it.
Of this nature is the fallacy in what is called, by Adam Smith and oth-
ers, the Mercantile Theory in Political Economy. That theory sets out
from the common maxim, that whatever brings in money enriches ; or that
every one is rich in proportion to the quantity of money he obtains.
From this it is concluded that the value of any branch of trade, or of the
trade of the country altogether, consists in the balance of money it brings
in; that any trade which carries more money out of the country than it
draws into it is a losing trade ; that therefore money should be attracted
into the country and kept thei'e, by prohibitions and bounties ; and a train
of similar corollaries. All for want of reflecting that if the riches of an
individual are in proportion to the quantity of money he can command, it
is because that is the measure of his power of purchasing money's worth ;
and is therefore subject to the proviso that he is not debarred from em-
ploying his money in such purchases. The premise, therefore, is only true
secundum quid; but the theory assumes it to be true absolutely, and in-
fers that increase of money is increase of riches, even when produced by
means subversive of the condition under which alone money can be riches.
A second instance is, the argument by which it used to be contended,
hefore the commutation of tithe, that tithes fell on the landlord, and were
a deduction from rent; because the rent of tithe-free land was always
higher than that of land of the same quality, and the same advantages of
situation, subject to tithe. Whether it be true or not tha,t a tithe falls on
rent, a treatise on Logic is not the place to examine ; but it is certain that
this is no proof of it. Whether the proposition be true or false, tithe-free
land must, by the necessity of the case, pay a higher rent. For if tithes
do not fall on rent, it must be because they fall on the consumer ; because
they raise the price of agricultural produce. But if the produce be raised
in price, the farmer of tithe-free as well as the farmer of tithed land gets
the benefit. To the latter the rise is but a compensation for the tithe he
pays ; to the first, who pays none, it is clear gain, and therefore enablea
him, and if there be freedom of competition, forces him, to pay so much
more rent to his landlord. The question remains, to what class of fallacies
36
562 FALLACIES.
this belongs. The premise is, that the owner of tithed land receives less
rent than the owner of tithe-free land ; the conclusion is, that therefore he
receives less than he himself would receive if tithe were abolished. But.
the premise is only true conditionally ; the owner of tithed land receives
less than what the owner of tithe-free land is enabled to receive when other
lands are tithed; while the conclusion is applied to a state of circum-
stances in which that condition fails, and in which, by consequence, the
premise will not be true. The fallacy, therefore, is d, dicto secundum quid
ad dictum simpliciter.
A third example is the opposition sometimes made to legitimate inter-
ferences of government in the economical affairs of society, grounded on a
misapplication of the maxim, that an individual is a better judge than the
government of what is for his own pecuniary interest. This objection,
was urged to Mr. Wakefield's principle of colonization ; the conoentratioa
of the settlers, by fixing such a price on unoccupied land as may preserve-
the most desirable proportion between the quantity of land in culture and
the laboring population. Against this it was argued, that if individuals-
found it for their advantage to occupy extensive tracts of land, they, being
better judges of their own interest than the legislature (which can only
proceed on general rules), ought not to be restrained from doing so. But
in this argument it was forgotten that the fact of a person's taking a large
tract of land is evidence only that it is his interest to take as much as
other people, but not that it might not be for his interest to content him-
self with less, if he could be assured that other people would do so too ;.
an assurance which nothing but a government regulation can give. If all
other people took much, and he only a little, he would reap none of the
advantages derived from the concentration of the population and the con-
sequent possibility of procuring labor for hire, but would have placed him-
self, without equivalent, in a situation of voluntary inferiority. The prop-
osition, therefore, that the quantity of land which people will take when
left to themselves is that which is most for their interest to take, is true
only secundum quid: it is only their interest while they have no guar-
antee for the conduct of one another. But the arrangement disregards
the limitation, and takes the proposition for true simpliciter.
One of the conditions oftenest dropped, when what would otherwise be
a true proposition is employed as a premise for proving others, is the con-
dition of time. It is a principle of political economy that prices, profits,
wages, etc., " always find their level ;" but this is often interpreted as if it
meant that they are always, or generally, at their level, while the truth
is, as Coleridge epigrammatically expresses it, that they are alwuys Jlndinff
their level, " which might be taken as a paraphrase or ironical definition of
a storm."
Under the same head of fallacy {d dicto secundum quid ad dictum sim-
pliciter) might be placed all the errors which are vulgarly called misappli-
cations of abstract truths ; that is, where a principle, true (as the common
expression is) in the abstract, that is, all modifying causes being supposed
absent, is reasoned on as if it were true absolutely, and no modifying cir-
cumstance could ever by possibility exist. This very common form of
error it is not requisite that we should exemplify here, as it will be partic-
ularly treated of hereafter in its application to the subjects on which it is
most frequent and most fatal, those of politics and society.*
* "An advocate," says Mr. De Morgan {Formal Logic, p. 270), "is sometimes guilty of
the argument a dicto secundum quid ad dictum simpliciter; it is his business to do for his
FALLACIES OF CONTUSION. 563
CHAPTER VII.
FALLACIES OF CONFTJSIOlir.
§ 1. Under this fifth and last class it is convenient to arrange all those
fallacies in which the source of error is not so much a false estimate of the
probative force of known evidence, as an indistinct, indefinite, and fluctua-
"ting conception of what the evidence is.
At the head of these stands that multitudinous body of fallacious rea-
sonings in which the source of error is the ambiguity of terms : when
something which is true if a word be used in a particular sense, is reasoned
on as if it were true in another sense. In such a case there is not a mal-
estimation of evidence, because there is not properly any evidence to the
point at all ; there is evidence, but to a different point, which from a con-
fused apprehension of the meaning of the terms used, is supposed to be
the same. This error will naturally be oftener committed in our ratiocina-
tions than in our direct inductions, because in the former we are decipher-
ing our own or other people's notes, while in the latter we have the things
themselves present, either to the senses or to the memory. Except, indeed,
when the induction is not from individual cases to a generality, but from
generalities to a still higher generalization ; in that case the fallacy of am-
biguity may affect the inductive process as well as the ratiocinative. It
occurs in ratiocination in two ways : when the middle term is ambiguous,
or when one of the terras of the syllogism is taken in one sense in the
premises, and in another sense in the conclusion.
Some good exemplifications of this fallacy are given by Archbishop
Whately. " One case," says he, " which may be regarded as coming under
the head of Ambiguous Middle, is (what I believe logical writers mean by
'Fallacia Figurm Dictionis'') the fallacy built on the grammatical struc-
ture of language, from men's usually taking for granted that paronymous
(or conjugate) words, i. e., those belonging to each other, as the substantive,
adjective, verb, etc., of the same root, have a precisely corresponding mean-
ing ; which is by no means universally the case. Such a fallacy could not
indeed be even exhibited in strict logical form, which would preclude even
the attempt at it, since it has two middle terms in sound as well as sense.
But nothing is more common in practice than to vary continually the terms
employed, with a view to grammatical convenience ; nor is there any thing
unfair in such a practice, as long as the meaning is preserved unaltered ;
e. g., ' murder should be punished with death ; this man is a murderer,
client all that his client might honestly do for himself. Is not the word in italics frequently
omitted ? Might any man honestly try to do for himself all that counsel frequently try to do
for him ? We are often reminded of the two men who stole the leg of mutton ; one could
swear he had not got it, the other that he had not taken it. The counsel is doing his duty
by his client, the client has left the matter to his counsel. / Between the unexecuted inten-
tion of the client, and the unintended execution of the counsel, there may he a wrong done,
and, if we are to believe the usual maxims, no wrong-doer."
The same writer justly remarks (p. 251) that there is a converse fallacy, a ditto simpliciter
ad dictum secundum quid, called by the scholastic logicians /aHacta accidentis; and another
which may be called a dicto secundum quid ad dictum secundum alterum quid (p. 265), For
apt instances of both, I must refer the reader to Mr. De Morgan's able chapter on Fallacies.
564 FALLACIES.
therefore he deserves to die,' etc. Here we proceed on the assumption (in
this case just) that to commit murder, and to be a murderer — to deserve
death, and to be one who ought to die, are, respectively, equivalent expres-
sions ; and it would frequently prove a heavy inconvenience to be debarred
this kind of liberty ; but the abuse of it gives rise to the Fallacy in ques-
tion ; e. g., projectors are unfit to be trusted ; this man has formed ?i project,
therefore he is unfit to be trusted : here the sophist proceeds on the hy-
pothesis that he who forms s, project must be a. projector : whereas the bad
sense that commonly attaches to the latter word, is not at all implied in the
former. This fallacy may often be considered as lying not in the Middle,
but in one of the terms of the Conclusion ; so that the conclusion drawn
shall not be, in reality, at all warranted by the premises, though it will ap-
pear to be so, by means of the grammatical aiBnity of the words ; e. g., to
be acquainted with the guilty is a presumption of guilt ; this man is so ac-
quainted, therefore we may presume that he is guilty : this argument pro-
ceeds on the supposition of an exact correspondence between presume and
presumption, which, however, does not really exist ; for ' presumption ' is
commonly used to express a kind of slight suspicion; whereas, ' to pre-
sume' amounts to actual belief. There are innumerable instances of a
non-correspondence in paronymous words, similar to that above instanced ;
as between art and artful, design and designing, faith and faithful, etc. ;
and the more slight the variation of the meaning, the more likely is the
fallacy to be successful; for when the words have become so widely re-
moved in sense as ' pity ' and ' pitiful,' every one would perceive such a
fallacy, nor would it be employed but in jest.*
" The present Fallacy is nearly allied to, or rather, perhaps, may be re-
garded as a branch of, that founded on etymology — viz., when a term is
used, at one time in its customary, and at another in its etymological sense.
Perhaps no example of this can be found that is more extensively and mis-
chievously employed than in the case of the word representative : assuming
that its right meaning must correspond exactly with the strict and original
sense of the verb ' represent,' the sophist persuades the multitude that a
member of the House of Commons is bound to be guided in all points by
the opinion of his constituents ; and, in short, to be merely their spokes-
man; whereas law and custom, which in this case may be considered as
fixing the meaning of the term, require no such thing, but enjoin the rep-
resentative to act according to the best of his own judgment, and on his
own responsibility."
The following are instances of great practical importance, in which argu-
ments are habitually founded on a verbal ambiguity.
The mercantile public are frequently led into this fallacy by the phrase
" scarcity of money." In the language of commerce, " money " has two
meanings: currency, or the circulating medium; and capital seeking in-
vestment, especially investment on loan. In this last sense the word is used
when the " money market " is spoken of, and when the " value of money "
is said to be high or low, the rate of interest being meant. The conse-
* An example of this fallacy is the popular error that strong drink must be a cause of
strength. There is here fallacy within fallacy ; for granting that the words " strong " and
" strength " were not (as they are) applied in a totally different sense to fermented liquors and
to the human body, there would still be involved the error of supposing that an effect must
be like its cause; that the conditions of a phenomenon are likely to resemble the phenomenon
itself; which we have already treated of as an a priori fallacy of the first rank. As well
might it be supposed that a strong poison will make the person who takes it strong.
FALLACIES OF CONFUSION. 565
qiience of this ambiguity is, that as soon as scarcity of money in the latter
of these senses begins to be felt — as soon as there is diflSculty of obtaining
loans, and the rate of interest is high — it is concluded that this must arise
from causes acting upon the quantity of money in the other and more pop-
ular sense ; that the circulating medium must have diminished in quantity,
or ought to be increased. I am aware that, independently of the double
meaning of the term, there are in the facts themselves some peculiarities,
giving an apparent support to this error ; but the ambiguity of the lan-
guage stands on the very threshold of the subject, and intercepts all at-
tempts to throw light upon it.
Another ambiguoiis expression which continually meets us in the polit-
ical controversies of the present time, especially in those which relate to
organic changes, is the phrase "influence of property" — which is sometimes
used for the influence of respect for superior intelligence or gratitude for
the kind ofiices which persons of large property have it so much in their
power to bestow; at other times for the influence of fear; fear of the
worst sort of power, which large property also gives to its possessor, the
power of doing mischief to dependents. To confound these two, is the
standing fallacy of ambiguity brought against those who seek to purify
the electoral system from corruption and intimidation. Persuasive influ-
ence, acting through the conscience of the voter, and carrying his heart
and mind with It, is beneficial — therefore (it is pretended) coercive influ-
ence, which compels him to forget that he is a moral agent, or to act in
opposition to his moral convictions, ought not to be placed under restraint.
Another word which is often turned into an instrument of the fallacy of
ambiguity, is Theory. In its most proper acceptation, theory means the
completed result of philosophical induction from experience. -In that
sense, there are erroneous as well as true theories, for induction may be
incorrectly performed, but theory of some sort is the necessary result of
knowing any thing of a subject, and having put one's knowledge into the
form of general propositions for the guidance of practice. In this, the
proper sense of the word. Theory is the explanation of practice. In an-
other and a more vulgar sense, theory means any mere fiction of the im-
agination, endeavoring to conceive how a thing may possibly have been
produced, instead of examining how it was produced. In this sense only
are theory and theorists unsafe guides; but because of this, ridicule or
discredit is attempted to be attached to theory in its proper sense, that is,
to legitimate generalization, the end and aim of all philosophy ; and a con-
clusion is represented as worthless, just because that has been done which,
if done correctly, constitutes the highest worth that a principle for the
guidance of practice can possess, namely, to comprehend in a few words
the real law on \vhich a phenomenon depends, or some property or relation
which is universally true of it.
"The Church" is sometimes understood to mean the clergy alone, some-
times the whole body of believers, or at least of communicants. The dec-
lamations respecting the inviolability of church property are indebted for
the greater part of their apparent force to this ambiguity. The clergy,
being called the church, are supposed to be the real owners of what is
called church-property ; whereas they are in truth only the managing mem-
bers of a much larger body of proprietors, and enjoy on their own part a
mere usufruct, not extending beyond a life interest.
The following is a Stoical argument taken from Cicero, De Finibus, book
the third : " Quod est bonum, omne laudabile est. Quod autem laudabile
666 FALLACIES.
est, omne honestum est. Bonum igituv quod est, honestum est." Here
the ambiguous word is laudabile, which in the minor premise means any-
thing which mankind are accustomed, on good grounds, to admire or
value; as beauty, for instance, or good fortune: but in the major, it de-
notes exclusively moral qualities. In much the same manner the Stoics
endeavored logically to justify as philosophical truths, their figurative and
rhetorical expressions of ethical sentiment: as that the virtuous man is
alone free, alone beautiful, alone a king, etc. Whoever has virtue has
Good (because it has been previously determined not to call any thing else
food) ; but, again. Good necessarily includes freedopa, beauty, and even
ingship, all these being good things ; therefore whoever has virtue has
all these.
The following is an argument of Descartes to prove, in his a priori
manner, the being of a God. The conception, says he, of an infinite Being
proves the real existence of such a being. For if there is not really any
such being, Zmust have made the conception ; but if I could make it, I can
also unmake it ; which evidently is not true ; therefore there must be, exter-
nally to myself, an archetype, from which the conception was derived. In
this argument (which, it may be observed, would equally prove the real
existence of ghosts and of witches) the ambiguity is in the pronoun I, by
which, in one place, is to be understood my will, in another the laws of
my nature. If the conception, existing as it does in my mind, had no
original without, the conclusion would unquestionably follow that Zmade
it; that is, the laws of my nature must have somehow evolved it: but that
my will made it, would not follow. Now when Descartes afterward adds
that I can not unmake the conception, he means that I can not get rid of
it by an act of my will : which is true, but is not the proposition required.
I can as much unmake this conception as I can any other : no conception
which I have once had, can I ever dismiss by mere volition ; but what
some of the laws of my nature have produced, other laws, or those same
laws in other circumstances, may, and often do, subsequently efface.
Analogous to this are some of the ambiguities in the free-will controversy ;
which, as they will come under special consideration in the concluding Book,
I only mention memorice causd. In that discussion, too, the word -Tis often
shifted from one meaning to another, at one time standing for my volitions,
at another time for the actions which are the consequences of them, or the
mental dispositions from which they proceed. The latter ambiguity is ex-
emplified in an argument of Coleridge (in his Aids to liejlection), in sup-
port of the freedom of the will. It is not true, he says, that a man is gov-
erned by motives ; " the man makes the motive, not the motive the man ;"
the proof being that " what is a strong motive to one man is no motive at
all to another." The premise is true, but only amounts to this, that differ-
ent persons have different degrees of susceptibility to the same motive ; as
they have also to the same intoxicating liquid, which, however, does not
prove that they are free to be drunk or not drunk, whatever quantity of the
fluid they may drink. What is proved is, that certain mental conditions in
the person himself must co-operate, in the production of the act, with the
external inducement; but those mental conditions also are the effect of
causes ; and there is nothing in the argument to prove that they can arise
without a cause — that a spontaneous determination of the will, without any
cause at all, ever takes place, as the free-will doctrine supposes.
The double use, in the free-will controversy, of the word Necessity, which
sometimes stands only for Certainty, at other times for Compulsion ; some-
FALLACIES OF CONFUSION. 567
times for what can not be prevented, at other times only for what we have
reason to be assured will not ; we shall have occasion hereafter to pursue
to some of its ulterior consequences.
A most important ambiguity, both in common and in metaphysical lan-
-guage, is thus pointed out by Archbishop "Whately in the Appendix to his
Logic : "Same (as well as One, Identical, and other words derived from
them) is used frequently in a sense very different from its primary one, as
.applicable to a single object; being employed to denote great similarity.
When several objects are undistinguishably alike, one single description will
.apply equally to any of them ; and thence they are said to be all of one and
ihe same nature, appearance, etc. As, e. g., when we say ' this house is built
of the same stone with such another,' we only mean that the stones are
undistihguishable in their qualities ; not that the one building was pulled
-down, and the other constructed with the materials. Whereas sameness,
in the primary sense, does not even necessarily imply similarity ; for if we
say of any man that he is greatly altered since such a time, we understand,
.and indeed imply by the very expression, that he is one person, though
different in several qualities. It is worth observing also, that Same, in
the secondary sense, admits, according to popular usage, of degrees : we
speak of two things being nearly the same, but not entirely : personal identi-
ty does not admit of degrees. Nothing, perhaps, has contributed more to the
*rror of Realism than inattention to this ambiguity. When several persons
-are said to have one and the same opinion, thought, or idea, many men, over-
looking the true simple statement of the case, which is, that they are all
ihinking alike, look for something more abstruse and mystical, and imag-
ine there must be some One Thing, in the pi'imary sense, though not an
individual which is present at once in the mind of each of these persons ;
and thence readily sprung Plato's theory of Ideas, each of which was, ac-
cording to him, one real, eternal object, existing entire and complete in
each of the individual objects that are known by one name."
It is, indeed, not a matter of inference, but of authentic history, that
Plato's doctrine of Ideas, and the Aristotelian doctrine (in this respect sim-
ilar to the Platonic) of substantial forms and second substances, grew up
in the precise way here pointed out; from the supposed necessity of find-
ing, in things which were said to have the same nature, or the same quali-
ties, something which was the same in the very sense in which a man is the
same as himself. All the idle speculations respecting ro 6u, to 'iv, to ofioiov,
and similar abstractions, so common in the ancient and in some modern
schools of thought, sprang from the same source. The Aristotelian logi-
cians saw, however, one case of the ambiguity, and provided against it with
their peculiar felicity in the invention of technical language, when they
■distinguished things which differed both specie and numero, from those
which differed numero tantum, that is, which were exactly alike (in some
particular respect at least) but were distinct individuals. An extension of
this distinction to the two meanings of the word Same, namely, things which
are the same specie tantum, and a thing which is the same numero as well
as specie, would have prevented the confusion which has been a source of
so much darkness and such an abundance of positive error in metaphysical
philosophy.
One of the most singular examples of the length to which a thinker of
eminence may be led away by an ambiguity of language, is afforded by this
'Very case. I refer to the famous argument by which Bishop Berkeley flat-
tered himself that he had forever put an end to " skepticism, atheism, and
568 FALLACIES.
irreljgion." It is briefly as follows: I thought of a thing yesterday; I
ceased to think of it; I think of it again to-day. I had, therefore, in my
mind yesterday an idea of the object ; I have also an idea of it to-day ;
this idea is evidently not another, but the very same idea. Yet an inter-
vening time elapsed in which I had it not. Where was the idea during
this interval? It must have been somewhere; it did not cease to exist;
otherwise the idea I had yesterday could not be the same idea ; no more
than the man I see alive to-day can be the same whom I saw yesterday if
the man has died in the mean while. Now an idea can not be conceived to
exist anywhere except in a mind ; and hence there must exist a Universal
Mind, in which all ideas have their permanent residence during the inter-
vals of their conscious presence in our own minds.
It is evident that Berkeley here confounded sameness numero with
sameness specie, that is, with exact resemblance, and assumed the former
where there was only the latter ; not perceiving that when we say we have
the same thought to-day which we had yesterday, we do not mean the same
individual thought, but a thought exactly similar: as we saj"^ that we have
the same illness which we had last year, meaning only the same sort of illness.
In one remarkable instance the scientific world was divided into two
furiously hostile parties by an ambiguity of language affecting a branch of
science which, more completely than most others, enjoys the advantage of
a precise and well-defined terminology. I refer to the famous dispute re-
specting the vis viva, the history of which is given at large in Professor
Playfair's Dissertation. The question was, whether the force of a mov-
ing body was proportional (its mass being given) to its velocity simply, or
to the square of its velocity : atid the ambiguity was in the word Force.
" One of the effects," says Playfair, " produced by a moving body is pro-
portional to the square of the velocity, while another is proportional to the
velocity simply :" from whence clearer thinkers were subsequently led to
establish a double measure of the efficiency of a moving power, one being
called vis viva, and the other momentum. About the facts, both partie.<»
were from the first agreed : the only question was, with which of the two
effects the term force should be, or could most conveniently be, associa-
ted. But the disputants were by no means aware that this was all; they
thought that force was one thing, the production of. effects another ; and
the question, by which set of effects the force which produced both the
one and the other should be measured, was supposed to be a question not
of terminology, but of fact.
The ambiguity of the word Infinite is the real fallacy in the amusing
logical puzzle of Achilles and the Tortoise, a puzzle which has been too
hard for the ingenuity or patience of many philosophers, and which no less
a thinker than Sir William Hamilton considered as insoluble ; as a sound
argument, though leading to a palpable falsehood. The fallacy, as Hobbes
hinted, lies in the tacit assumption that whatever is infinitely divisible is
infinite ; but the following solution (to the invention of which I have no
claim) is more precise and satisfactory.
The argument is, let Achilles run ten times as fast as the tortoise, yet
if the tortoise has the start, Achilles will never overtake him. For sup-
pose them to be at first separated by an interval of a thousand feet : when.
Achilles has run these thousand feet, the tortoise will have got on a hun-
dred ; when Achilles has run those hundred, the tortoise will have run ten,
and so on forever : therefore Achilles may run forever without overtaking
the tortoise.
FALLACIES OF CONFUSION.
5G9
"Now the " forever," in the conclusion, means, for any length of time
that can be supposed ; but in the premises, " ever " does not mean any
length of time ; it means any number of subdivisions of time. It means
that we may divide a thousand feet by ten, and that quotient again by ten,
and so on as often as we please ; that there never needs be an end to the
subdivisions of the distance, nor consequently to those of the time in which
it is performed. But an unlimited number of subdivisions may be made
of that which is itself limited. The argument proves no other infinity of
duration than may be embraced within five minutes. As long as the five
minutes_ are not expired, what remains of them may be divided by ten,
and again by ten, as often as we like, which is perfectly compatible with
their being only five minutes altogether. It proves, in short, that to pass
through this finite space requires a time which is infinitely divisible, but
not an infinite time; the confounding of which distinction Hobbes had
already seen to be the gist of the fallacy.
The following ambiguities of the word right (in addition to the obvious
and familiar one of a right and the ac^eotive right) are extracted from a
forgotten paper of my own, in a periodical :
" Speaking morally, you are said to have a right to do a thing, if all
persons are morally bound not to hinder you from doing it. But, in an-
other sense, to have a right to do a thing is the opposite of having no
right to do it, i. e., of being under a moral obligation to forbear doing it.
In this sense, to say that you have a right to do a thing, means that you
may do it without any breach of duty on your part; that other persons
not only ought not to hinder you, but have no cause to think worse of you
for doing it. This is a perfectly distinct proposition from the preceding.
The right which you have by virtue of a duty incumbent upon other per-
sons, is obviously quite a different thing from a right consisting in the
absence of any duty incumbent upon yourself. Yet the two things are
perpetually confounded. Thus, a man will say he has a right to publish
his opinions; which may be true in this sense, that it would be a breach
of duty in any other person to interfere and prevent the publication : but
he assumes thereupon that, in publishing his opinions, he himself violates
no duty ; which may either be true or false, depending, as it does, on his
having taken due pains to satisfy himself, first, that the opinions are true,
and next, that their publication in this manner, and at this particular junc-
ture, will probably be beneficial to the interests of truth on the whole.
" The second ambiguity is that of confounding a I'ight of any kind, with
a right to enforce that right by resisting or punishing a violation of it.
People will say, for example, that they have a right to good government,
which is undeniably frue, it being the moral duty of their governors to
govern them well. But in granting this, you are supposed to have admit-
ted their right or liberty to turn out their governors, and perhaps to pun-
ish them, for having failed in the performance of this duty ; which, far
from being the same thing, is by no means universally true, but depends
on an immense number of varying circumstances," requiring to be con-
scientiously weighed before adopting or acting on such a resolution. This
last example is (like others which have been cited) a case of fallacy within
fallacy; it involves not only the second of the two ambiguities pointed
out, but the first likewise.
One not unusual form of the Fallacy of Ambiguous Terms is known
technically as the Fallacy of Composition and Division ; when the same
term is collective in the premises, distributive in the conclusion, or vic^
570 FALLACIES.
versa; or when the middle terra is collective in one premise, distributive
in the other. As if one were to say (I quote from Archbishop Whately),
"All the angles of a triangle ai-e equal to two right angles: ABC is.
an angle of a triangle ; therefore A B C is equal to two right angles
There is no fallacy more common, or more likely to deceive, than the one
now before us. The form in which it is most usually employed is to es-
tablish some truth, separately, concerning each single member of a certain
class, and thence to infer the same of the whole collectively.'''' As in the
argument one sometimes hears, to prove that the world could do without
great men. If Columbus (it is said) had never lived, America would stilL
have been discovered, at most only a few years later; if Newton had never
lived, some other person would have discovered the law of gravitation j
and so forth. Most true : these things would have been done, but in all
probability not till some one had again been found with the qualities of
Columbus or Newton. Because any one great man might have had his
place supplied by other great men, the argument concludes that all great
men could have been dispensed with. The term "great men" is distribu-
tive in the premises and collective in the conclusion.
" Such also is the fallacy which probably operates on most adventurers
in lotteries ; e. g., ' the gaining of a high prize is no uncommon occuri'ence ;
and what is no uncommon occurrence may reasonably be expected ; there-
fore the gaining of a high prize may reasonably be expected ;' the conclu-
sion, when applied to the individual (as in practice it is), must be under-
stood in the sense of ' reasonably expected by a certain individual/' there-
fore for the major premise to be true, the middle term must be under-
stood to mean, 'no uncommon occurrence to some one particular person;'
whereas for the minor (which has been placed first) to be true, you must
understand it of 'no uncommon occurrence to some one or other/ and thus-
you will have the Fallacy of Composition.
" This is a Fallacy with which men are extremely apt to deceive them-
selves; for when a multitude of particulars are presented to the mind,
many are too weak or too indolent to take a comprehensive view of them,
but confine their attention to each single point, by turns ; and then decide,
infer, and act accordingly ; e. g., the imprudent spendthrift, finding that he
is able to afford this, or that, or the other expense, forgets that all of them
together will ruin him." The debauchee destroys his health by successive
acts of intemperance, because no one of those acts would be of itself sufii-
cient to do him any serious harm. A sick person reasons with himself,
" one, and another, and another, of my symptoms do not prove that I have
a fatal disease ;" and practically concludes that all taken together do not
prove it.
§ 2. We have now sufficiently exemplified one of the principal Genera
in this Order of Fallacies ; where, the source of error being the ambiguity
of terms, the premises are verbally what is required to support the conclu-
sion, but not really so. In the second great Fallacy of Confusion they are
neither verbally nor really sufficient, though, from their multiplicity and
confused arrangement, and still oftener from defect of memory, they ai-e
not seen to be what they are. The fallacy I mean is that of Petitio Prin-
cipii, or begging the question; including the more complex and not un-
common variety of it, which is termed Reasoning in a Circle.
Petitio Principii, as defined by Archbishop Whately, is the fallacy "in
which the premise either appears manifestly to be the same as the conclu-
FALLACIES OF CONFUSION.
571
sion, or is actually proved from the conclusion, or is such as would natu-
rally and properly so be proved." By the last clause I presume is meant,
that it is not susceptible of any other proof; for otherwise, there would be
no fallacy. To deduce from a proposition propositions from which it
would itself more naturally be deduced, is often an allowable deviation
from tile usual didactic order; or at most, what, by an adaptation of a
phrase familiar to mathematicians, may be called a logical inelegance*
The employment of a proposition to prove that on which it is itself de-
pendent for proof, by no means implies the degree of mental imbecility
which might at first be supposed. The difficulty of comprehending how
this fallacy could possibly be committed, disappears when we reflect that
all persons, even the instructed, hold a great" number of opinions without
exactly recollecting how they came by them. Believing that they have at
some former time verified them by sufficient evidence, but having forgotten
what the evidence was, they may easily be betrayed into deducing from
them the very propositions which are alone capable of serving as premises
for their establishment. "As if," says Archbishop Whately, "one should
attempt to prove the being of a God from the authority of Holy Writ;"
which might easily happen to one with whom both doctrines, as funda-
mental tenets of his religious creed, stand on the same ground of familiar
and traditional belief.
Arguing in a circle, however, is a stronger case of the fallacy, and im-
plies more than the mere passive reception of a piemise by one who does
not remember how it is to be proved. It implies an actual attempt to
prove two propositions reciprocally from one another; and is seldom re-
sorted to, at least in express terms, by any person in his own speculations,
but is committed by those who, being hard pressed by an adversary, are
forced into giving reasons for an opinion of which, when they began to ar-
gue, they had not sufficiently considered the grounds. As in the following
example from Archbishop Whately : " Some mechanicians attempt to prove
(what they ought to lay down as a probable but doubtful hypothesis)]- that
every particle of matter gravitates equally : ' why ?' ' because those bodies
which contain more particles ever gravitate more strongly, i. e., are hea\ -
ier:' 'but (it may be urged) those which are heaviest are not always more
bulky ;' ' no, but they contain more particles, though more closely con-
densed:' 'how do you know that?' 'because they are heavier:' 'how does
that prove it ?' ' because all particles of matter gravitating equally, that mass
which is specifically the heavier must needs have the more of them in the
same space.' " It appears to me that the fallacious reasoner, in his private
thoughts, would not be likely to proceed beyond the first step. He would
acquiesce in the sufficiency of the reason first given, " bodies which contain
more particles are heavier." It is when he finds this questioned, and is
called upon to prove it, without knowing how, that he tries to establish his
* In his later editions, Archbishop Whately confines the name of Petitio Principii "to
those cases in which one of the premises either is manifestly the same in sense with the con-
clusion, or is actually proved from it, or is such as the persons you are addressing are not
likely to know, or to admit, except as an inference from the conclusion; as, e.g., if any one
should infer the authenticity of a certain history, from its recording such and such facts, the
reality of which rests on the evidence of that history. "
t No longer even a probable hypothesis, since the establishment of the atomic theory ; it
being now certain that the integral particles of different substances gravitate unequally. It
IS true that these particles, though real minima for the purposes of chemical combination, may
not be the ultimate particles of the substance ; and this doubt alone renders the hypothesis
admissible, even as an hypothesis.
572 FALLACIES.
premise by supposing proved what he is attempting to prove by it._ The
most effectual way, in fact, of exposing a petitio priucipii, when circum-
stances allow of it, is by challenging the reasoner to prove his premises;
which if he attempts to do, he is necessarily driven into arguing in a circle.
It is not uncommon, however, for thinkers, and those not of the lowest
description, to be led even in their own thoughts, not indeed into ffcrraally
proving each of two propositions from the other, but into admitting propo-
sitions which can only be so proved. In the preceding example the two
together form a complete and consistent, though hypothetical, explanation
of the facts concerned. And the tendency to mistake mutual coherency
for truth — to trust one's safety to a strong chain though it has no point of
support — is at the bottom of much which, when reduced to the strict forms of
argumentation, can exhibit itself no otherwise than as reasoning in a circle.
All experience bears testimony to the enthi-alling effect of neat concatena-
tion in a system of doctrines, and the difficulty with which people admit the
persuasion that any thing which holds so w^ell together can possibly fall.
Since every case where a conclusion which can only be proved from cer-
tain premises is used for the proof of those premises, is a case of petitio
principii, that fallacy includes a very great proportion of all incorrect rea-
soning. It is necessary, for completing our view of the fallacy, to exempli-
fy some of the disguises under which it is accustomed to mask itself, and
to escape exposure.
A proposition would not be admitted by any person in his senses as a
coroUaiy from itself, unless it were expressed in language which made it
seem different. One of the commonest modes of so expressing it, is to
present the proposition itself in abstract terms, as a proof of the same
proposition expressed in concrete language. This is a very frequent mode,
not only of pretended proof, but of pretended explanation ; and is parodied
when Molifere (ie Malade Imaginaire) makes one of his absurd physi-
cians say,
Mihi a docto doctore,
Demandatur causam et rationem quare
Opium facit dormire.
A quoi respondeo,
Quia est in eo
Virtus dormitiva,
Cujus est natura
Sensus assoupire.
The words liTature and Essence are grand instruments of this mode of
begging the question, as in the well-known argument of the scholastic
theologians, that the mind thinks always, because the essence of the mind
is to think. Locke had to point out, that if by essence is here meant some
property which must manifest itself by actual exercise at all times, the
premise is a direct assumption of the conclusion ; while if it only means
that to think is the distinctive property of a mind, thei-e is no connection
between the premise and the conclusion, since it is not necessary that a dis-
tinctive property should be perpetually in action.
The following is one of the modes in which these abstract terms, Nature
and Essence, are used as instruments of this fallacy. Some particular prop-
erties of a thing are selected, more or less arbitrarily, to be termed its nature
or essence; and when this has been done, these properties are supposed to
be invested with a kind of indefeasibleness; to have become paramount to
all the other properties of the thing, and incapable of being prevailed over
FALLACIES OF CONFUSION. 573
or counteracted by them. As when Aristotle, in a passage already cited,
"decides that there is no void on such arguments as this: in a void there
could be no difference of up and down ; for as in nothing there ai-e no dif-
ferences, so there are none in a privation or negation ; but a void is merely
a privation or negation of matter ; therefore, in a void, bodies could not
move up and down, which it is in their nature to do."* In other words,
it is in the nature of bodies to move up and down, ergo any physical fact
which supposes them not so to move, can not be authentic. This mode of
reasoning, by which a bad generalization is made to overrule all facts which
contradict it, is Petitio Principii in one of its most palpable forms.
None of the modes of assuming what should be proved are in more fre-
quent use than what are termed by Bentham " question-begging appella^
tives ;" names which beg the question under the disguise of stating it.
The most potent of these are such as have a laudatory or vituperative
character. For instance, in politics, the word Innovation. The dictionary
meaning of this term being merely " a change to something new," it is dif-
ficult for the defenders even of the most salutary improvement to deny
that it is an innovation ; yet the word having acquired in common usage a
vituperative connotation in addition to its dictionary meaning, the admis-
sion is always construed as a large concession to the disadvantage of the
thing proposed.
The following passage from the argument in refutation of the Epicu-
reans, in the second book of Cicero, " De Finibus," affords a fine example
of this sort of fallacy : " Et quidem illud ipsum non nimium probo (et
tantum patior) philosophum loqui de cupiditatibus finiendis. An potest
cupiditas finiri ? toUenda est, atque extrahenda radicitus. Quis est enim,
in quo sit cupiditas, quin recte cupidus dici possit ? Ergo et avarus erit,
sed finite : adulter, verum habebit modum : et luxuriosus eodem modo.
Qualis ista philosophia est, quse non interitum afferat pravitatis, sed sit
contenta mediocritate vitiorum ?" The question was, whether certain de-
sires, when kept within bounds, are vices or not ; and the argument de-
,cides the point by applying to them a word (cupiditas) which implies vice.
It is shown, however, in the remarks which follow, that Cicero did not in-
tend this as a serious argument, but as a criticism on what he deemed an
inappropriate expression. " Rem ipsam prorsus probo : elegantiam desi-
dero. Appellet hsec desideria naturae; cupiditatis nomen servet alio," etc.
But many persons, both ancient and modern, have employed this, or some-
thing equivalent to it, as a real and conclusive argument. We may re-
mark that the passage respecting cupiditas and cupidus is also an example
of another fallacy already noticed, that of Paronymous Terms.
Many more of the arguments of the ancient moralists, and especially of
the Stoics, fall within the definition of Petitio Principii. In the " De Fini-
bus," for example, which I continue to quote as being probably the best
extant exemplification at once of the doctrines and the methods of the
schools of philosophy existing at that time; of what value as arguments
are such pleas as those of Cato in the third book : That if virtue were not
happiness, it could not be a thing to boast of : That if death or pain were
evils, it would be impossible not to fear them, and it could not, therefore,
be laudable to despise them, etc. In one way of viewing these arguments,
they may be regarded as appeals to the authority of the general sentiment
of mankind which had stamped its approval upon certain actions and char-
* Hist. Ind. <Sc., i.,34.
574 FALLACIES.
acters by the phrases referred to ; but that such could have been the mean-
ing intended is very unlikely, considering the contempt of the ancient phi-
losophers for vulgar opinion. In any other sense they are clear cases of
Petitio Principii, since the word laudable, and the idea of boasting, im-
ply principles of conduct ; and practical maxims can only be proved from
speculative truths, namely, from the properties of the subject-matter, and
can not, therefore, be employed to prove those properties. As well might
it be argued that a government is good because we ought to support it, or
that there is a God because it is our duty to pray to him.
It is assumed by all the disputants in the " De Finibus " as the founda-
tion of the inquiry into the summum honum, that " sapiens semper beatus
est." Not simply that wisdom gives the best chance of happiness, or that
wisdom consists in knowing what happiness is, and by what things it is
promoted ; these propositions would not have been enough for them ; but
that the sage always is, and must of necessity be, happy. The idea that
wisdom could be consistent with unhappiness, was always rejected as inad-
missible : the reason assigned by one of the interlocutors, near the begin-
ning of the third book, being, that if the wise could be unhappy, there was
little use in pursuing wisdom. But by unhappiness they did not mean
pain or suffering; to that it was granted that the wisest person was liable
in common with others : he was happy, because in possessing wisdom he
had the most valuable of all possessions, the most to be sought and prized
of all things, and to possess the most valuable thing was to be the most
happy. By laying it down, therefore, at the commencement of the inquiry,
that the sage must be happy, the disputed question respecting the sum-
mum honum, was in fact begged ; with the further assumption, that pain
and suffering, so far as they can co-exist with wisdom, are not unhappiness,
and are no evil.
The following are additional instances of Petitio Principii, under more
or less of disguise.
Plato, in the Sophistes, attempts to prove that things may exist which
are incorporeal, by the argument that justice and wisdom are incorporeal,
and justice and wisdom must be something. Here, if by something be
meant, as Plato did in fact mean, a thing capable of existing in and by
itself, and not as a quality of some other thing, he begs the question in
asserting that justice and wisdom must be something ; if he means any
thing else, his conclusion is not proved. This fallacy might also be class-
ed under ambiguous middleterm ; something, in the one premise, meaning
some substance, in the other merely some object of thought, whether sub-
stance or attribute.
It was formerly an argument employed in proof of what is now no long,
er a popular doctrine, the infinite divisibility of matter, that every portion
of matter however small, must at least have an upper and an under sur
face. Those who used this argument did not see that it assumed the very
point in dispute, the impossibility of arriving at a minimum of thickness;
for if there be a minimum, its upper and under surface will of course be
one ; it will be itself a surface, and no more. The argument owes its very
considerable plausibility to this, that the premise does actually seem more
obvious than the conclusion, though really identical with it. As expressed
in the premise, the proposition appeals directly and in concrete language
to the incapacity of the human imagination for conceiving a minimum.
Viewed in this light, it becomes a case of the a priori fallacy or natural
prejudice, that whatever can not be conceived can not exist. Every fal-
FALLACIES OF CONFUSION.
573
Jacy of Confusion (it is almost unnecessary to repeat) will, if cleared up,
become a fallacy of some other sort ; and it will be found of deductive or
ratiocinative fallacies generally, that when they mislead, there is mostly, as
in this case, a fallacy of some other description lurking under them, by
virtue of which chiefly it is that the verbal juggle, which is the outside or
body of this kind of fallacy, passes undetected.
Euler's Algebra, a book otherwise of great merit, but full, to overflow-
ing, of logical errors in respect to the foundation of the science, contains
the following argument to prove that minus multiplied by minus gives
plus, a doctrine the opprobrium of all mere mathematicians, and which
Enler had not a glimpse of the true method of proving. He says minus
multiplied by minus can not give minus; for minus multiplied hy plus
gives minus, and minus multiplied by minus can not give the same prod-
uct as minus multiplied by plus. Now one is obliged to ask, why minus
multiplied by minus must give any product at all ? and if it does, why its
product can not be the same as that of minus multiplied by plus ? for this
would seem, at the first glance, not more absurd than that minus by minus
should give the same as plus by plus, the proposition which Euler prefers
to it. The premise requires proof, as much as the conclusion ; nor can it
be proved, except by that more comprehensive view of the nature of mul-
tiplication, and of algebraic processes in general, which would also supply
a far better proof of the mysterious doctrine whic^ Euler is here endeavor-
ing to demonstrate.
A striking instance of reasoning in a circle is that of some ethical writers,
who first take for their standard of moral truth what, being the general,
they deem to be the natural or instinctive sentiments and perceptions of
mankind, and then explain away the numerous instances of divergence
from their assumed standard, by representing them as cases in which the
perceptions are unhealthy. Some particular mode of conduct or feeling is
affirmed to be unnatural; why? because it is abhorrent to the universal
and natural sentiments of mankind. Finding no such sentiment in your-
self, you question the fact ; and the answer is (if your antagonist is polite),
that you are an exception, a peculiar case. But neither (say you) do I
find in the people of some other country, or of some former age, any such
feeling of abhorrence; "ay, but their feelings were sophisticated and un-
healthy."
One of the most notable specimens of reasoning in a circle is the doc-
trine of Hobbes, Rousseau, and' others, which rests the obligations by
which human beings are bound as members of society, on a supposed so-
cial compact. I waive the consideration of the fictitious nature of the com-
pact itself; but when Hobbes, through the whole Leviathan, elaborately
deduces the obligation of obeying the sovereign, not from the necessity or
utility of doing so, but from a promise supposed to have been made by
our ancestors, on renouncing savage life and agreeing to establish political
society, it is impossible not to retort by the question, Why are we bound
to keep a promise made for us by others ? or why bound to keep a promise
at all? No satisfactory ground can be assigned for the obligation, except
the mischievous consequences of the absence of faith and mutual confidence
among mankind. We are, therefore, brought round to the interests of so-
ciety, as the ultimate ground of the obligation of a promise ; and yet those
interests are not admitted to be a sufficient justification for the existence
of government and law. Without a promise it is thought that we should
not he bound to that which is implied in all modes of living in society.
6'J6 FALLACIES.
namely, to yield a general obedience to the laws therein established ; and
BO necessary is the promise deemed, that if none has actually been made,,
some additional safety is supposed to be given to the foundations of so-
ciety by feigning one.
§ 3. Two principal subdivisions of the class of Fallacies of Confusion
having been disposed of ; there remains a third, in which the confusion is
not, as in the Fallacy of Ambiguity, in misconceiving the import of the
premises, nor, as in Petitio Principii, in forgetting what the premises are,
but in mistaking the conclusion which is to be proved. This is the fallacy
of Ignoratio Elenchi, in the widest sense of the phrase ; also called by
Archbishop Whately the Fallacy of Irrelevant Conclusion. His examples
and remarks are highly worthy of citation.
" Various kinds of propositions are, according to the occasion, substi-
tuted for the one of which proof is required ; sometimes the particular for
the universal ; sometimes a proposition with different terms ; and various
are the contrivances employed to effect and to conceal this substitution,
and to make the conclusion which the sophist has drawn, answer practical-
ly the same purpose as the one he ought to have established. We say,
'practically the same purpose,' because it will vei-y often happen that some
emotion will be excited, some sentiment impressed on the mind (by a dex-
terous employment of this fallacy), such as shall bring men into the dispp:-
sition requisite for your purpose ; though they may not have assented to,
or even stated distinctly in their own minds, the proposition which it was
your business to establish. Thus if a sophist has to defend one who has
been guilty of some serious offense, which he wishes to extenuate, though
he is unable distinctly to prove that it is not such, yet if he can succeed in
making the audience laugh at some casual matter, he has gained practical-
ly the same point. So also if any one has pointed out the extenuating cii'-
cumstances in some particular case of offense, so as to show that it differs
widely from the generality of the same class, the sophist, if he finds him-
self unable to disprove these circumstances, may do away the force of
them, by simply referring the action to that very class, which no one can
deny that it belongs to, and the very name of which will excite a feeling^
of disgust sufficient to counteract the extenuation ; e. g., let it be a case of
peculation, and that many mitigating circumstances have been brought
forward which can not be denied; the sophistical opponent will reply,
• Well, but after all, the man is a rogue, and there is an end of it ;' now in
reality this was (by hypothesis) never the question ; and the mere asser-
tion pf what was never denied ought not, in fairness, to be regarded as
decisive; but, practically, the odiousness of the word, arising in great
measure from the association of those very circumstances which belong to
most of the class, but which we have supposed to be absent in this par-
ticular instance, excites precisely that feeling of disgust which, in effect,,
destroys the force of the defense. In like manner we may refer to this
head all cases of improper appeal to the passions, and every thing else
which is mentioned by Aristotle as extraneous to the matter in hand (e^w
Tov Trpay/iaTog)."
Again, " instead of proving that ' this prisoner has committed an atro-
cious fraud,' you prove that the fraud he is accused of is atrocious ; instead
of proving (as in the well-known tale of Cyrus and the two coats) that the
taller boy had a right to force the other boy to exchange coats with him,
you prove that the exchange would have been advantageous to both j in-
FALLACIES OF CONFUSION. 57^
stead of proving that the poor ought to be relieved in this way rather than
in that, you prove that the poor ought to be relieved ; instead of proving
that the irrational agent — whether a brute or a madman — can never be de-
terred from any act by apprehension of punishment (as, for instance, a dog
from uheep-biting, by fear of being beaten), you prove that the beating of
one dog does not operate as an example to other dogs, etc.
" It is evident that Ignoratio Elenchi may be employed as well for the
apparent refutation of your opponent's proposition, as for the apparent es-
tablishment of your own ; for it is substantially the same thing, to prove
whatwas not denied or to disprove what was not asserted. The latter
practice is not less common, and it is more offensive, because it frequen1>
ly amounts to a personal affront, in attributing to a person opinions, etc.
which he perhaps holds in abhorrence. Thus, when in a discussion one
party vindicates, on the ground of general expediency, a particular in-
stance of resistance to government in a case of intolerable oppression, the
opponent may gravely maintain, ' that we ought not to do evil that good
may come ;' a proposition which of course had never been denied, the point
in dispute being, ' whether resistance in this particular case were doing evil
or not' Or again, by way of disproving the assertion of the right of pri-
vate judgment in religion, one may hear a grave argument to prove that 'it
is impossible every one can be right in, his judgment.'' "
The works of controversial writers are seldom free from this fallacy. The
attempts, for instance, to disprove the population doctrines of Malthus, have
been mostly cases of ignoratio elenchi. Malthus has been supposed to be
refuted if it could be shown that in some countries or ages population has
been nearly stationai-y ; as if he had asserted that population always in-
creases in a given ratio, or had not expressly declared that it increases only
in so far as it is not restrained by prudence, or kept down by poverty and
disease. Or, perhaps, a collection of facts is produced to prove that in some
one country the people are better off with a dense population than they
are in another country with a thin one ; or that the people have become
more numerous and better off at the same time. As if the assertion were
that a dense population could not possibly be well off ; as if it were not
part of the very doctrine, and essential to it, that where there is a more
abundant production there may be a greater population without any increase
of poverty, or even with a diminution of it.
The favorite argument. against Berkeley's theory of the non-existence of
matter, and the most popularly effective, next to a " grin "* — an argument,
moreover, which is not confined to " coxcombs," nor to men like Samuel
Johnson, whose greatly overrated ability certainly did not lie in the direc-
tion of metaphysical speculation, but is the stock argument of the Scotch
school of metaphysicians — is a palpable Ignoratio Elenchi. The argument
is perhaps as frequently expressed by gesture as by words, and one of its
commonest forms consists in knocking a stick against the ground. This
short and easy confutation overlooks the fact, that in denying matter, Berke-
ley did not deny any thing to which our senses bear witness, and therefore
can not be answered by any appeal to them. His skepticism related to the
supposed substratum, or hidden cause of the appearances perceived by our
senses ; the evidence of which, whatever may be thought of its conclusive-
ness, is certainly not the evidenqe of sense. And it will always remain a
signal proof of the want of metaphysical profundity of Reid, Stewart, and,
* "And coxcombs vanquish Berkeley with a grin."
37
578 FALLACIES.
I am sorry to add, of Brown, that they should have persisted in asserting
that Berkeley, if he believed his own doctrine, was bound to walk into the
kennel, or run his head against a post. As if persons who do not recognize
an occult cause of their sensations could not possibly believe that a fixed
order subsists among the sensations themselves. Such a want of compre-
hension of the distinction between a thing and its sensible manifestation,
or, in metaphysical language, between the noumenon and the phenomenon,
would be impossible to even the dullest disciple of Kant or Coleridge.
It would be easy to add a greater number of examples of this fallacy, as
well as of the others which I have attempted to characterize. But a more
copious exemplification does not seem to be necessary ; and the intelligent
reader will have little difficulty in adding to the catalogue from his own
reading and experience. We shall, therefore, here close our exposition of
the general principles of logic, and proceed to the supplementary inquiry
which is necessary to complete our design.
BOOK VI.
ON THE LOGIC OF THE MOEAL SCIENCES.
"Si rhomme pent pre'dire, avec une assurance presque entifere, les ph^nomfenes dont il con-
nait les lois ; si lors meme qu'elles lui sont inconuues, il peut, d'apres I'exp^rience, pr^voir
Avec une grande probabilite les evenemens de I'avenir ; pourquoi regarderait-on comme une
entreprise chimerique, celle de tracer avec quelque vraisemblance le tableau des destinies futures
de I'espfece humaine, d'aprfes les resultats de son histoire ? Le seul fondement de croyance
■dans les sciences naturelles, est cette idee, que les lois gen^rales, connues ou ignorees, qui
rfeglent les phenomfenes de I'univers, sont necessaires et constantes ; et par quelle raison ce
principe serait-il moins vrai pour le d^veloppement des facult^s intellectnelles et morales de
ihomme, que pour les autres operations de la nature ? Enfin, puisque des opinions formees
d'apres I'exp^rience sont la seule rfegle de la conduite des hommes les plus sages, pour-
•quoi interdirait-on au philosophe d'appuyer ses conjectures sur cette m6me base, pourvu qu'il
ne leur attribue pas une certitude superienre h, celle qui peut naitre du nombre, de la Constance,
Ae I'exactitude des observations ?" — Condorcbt, Esquisse cCun Tableau Historique des Pro-
gres de V Esprit Humain.
CHAPTER I.
INTEODUCTOEY EBHAEKS.
§ 1. Peinciples of Evidence and Theories of Method are not to be con-
structed a priori. The laws of our rational faculty, like those of every
other natural agency, are only learned by seeing the agent at work. The
earlier achievements of science were made without the conscious observ-
ance of any Scientific Method ; and we should never have known by what
process truth is to be ascertained, if we had not previously ascertained
many truths. But it was only the easier problems which could be thus
resolved : natural sagacity, when it tried its strength against the more dif-
ficult ones, either failed altogether, or, if it succeeded here and there in ob-
taining a solution, had no sure means of convincing others that its solution
was correct. In scientific investigation, as in all other works of human
skill, the way of obtaining the end is seen as it were instinctively by su-
perior minds in some comparatively simple case, and is then, by judicious
generalization, adapted to the variety of complex cases. We learn to do
a thing in difficult circumstances, by attending to the manner in which we
have spontaneously done the same thing in easier ones.
This truth is exemplified by the history of the various branches of knowl-
edge which have successively, in the ascending order of their complication,
assumed the character of sciences; and will doubtless receive fresh con-
firmation from those of which the final scientific constitution is yet to
come, and which are still abandoned to the uncertainties of vague and
popular discussion. Although several other sciences have emerged from
this state at a comparatively recent date, none now remain in it except
those which relate to man himself, the most complex and most difficult
subject of study on which the human mind can be engaged.
580 LOGIC OF THE MORAL SCIENCES.
Concerning the physical nature of man, as an organized being — thongb
there is still much uncertainty and much controversy, which can only be
terminated by the general acknowledgment and employment of stricter
rules of induction than are commonly recognized— there is, however, a
considerable body of truths which all who have attended to the subject
consider to be fully established; nor is there now any radical imperfectioa
in the method observed in the department of science by its most distin-
guished modern teachers. But the laws of Mind, and, in even a greater
degree, those of Society, are so far from having attained a similar state
of even partial recognition, that it is still a controversy whether they are
capable of becoming subjects of science in the strict sense of the term:
and among those who are agreed on this point, there reigns the most ir-
reconcilable diversity on almost every other. Here, therefore, if anywhere,
the principles laid down in the preceding Books may be expected to be
useful.
If on matters so much the most important with which human intellect
can occupy itself a more general agreement is ever to exist among think-
ers ; if what has been pronounced " the proper study of mankind " is not
destined to remain the only subject which Philosophy can not succeed in
rescuing from Empiricism; the same process through which the laws of
many simpler phenomena have by general acknowledgment been placed
beyond dispute, must be consciously and deliberately applied to those
more difficult inquiries. If there are some subjects on which the results
obtained have finally received the unanimous assent of all who have attend-
ed to the proof, and others on which mankind have not yet been equally
successful ; on which the most sagacious minds have occupied themselves
from the earliest date, and have never succeeded in establishing any con-
siderable body of truths, so as to be beyond denial or doubt ; it is by gen-
eralizing the methods successfully followed in the former inquiries, and
adapting them to the latter, that we may hope to remove this blot on the
face of science. The remaining chapters are an endeavor to facilitate this
most desirable object.
§ 2. In attempting this, I am not unmindful how little can be done to-
ward it in a mere treatise on Logic, or how vague and unsatisfactory all
precepts of Method must necessarily appear when not practically exempli-
fied in the establishment of a body of doctrine. Doubtless, the most effect-
ual mode of showing how the sciences of Ethics and Politics may be con-
structed would be to construct them : a task which, it needs scarcely be
said, I am not about to undertake. But even if there were no other ex-
amples, the memorable one of Bacon would be sufficient to demonstrate,
that it is sometimes both possible and useful to point out the way, though
without being one's self prepared to adventure far into it. And if more
were to be attempted, this at least is not a proper place for the attempt.
In substance, whatever can be done in a work like this for the Logic of
the Moral Sciences, has been or ought to have been accomplished in the
five preceding Books ; to which the present can be only a kind of supple-
ment or appendix, since the methods of investigation applicable to moral
and social science must have been already described, if I have succeeded
in enumerating and characterizing those of science in general. It remains,
however, to examine which of those methods are more especially suited
to the various branches of moral inquiry ; under what peculiar facilities
or difficulties they are there employed; how far the unsatisfactory state
LIBERTY AND NECESSITY. 58]
of those inquiries is owing to a wrong choice of methods, how far to want
of skill in the application of right ones ; and what degree of ultimate suc-
oess may be attained or hoped for by a better choice or more careful em-
ployment of logical processes appropriate to the case. In other words,
whether moral sciences exist, or can exist ; to what degree of perfection
they are susceptible of being carried ; and by what selection or adaptation
of the methods brought to view in the previous part of this work that de-
gree of perfection is attainable.
At the threshold of this inquiry we are met by an objection, which, if
not removed, would be fatal to the attempt to treat human conduct as a
subject of science. Are the actions of human beings, like all othei- natural
events, subject to invariable laws ? Does that constancy of causation, which
is the foundation of every scientific theory of successive phenomena, really
obtain among them ? This is often denied ; and for the sake of systematic
completeness, if not from any very urgent practical necessity, the question
should receive a deliberate answer in this place. We shall devote to the
subject a chapter apart.
CHAPTER II.
OF LIBEETT AND NBCESSITT.
§ 1. The question, whether the law of causality applies in the same strict
sense to human actions as to other phenomena, is the celebrated contro-
versy concerning the freedom of the will ; which, from at least as far back
as the time of Pelagius, has divided both the philosophical and the relig-
ious world. The affirmative opinion is commonly called the doctrine of
Necessity, as asserting humaavplitjons ^d actions_to_be_necessary:jLn.dJii.
§vitable^ The negative maintains that therwiHTTnot determined, like oth-
er phenomena, by antecedents, but determines itself ; that our volitions are
not, properly speaking, the effects of causes, or at least have no causes
which they uniformly and implicitly obey.
I have already made it sufficiently apparent that the former of these
opinions is that which I consider the true one ; but the misleading terms
in which it is often expressed, and the indistinct manner in which it is usu-
ally apprehended, have both obstructed its reception, and perverted its in-
fluence when received. The metaphysical theory of free-will, as held by
philosophers (for the practical feeling of it, common in a greater or less
degree to all mankind, is in no way inconsistent with the contrary theory),
was invented because the supposed alternative of admitting human actions
to be necessary was deemed inconsistent with every one's instinctive con-
sciousness, as well as humiliating to the pride and even degrading to the
moral nature of man. Nor do I deny that the doctrine, as sometimes held,
is open to these imputations; for the misapprehension in which I shall be
able to show that they originate, unfortunately is not confined to the oppo-
nents of the doctrine, but is participated in by many, perhaps we might
say by most, of its supporters.
§ 2. Correctly conceived, the doctrine called Philosophical Necessity is
simply this: that, given_the- motives which are present to an individual's
mindjind^ivenjiikewise^the characterand disposition of the individual, the
maiiiiirlnjvhiofirhe will actmight be unerringlyJnf erred; that if we knew
582 LOGIC OF THE MORAL SCIENCES.
the person thoroughly, and knew all the inducements which are acting upon
him, we could foretell his conduct with as much certainty as we can pre-
dict any physical event. This proposition I take to be a mere interpreta-
tion of universal experience, a statement in words of what every one is in.
ternally convinced of. No one who believed that he knew thoroughly the
circumstances of any case, and the characters of the different persons con-
cerned, would hesitate to foretell how all of them would act. Whatever
degree of doubt he may in fact feel, arises from the uncertainty whether he
really knows the circumstances, or the character of some one or other of
the persons, with the degree of accuracy required ; but by no means from
thinking that if he did know these things, there could be any uncertainty
what the conduct would be. Nor does this full assurance conflict in the
smallest degree with what is called our feeling of freedom. We do not
feel ourselves the less free, because those to whom we are intimately known
are well assured how we shall will to act in a particular case. We often^
on the contrary, regard the doubt what our conduct will be, as a mark of
ignorance of our character, and sometimes even resent it as an imputation.
The religious metaphysicians who have asserted the freedom of the. will, .
have always maintained it to be consistent with divine foreknowledge of
our actions : and if with divine, then with any other foreknowledge. We
may be free, and yet another may have reason to be perfectly certain what
use we shall make of our freedom. It is not, therefore, the doctrine that
our volitions and actions are invariable consequents _af. our.,_antecedent
states of mind, that is either contradicted by our consciousnessTorlelt to
be degrading.
But the doctrine of causation, when considered as obtaining between our
volitions and their antecedents, is almost universally conceived as involving
more than this. Many do not believe, and very few practically feel, that
there is nothing in causation but invariable, certain, and unconditional se-
quence. There are few to whom mere constancy of succession appears a
sufficiently stringent bond of union for so peculiar a relation as that of
cause and effect. Even if the reason repudiates, the imagination retains,
the feeling of some moi-e intimate connection, of some peculiar tie, or mys-
terious constraint exercised by the antecedent over the consequent. Now
this it is which, considered as applying to the human will, conflicts with
our consciousness, and revolts our feelings. We are certain that, in the
case of our volitions, there is not this mysterious constraint. We know
that we are not compelled, as by a magical spell, to obey any particular
motive. We feel, that if we wished to prove that we have the power of
resisting the motive, we could do so (that wish being, it needs scarcely be
observed, a new antecedent); and it would be humiliating to our pride, and
(what is of niore importance) paralyzing to our desire of excellence, if we
thought otherwise. But neither is any such mysterious compulsion now
supposed, by the best philosophical authorities, to be exercised by any otho
er cause over its effect. Those who think that causes draw their effects af-
ter them by a mystical tie, are right in believing that the relation between
volitions and their antecedents is of another nature. But they should go
farther, and admit that this is also true of all other effects and their anter
cedents. If such a tie is considered to be involved in the word Necessity^
the doctrine is not true of human actions; but neither is it then true of inr
animate objects. It would be more correct to say that matter is not bound
by necessity, than that mind is so.
That the free-will metaphysicians, being mostly of the school which re^
LIBERTY AND NECESSITY. 58a
jects Hume's and Brown's analysis of Cause and Effect, should miss their
way for want of the light which that analysis affords, can not surprise us.
The wonder is, that the necessitarians, who usually admit that philosophic-
al theory, should in practice equally lose sight of it. The very same mis-
conception of the doctrine called Philosophical Necessity, which prevents
the opposite party from recognizing its truth, I believe to exist more or
less obscurely in the minds of most necessitarians, however they may in
words disavow it. I am much mistaken if they habitually feel that the-
necessity which they recognize in actions is but uniformity of order, and
capability of being predicted. They have a feeling as if there wei-e at bot-
tom a stronger tie between the volitions and their causes ; as if, when they
asserted that the will is governed by the balance of motives, they meant
something more cogent than if they had only said, that whoever knew the
motives, and our habitual susceptibilities to them, could predict how we
should will to act. They commit, in opposition to their own scientific
system, the very same mistake which their adversaries commit in obedience-
to theirs ; and in consequence do really in some instances suffer those de-
pi'essing consequences which their opponents erroneously impute to the
doctrine itself.
§ 3. I am inclined to think that this error is almost wholly an effect of
the associations with a word, and that it would be prevented, by foi-bear-
ine to employ, for the expression of the simple fact of causation, so ex-
tremely inappropriate a term as Necessity. That word, in its other ac- 1
captations, involves much more than mere uniformity of sequence : it im- '
plies irresistibleness. Applied to the will, it only means that the given
cause will be followed by the effect, subject to all possibilities of counter-
action by other causes ; but in common use it stands for the operation of
those causes exclusively which are supposed too powerful to be counter-
acted at all. When we say that all human actions take place of necessity,
we only mean that they will certainly happen .if nothing prevents; when
we say that dying of want, to those who can not get food, is a necessity,
we mean that "it will certainly happen whatever may be done to prevent it.
The application of the same term to the agencies on which human actions
depend, as is used to express those agencies of nature which are really un-
controllable, can not fail, when habitual, to create a feeling of uncontrol-
lableness in the former also. This, however, is a mere illusion. There are
physical sequences which we call necessary, as death for want of food or
air ; there are others which, though as much cases of causation as the for-
mer, are not said to be necessary, as death from poison, which an antidote,
or the use of the stomach-pump, will sometimes avert. It is apt to be for-
gotten by people's feelings, even if remembered by their understandings,,
that human actions are in this last predicament : they are never (except in
some cases of mania) ruled by any one motive with such absolute sway
that there is no room for the influence of any other. Thc-cau&es.there- /
forg,,OB which action depends,.arenexer uncontrollable; and any given ef-
fect is only necessary provided that the causes tending to produce it are
not controlled. That whatever happens, could not have happened other-
wise, unless something had taken place which was capable of preventing it,
no one surely needs hesitate to admit. But to call this by the name Neces-
sity is to use the term in a sense so different from its primitive and famil-
iar meaning, from that which it bears in the common occasions of life, as.
to amount almost to a play upon words. The associations derived from
584 LOGIC OF THE MORAL SCIENCES.
the ordinary sense of tbe term will adhere to it in spite of all we can do ;
and though the doctrine of Necessity, as stated by most who hold it, is very
remote from fatalism, it is probable that most necessitarians are fatalists,
more or less, in their feelings.
A fatalist believes, or half believes (for nobody is a consistent fatalist),
not only that whatever is about to happen will be the infallibla rssult of
the causes which produce it (which is the true necessitarian doctrine), but
moreover that there is no use in struggling against it ; that it will happen^
however we may strive to prevent it. Now, a necessitarian, believing that
our actions follow from our characters, and that our characters follow from
our organization, our education, and our circumstances, is apt to be, with
more or less of consciousness on his part, a fatalist as to his own actions,
and to believe that his nature is such, or that his education and circum-
stances have so moulded his character, that nothing can now prevent him
from feeling and acting in a particular way, or at least that no effort of his
own can hinder it. In the words of the sect which in our own day has
most perseveringly inculcated and most perversely misunderstood this great
doctrine, his character is formed for him, and not hy him; therefore his
wishing that it had been formed diflEerently is of no use ; he has no power
to alter it. But this is a grand error. He has, to a certain extent, a pow-
der to alter his character. Its being, in the ultimate resort^ formed for hiraj
is not inconsistent with its being, in psyt, formed hy him as one of the in-
termediate agents. His character is formed by his'cii-cumstances (includ-
ing among these his particular organization) ; ^ut his own_desire Jo^mould
it in a particular way, is one of those circumstances, andTSy no means oni^
the least influential. We can not, indeed, directly will to be different from
wliat we are. Bat neither did those who are supposed to have formed our
■characters directly will that we should be what we are. Their will had no
direct power except over their own actions. They made us what they did
make us, by willing, not the end, but the requisite means ; and we, when
our habits are not too inveterate, can, by similarly willing the requisite
means, make ourselves different. If they could place us under the influence
of certain circumstances, we, in like manner, can place ourselves under the
influence of other circumstances. We are exactly as capable of making
our own character, if we will, as others are of making it for us.
Yes (answers the Owenite), but these words, " if we will," surrender the
whole point: since the will to alter our own character is gbiBH usuiot by
any efforts of ours, but by circumstances which. we_can_not help, it comes
to us either from external causes, or not^t all. Most trueT^niie Owenite
■stops here, he is in a position from which nothing can expel him' Our
character is formed by us as well as for us ; but the wish which induces
us to attempt to form it is formed for us ; and how ? Not, in general, by
our organization, nor wholly by our education, but by our experience ; ex-
perience of the painful consequences of the character we previously had ;
•or by some strong feeling of admiration or aspiration, accidentally aroused.
But to think that we have no power of altering our character, and to think
that we shall not use our power unless we desire to use it, are very differ-
ent things, and have a very different effect on the mind. A person who
does not wish to alter his character, can not be the person who is supposed
to feel discouraged or paralyzed by thinking himself unable to do it. The
•depressing effect of the fatalist doctrine can only be felt where there is a
wish to do what that doctrine represents as impossible. It is of no conse-
•quence what we think foi-ms our character, when we have no desire of our
LIBEETY AND NECESSITY. 585
own about forming it; but it is of great consequence that we should not
be prevented from forming such a desire by thinking the attainment im-
practicable, and that if we have the desire, we should know that the work
is not so irrevocably done as to be incapable of being altered.
And indeed, if we examine closely, we shall find that this feeling, of our
being able to modify our own character if we wish, is itself the feeling of
moral freedom which we are conscious of. A person feels morally free
who feels that hishabits or his temptations are not his masters, but he
theirs; who, even in yielding to them, knows that he could resist; that
were he desirous of altogether throwing them off, there would not b&
required for that purpose a stronger desire than he knows himself to be
capable of feeling. It is of course necessary, to render our consciousness
of freedom complete, that we should have succeeded in making our char-
acter all we have hitherto attempted to make it; for if we have wished
and not attained, we have, to that extent, not power over our own charac-
ter; we are not free. Or at least, we must feel that our wish, if not strong
enough to alter our character, is strong enough to conquer our character
when the two are brought into conflict in any particular case of conduct.
And hence it is said with truth, that none but a person of confirmed virtue
is completely free.
The application of so improper a term as Necessity to the doctrine of
cause and effect in the matter of human character, seems to me one of the
most signal instances in philosophy of the abuse of terms, and its practical
consequences one of the most striking examples of the power of language
over our associations. The subject will never be generally understood
until that objectionable term is dropped. The free-will doctrine, by keep-
ing in view precisely that portion of the truth which the word Necessity
puts out of sight, namely the_ power of the mindjto_co-ojierate inthe-ior-
m^on of its own cbarafiter, has given to its adherents a practical feel-
ing much nearer to the truth than has generally (I believe) existed in the
minds of necessitarians. The latter may have had a stronger sense of the
importance of what human beings can do to shape the characters of one
another ; but the free-will doctrine has, I believe, fostered in its supporters
a much stronger spirit of self-culture.
§ 4. There is still one fact which requires to be noticed (in addition to
the existence of a power of self-formation) before the doctrine of the cau-
sation of human actions can be freed from the confusion and misapprehen-
sions which surround it in many minds. When the will is said to be de-
termined by motives, a motive does not mean always, or solely, the antici-
pation of a pleasure or of a pain. I shall not here inquire whether it be
true that, in the commencement, all our voluntary actions are mere means
consciously employed to obtain some pleasure or avoid some pain. It is
at least certain that we gradually, through the influence of association,,
come to desire the means without thinking of the end; the action itself
ijbecomes an object of desire, and is performed without reference to any
motive beyond itself. Thus far, it may still be objected that, the action
having through association become pleasurable, we are, as much as be-
fore, moved to act by the anticipation of a pleasure, namely, the pleasure
of the action itself. But granting this, the matter does not end here. As
we proceed in the formation of habits, and become accustomed to will a
particular act or a particular course of conduct because it is pleasurable,
we at last continue t* will it without any reference to its being pleasura-
586 LOGIC OF THE MORAL SCIENCES.
ble. Although, from some change in us or in our circumstances, we have
ceased to find any pleasure in the action, or perhaps to anticipate any
pleasure as the- consequence of it, we still continue to desire the action, and
consequently to do it. In this manner it is that habits of hurtful excess
continue to be practiced although they have ceased to be pleasurable ; and
in this manner also it is that the habit of willing to persevere in the course
which he has chosen, does not desert the moral hero, even when the re-
ward, however real, which he doubtless receives from the consciousness of
well-doing, is any thing but an equivalent for the sufferings he undergoes,
•or the wishes which he may have to renounce.
A habit of willing is commonly called a purpose ; and among the causes
of our volitions, and of the actions which flow from them, must be reckon-
ed not only likings and aversions, but also purposes. It is only when our
purposes have become independent of the feelings of pain or pleasure from
which they originally took their rise, that we are said to have a confirmed
character. "A character," says Novalis, " is a completely fashioned will :"
and the will, once so fashioned, may be steady and constant, when the pas-
«ive susceptibilities of pleasure and pain are greatly weakened or material-
ly changed.
With the corrections and explanations now given, the doctrine of the
causation of our volitions by motives, and of motives by the desirable ob-
jects offered to us, combined with our particular susceptibilities of desire,
may be considered, I hope, as sufficiently established for the purposes of
this treatise.*
CHAPTER III.
THAT THBEB IS, OK MAT BE, A SCIENCE OF HUMAN NATDEB.
§ 1. It is a common notion, or at least it is implied in many common
modes of speech, that the thoughts, feelings, and actions of sentient beings
are not a subject of science, in the same strict sense in which this is true
of the objects of outward nature. This notion seems to involve some con-
fusion of ideas, which it is necessary to begin by clearing up.
Any facts are fitted, in themselves, to be a subject of science which fol-
low one another according to constant laws, although those laws may not
have been discovered, nor even be discoverable by our existing resources.
Take, for instance, the most familiar class of meteorological phenomena,
those of rain and sunshine. Scientific inquiry has not yet succeeded in as-
certaining the order of antecedence and consequence among these phenome-
na, so as to be able, at least in our regions of the earth, to predict them with
•certainty, or even with any high degree of probability. Yet no one doubts
that the phenomena depend on .laws, and that these must be derivative
laws resulting from known ultimate laws, those of heat, electricity, vapori-
zation, and elastic fluids. Nor can it be doubted that if we were acquaint-'
•ed with all the antecedent circumstances, we could, even fi"om those more
'general laws, predict (saving difiiculties of calculation) the state of the
weather at any future time. Meteorology, therefore, not only has in itself
■every natural requisite for being, but actually is, a science ; though, from
the difficulty of observing the facts on which the phenomena depend (a dif-
* Some arguments and explanations, supplementavj to those in the text, will be found in
An Examination of Sir William Hamilton's Philosophy, chap. xxvi.
HUMAN NATUKE A SUBJECT OF SCIENCE. 587
Acuity inherent in the peculiar nature of those phenomena), tho science is
extremely imperfect ; and were it perfect, might probably be of little avail
in practice, since the data requisite for applying its principles to particular
instances would rarely be procurable.
A case may be conceived, of an intermediate character, between the per-
iection of science and this its extreme imperfection. It may happen that
the greater causes, those on which the principal part of the phenomena
■depends, are within the reach of observation and measurement ; so that if
no other causes intervened, a complete explanation could be given not only
of the phenomena in general, but of all the variations and modifications
which it admits of. But inasmuch as other, perhaps many other causes,
separately insignificant in their effects, co-operate or conflict in many or in
all cases with those greater causes, the effect, accordingly, presents more
or less of aberration from what would be produced by the greater causes
alone. Now if these minor causes are not so constantly accessible, or not
accessible at all, to accurate observation, the principal mass of the effect
may still, as before, be accounted for, and even predicted ; but there will
be variations and modifications which we shall not be competent to explain
thoroughly, and our predictions will not be fulfilled accurately, but only ap-
proximately.
It is thus, for example, with the theory of the tides. No one doubts
that Tidology (as Dr. Whewell proposes to call it) is really a science. As
much of the phenomena as depends on the attraction of the sun and moon
is completely understood, and may, in any, even unknown, part of the
earth's surface, be foretold with certainty ; and the far greater part of the
phenomena depends on those causes. But circumstances of a local or cas-
ual nature, such as the configuration of the bottom of the ocean, the degree
of confinement from shores, the direction of the wind, etc., influence, in
many or in all places, the height and time of the tide ; and a portion of
these circumstances being either not accurately knowable, not precisely-
measurable, or not capable of being certainly foreseen, the tide in known
places commonly varies from the calculated result of general principles
by some difference that we can not explain, and in unknown ones may
vary from it by a difference that we are not able to foresee or conjecture.
Nevertheless, not only is it certain that these variations depend on causes,
and follow their causes by laws of unerring uniformity ; not only, there-
fore, is tidology a science, like meteorology, but it is, what hitherto at
least meteorology is not, a science largely available in practice. General
laws may be laid down respecting the tides, predictions may be founded
on those laws, and the result will in the main, though often not with com-
plete accuracy, correspond to the predictions.
And this is what is or ought to be meant by those who speak of sciences
which are not exact sciences. Astronomy was once a science, without be-
ing an exact science. It could not become exact until not only the general
course of the planetary motions, but the perturbations also, were_ account-
ed for, and referred to their causes. It has become an exact science, be-
cause its phenomena have been brought under laws comprehending the
Tvhole of the causes by which the phenomena are influenced, whether in a
great or only in a trifling degree, whether in all or only in some cases, and
assigning to each of those causes the share of effect which really belongs
to it. But in the theory of the tides the only laws as yet accurately as-
certained are those of the causes which affect the phenomenon in all cases,
and in a considerable degree; while others which affect it in some cases
588 LOGIC OF THE MOEAL SCIENCES.
only, or, if in all, only in a slight degree, have not been saffieiently ascer-
tained and studied to enable us to lay down their laws ; still less to deduce
the completed law of the phenomenon, by compounding the effects of th&
greater with those of the minor causes. Tidology, therefore, is not yet
an exact science; not from any inherent incapacity of being so, but from
the difficulty of ascertaining with complete precision the real derivative uni-
formities. By combining, however, the exact laws of the greater causes,.
and of such of the minor ones as are sufficiently known, with such empir-
ical laws or such approximate generalizations respecting the miscellaneous-
variations as can be obtained by specific observa;tion, we can lay down
general propositions which will be true in the main, and on which, with-
allowance for the degree of their probable inaccuracy, we may safely
ground our expectations and our conduct.
§ 2. The science of human nature is of this description. It falls far
short of the standard of exactness now realized in Astronomy ; but there i»
no reason that it should not be as much a science as Tidology is, or as As-
tronomy was when its calculations had only mastered the main phenome-
na, but not the perturbations.
The phenomena with which this scienceis conversant being the thoughts,,
feelings, and actions of human beings, it would have attained the ideal per-
fection of a science if it enabled us to foretell how an individual would
think, feel, or act throughout life, with the same certainty with which as-
tronomy enables us to predict the places and the occultations of the heaven-
ly bodies. It needs scarcely be stated that nothing appi'oaching to this can
be done. The actions of individuals could not be predicted with scientifie
accuracy, were it only because we can not foresee the whole of the circum-
stances in which those individuals will be placed. But further, even in any
given combination of (present) circumstances, no assertion, which is both
precise and universally true, can be made respecting the manner in which
human beings will think, feel, or act. This is not, however, because every
person's modes of thinking, feeling, and acting do not depend on causes ;,
nor can we doubt that if, in the case of any individual, our data could be
complete, we even now know enough of the ultimate laws by which mental
pheaomena are determined, to enable us in many cases to predict, with tol-
erable certainty, what, in the greater number of supposable combinations of
circumstances, his conduct or sentiments would be. But the impressions and
actions of human beings are not solely the result of their present circum-
stances, but the joint result of those circumstances and of the characters of
the individuals; and the agencies which determine human character are
so numerous and diversified (nothing which has happened to the person
throughout life being without its portion of influence), that in the aggregate
they are never in any two cases exactly similar. Hence, even if our science
of human nature were theoretically perfect, that is, if we could calculate any
character as we can calculate the orbit of any planet, /rom given data; still,
as the data are never all given, noi- ever precisely alike in different cases,
we could neither make positive predictions, nor lay down universal propo-
sitions.
Inasmuch, however, as many of those effects which it is of most impor-
tance to render amenable to •human foresight and control are determined,
like the tides, in an incomparably greater degree by general causes, than by
all partial causes taken together ; depending in the main on those circum-
stances and qualities which are common to all mankind, or at least to large
LAWS OF MIND. Sgg
bodies of them, and only in a small degree on the idiosyncrasies of organi-
zation or the peculiar history of individuals ; it is evidently possible with
regard to all such effects, to make predictions which will almost always
be verified, and general propositions which are almost always true. And
whenever it is sufficient to know how the great majority of the human race,
or of some nation or class of persons, will think, feel, and act, these propo-
sitions are equivalent to universal ones. For the purposes of political and
social science this is sufficient. As we formerly remarked,* an approximate
generalization is, in social inquiries, for most practical purposes equivalent
to an exact one ; that which is only probable when asserted of individual
human beings indiscriminately selected, being certain when affirmed of the
ijhai'acter and collective conduct of masses.
It is no disparagement, therefore, to the science of Human Nature, that
those of its general propositions which descend sufficiently into detail to
serve as a foundation for predicting phenomena in the concrete, are for
the most part only approximately true. But in order to give a genuinely
scientific character to the study, it is indispensable that these approximate
generalizations, which in themselves would amount only to the lowest kind
of empirical laws, should be connected deductively with the laws of nature
from which they result ; should be resolved into the properties of the causes
on which the phenomena depend. In other words, the science of Human
Nature may be said to exist in proportion as the approximate truths, which
compose a practical knowledge of mankind, can be exhibited as corollaries
from the universal laws of human nature on which they rest ; whereby the
proper limits of those approximate truths would be shown, and we should
be enabled to deduce others for any new state of circumstances, in antici-
pation of specific experience.
The proposition now stated is the text on which the two succeeding
chapters will furnish t^e comment.
CHAPTER IV.
OF THE LAWS OF MIND.
§ 1. What the Mind is, as well as what Matter is, or any other question
respecting Things in themselves, as distinguished from their sensible man-
ifestations, it would be foreign to the purposes of this treatise to consider.
Here, as throughout our inquiry, we shall keep clear of all speculations re-
specting the mind's own nature, and shall understand by the laws of mind
those of mental Phenomena ; of the various feelings or states of conscious-
ness of sentient beings, These, according to the classification we have uni-
formly followed, consist of Thoughts, Emotions, Volitions, and Sensations ;
the last being as truly states of Mind as the three former. It is usual, in-
deed, to speak of sensations as states of body, not of mind. But this is
the common confusion, of giving one and the same name to a phenomenon
and to the approximate cause or conditions of the phenomenon. The im-
mediate antecedent of a sensation is a state of body, but the sensation it-
self is a state of mind. If the word Mind means any thing, it means that
which feels. Whatever opinion we hold respecting the fundamental iden-
tity or diversity of matter and mind, in any case the distinction between
* Supra, p. 424.
590 LOGIC OF THE MORAL SCIENCES.
mental and physical facts, between the internal and the external world,
will always- remain, as a matter of classification ; and in that classification,
sensations, like all other feelings, must be ranked as mental phenomena.
The mechanism of their production, both in the body itself and in what is
called outward nature, is all that can with any propriety be classed as
physical.
The phenomena of mind, then, are the various feelings of our nature,
both those improperly called physical and those peculiarly designated as
mental ; and by the laws of mind, I mean the laws according to which
those feelings generate one another.
§ 2. All states of mind are immediately caused either by other states of
mind, or by states of body. When a state of mind is produced by a state
of mind, I call the law concerned in the case a law of Mind. When a state
of mind is produced directly by a state of body, the law is a law of Body^
and belongs to physical science.
With regard to those states of mind which are called sensations, all are
agreed that these have for their immediate antecedents, states of body.
Every sensation has for its proximate cause some affection of the portion
of our frame called the nervous system, whether this affection originates
in the action of some external object, or in some pathological condition of
the nervous organization itself. The laws of this portion of our nature —
the varieties of our sensations, and the physical conditions on which they
proximately depend — manifestly belong to the province of Physiology.
Whether the remainder of our mental states are similarly dependent on
physical conditions, is one of the vexatce questiones in the science of hu-
man nature. It is still disputed whether our thoughts, emotions, and vo-
litions are generated through the intervention of material mechanism;
whether we have organs of thought and of emotioij, in the same sense in
which we have organs of sensation. Many eminent physiologists hold the
aflSrniative. These contend that a thought (for example) is as much the
result of nervous agency, as a sensation ; that some particular state of our
nervous system, in particular of that central portion of it called the brain,
invariably precedes, and is presupposed by, every state of our conscious-
ness. According to this theory, one state of mind is n&Ver really produced
by another : -all are produced by states of body. When one thought seems
to call up another by association, it is not really a thought which recalls a
thought ; the association did not exist between the two thoughts, but be-
tween the two states of the brain or nerves which preceded the thoughts :
one of those states recalls the other, each being attended in its passage by
the particular state of consciousness which is consequent on it. On this
theory the uniformities of succession among states of mind would be mer^
derivative uniformities, resulting fi-om the laws of succession of the bodi-
ly states which cause them. There would be no original mental laws, no
Laws of Mind in the sense in which I use the term, at all; and mental
science would be a mere branch, though the highest and most recondite-
branch, of the science of physiology. M. Comte, accordingly, claims the
scientific cognizance of moral and intellectual phenomena exclusively for
physiologists ; and not only denies to Psychology, or Mental Philosophy
properly so called, the character of a science, but places it, in the chimer-
ical nature of its objects and pretensions, almost on a par with astrology.
But, after all has been said which can be said, it remains incontestable
that there exist uniformities of succession among states of mind, and that
LAWS OF IIIND.
591
these can be ascertained by observation and experiment. Further, that
every mental state has a nervous state for its immediate antecedent and
proximate cause, though extremely probable, can not hitherto be said to
be proved, in the conclusive manner in which this can be proved of sensa-
tions ; and even were it certain, yet every one must admit that we are
wholly ignorant of the characteristics of these nervous states ; we know
not, and at present have no means of knowing, in what respect one of them
differs from another; and our only mode of studying their successions or
co-existences must be by observing the successions and co-existences of the
mental states, of which they are supposed to be the generators or causes.
The successions, therefore, which obtain among mental phenomena, do not
admit of being deduced from the physiological laws of our nervous organi-
zation ; and all real knowledge of them must continue, for a long time at
least, if not always, to be sought in the direct study, by observation and
experiment, of the mental successions themselves. Since, therefore, the or-
der of our mental phenomena must be studied in those phenomena, and
not inferred from the laws of any phenomena more general, there is a dis-
tinct and separate Science of Mind.
The relations, indeed, of that science to the science of physiology must
never be overlooked or undervalued. It must by no means be forgotten
that the laws of mind may be derivative laws resulting from laws of ani-
mal life, and that their truth, therefore, may ultimately depend on physic-
al conditions ; and the influence of physiological states or physiological
changes in altering or counteracting the mental successions, is one of the
most important departments of psychological study. But, on the other
hand, to reject the resource of psychological analysis, and construct the
theory of the mind solely on such data as physiology at present affords,
seems to me as great an error in principle, and an even more serious one
in practice. Imperfect as is the science of mind, I do not scruple to affirm
that it is in a considerably more advanced state than the portion of physi-
ology which corresponds to it ; and to discard the former for the latter ap-
pears to me an infringement of the true canons of inductive philosophy,
which must produce, and which does produce, erroneous conclusions in
some very important departments of the science of human nature.
§ 3. The subject, then, of Psychology is the uniformities of succession,
the laws, whether ultimate or derivative, according to which one mental
state succeeds another ; is caused by, or at least, is caused to follow, an-
other. Of these laws some are general, others more special. The follow-
ing are examples of the most general laws :
First. Whenever any state of consciousness has once been excited in us,
no matter by what cause, an inferior degree of the same state of conscious-
ness, a state of consciousness resembling the former, but inferior in intensi-
ty, is capable of being reproduced in us, without the pi-esence of any such
cause as excited it at first. Thus, if we have once seen or touched ^n ob-
ject, we can afterward think of the object though it be absent from our
sight or from our touch. If we have been joyful or grieved at some event,
we can think of or remember our past joy or grief, though no new event
of a happy or painful nature has taken place. When a poet has put to-
gether a mental picture of an imaginary object, a Castle of Indolence, a
Una, or a Hamlet, he can afterward think of the ideal object he has created,
without any fresh act of intellectual combination. This law is expressed by
saying, in the language of Hume, that every mental impression has its idea.
592 LOGIC OF THE MORAL SCIENCES.
Secondly. These ideas, or secondary mental states, are excited by our
impressions, or by other ideas, according to certain laws which are called
Laws of Association. Of these laws the first is, that similar ideas tend to
•excite one another. The second is, that when two impressions have been
frequently experienced (or even thought of) either simultaneously or in im-
mediate succession, then whenever one of these impressions, or the idea of
it, recurs, it tends to excite the idea of the other. The third law is, that
greater intensity in either or both of the impressions is equivalent, in ren-
dering them excitable by one another, to a greater frequency of conjunc-
tion. These are the laws of ideas, on which I shall not enlarge in this
place, but refer the reader to works professedly psychological, in particular
to Mr. James Mill's Analysis of the Pfienomena of the Human Mind,
where the principal laws of association, along with many of their applica-
tions, are copiously exemplified, and with a masterly hand.*
These simple or elementary Laws of Mind have been ascertained by the
ordinary methods of experimental inquiry ; nor could they have been as-
•certained in any other manner. But a certain number of elementary laws
having thus been obtained, it is a fair subject of scientific inquiry how far
those laws can be made to go in explaining the actual phenomena. It is
obvious that complex laws of thought and feeling not only may, but must,
be generated from these simple laws. And it is to be remarked, that the
case is not always one of Composition of Causes : the effect of concurring
causes is not always precisely the sum of the effects of those causes when
separate, nor even always an effect of the same kind with them. Revert-
ing to the distinction which occupies so prominent a place in the theory of
induction, the laws of the phenomena of mind are sometimes analogous to
mechanical, but sometimes also to chemical laws. When many impressions
or ideas are operating in the mind together, there sometimes takes place
a process of a similar kind to chemical combination. When impressions
have been so often experienced in conjunction, that each of them calls up
readily and instantaneously the ideas of the whole group, those ideas some-
times melt and coalesce into one another, and appear not several ideas, but
one ; in the same manner as, when the seven prismatic colors are present-
ed to the eye in rapid succession, the sensation produced is that of white.
But as in this last case it is correct to say that the seven colors when they
rapidly follow one another generate white, but not that they actually are
white ; so it appears to me that the Complex Idea, formed by the blending
together of several simpler ones, should, when it really appears sirtiple
(that is, when the separate elements are not consciously distinguishable in
it), be said to result from, or he generated by, the simple ideas, not to con-
sist of them. Our idea of an orange really consists of the simple ideas of
a certain color, a certain form, a certain taste and smell, etc., because we can,
by interrogating our consciousness, perceive all these elements in the idea.
* When this chapter was written, Professor Bain had not yet published even the first part
("The Senses and the Intellect") of his profound Treatise on the Mind. In this the laws
of association have been more comprehensively stated and more largely exemplified than by
any previous writer ; and the work, having been completed by the publication of " The Emo-
tions and the Will," may now be referred to as incomparably the most complete analytical ex-
position of the mental phenomena, on the basis of a legitimate Induction, which has yet been
produced. More recently still, Mr. Bain has joined with me in appending to a new edition
of the "Analysis," notes intended to bring up .the analytic science of Mind to its latest im-
provements.
Many striking applications of the laws of association to the explanation of complex mental
phenomena are also to be found in Mr. Herbert Spencer's "Principles of Psychology."
LAWS OF MIND. 593
But we can not perceive, in so apparently simple a feeling as our percep-
tion of the shape of an object by the eye, all that multitude of ideas de-
rived from other senses, without which it is well ascertained that no such
visual perception would ever have had existence ; nor, in our idea of Ex-
tension, can we discover those elementary ideas of resistance, derived from
our muscular frame, in which it has been conclusively shown that the idea
originates. These, therefore, are cases of mental chemistry ; in which it is
proper to say that the simple ideas generate, rather than that they compose,
the complex ones.
With respect to all the other constituents of the mind, its beliefs, its ab-
struser conceptions, its sentiments, emotions, and volitions, there are some
(among whom are Hartley and the author of the Analysis) who think that
the whole of these are generated from simple ideas of sensation, by a chem-
istry similar to that which we have just exemplified. These philosophers
have made out a great part of their' case, but I am not satisfied that they
have established the whole of it. They have shown that there is such a
thing as mental chemistry ; that the heterogeneous nature of a feeling A,
considered in relation to B and C, is no conclusive argument against its
being generated from B and C. Having proved this, they proceed to
show, that where A is found, B and C were, or may have been present, and
why, thei'efore, they ask, should not A have been generated from B and
€ ? But even if this evidence were carried to the highest degree of com-
pleteness which it admits of ; if it were shown (which hitherto it has not,
in all cases, been) that certain groups of associated ideas not only might
have been, but actually were, present whenever the more recondite mental
feeling was experienced ; this would amount only to the Method of Agree-
ment, and could not prove causation until confirmed by the more conclu-
sive evidence of the Method of Difference. If the question be whether
Belief is a mere case of close association of ideas, it would be necessary
to examine experimentally if it be true that any ideas whatever, provided
they are associated with the required degree of closeness, give rise to be-
lief. If the inquiry be into the origin of moral feelings, the feeling for ex-
ample of moral reprobation, it is necessary to compare all the varieties of
actions or states of mind which are ever morally disapproved, and see
whether in all these cases it can be shown, or reasonably surmised, that the
action or state of mind had become connected by association, in the disap-
proving mind, with some particular class of hateful or disgusting ideas ;
and the method employed is, thus far, that of Agreement. But this is not
•enough. Supposing this proved, we must try further by the Method of
Difference, whether this particular kind of hateful or disgusting ideas,
when it becomes associated with an action previously indifferent, will ren-
■der that action a subject of moral disapproval. If this question can be
answered in the afiirmative, it is shown to be a law of the human mind,
that an association of that particular description is the generating cause of
moral reprobation. That all this is the case has been rendered extremely
probable, but the experiments have not been tried with the degree of pre-
•cision necessary for a complete and absolutely conclusive induction.*
It is further to be remembered, that even if all which this theory of
* In the case of the moral sentiments the place of direct experiment is to a considerable
■extent supplied by historical experience, and we are able to trace with a tolerable approach to
certainty the particular associations by which those sentiments are engendered. This has
been attempted, so far as respects the sentiment of justice, in a little work by the present aii-
*hor, entitled Utilitarianism.
38
594 LOGIC OF THE MORAL SCIENCES.
mental phenomena contends for could be proved, we should not be the
more enabled to resolve the laws of the more complex feelings into those
of the simpler ones. The generation of one class of mental phenomena
from another, whenever it can be made out, is a highly interesting fact in
psychological chemistry; but it no more supersedes the necessity of an
experimental study of the generated phenomenon, tlian a knowledge of the
properties of oxygen and sulphur enables us to' deduce those of sulphuric
acid without specific observation and experiment. Whatever, therefore,
may be the final issue of the attempt to account for the origin of our judg-
ments, our desires, or our volitions, from simpler mental phenomena, it is
not the less imperative to ascertain the sequences of the complex phenom-
ena themselves, by special study in conformity to the canons of Induction.
Thus, in respect to Belief, psychologists will always have to inquire what
beliefs we have by direct consciousness, and according to what laws one
belief produces another ; what are the laws in virtue of which one thing is
recognized by the mind, either rightly or erroneously, as evidence of an-
other thing. In regard to Desire, they will have to examine what objects
we desire naturally, and by what causes we are made to desire things
originally indifferent, or even disagreeable to us; and so forth. It may be
remarked that the general laws of association prevail among these more
intricate states of mind, in the same manner as among the simpler ones.
A desire, an emotion, an idea of the higher order of abstraction, even our
judgments and volitions, when they have become habitual, are called up by
association, according to precisely the same laws as our simple ideas.
§ 4. In the course of these inquiries, it will be natural and necessary to
examine how far the production of one state of mind by another is influ-
enced by any assignable state of body. The commonest observation shows
that different minds are susceptible in very diffei-ent degrees to the action
of the same psychological causes. The idea, for example, of a given desira-
ble object will excite in different minds very different degrees of intensity
of desire. The same subject of meditation, presented to different minds,
will excite in them very unequal degrees of intellectual action. These
differences of mental susceptibility in different individuals may be, first,
original and ultimate facts ; or, secondly, they may be consequences of the
previous mental history of those individuals; or, thirdly and lastly, they
may depend on varieties of physical organization. That the previous men-
tal history of the individuals must have some share in producing or in
modifying the whole of their mental character, is an inevitable conse-
quence of the laws of mind ; but that differences of bodily structure also
co-operate, is the opinion of all physiologists, confirmed by common experi-
ence. It is to be regretted that hitherto this experience, being accepted in
the gross, without due analysis, has been made the groundwork of empiric-
al generalizations most detrimental to the progress of real knowledge.
It is certain that the natural differences which really exist in the mental
predispositions or susceptibilities of different persons are often not uncon-
nected with diversities in their organic constitution. But it does not
therefore follow that these organic differences must in all cases influence
the mental phenomena directly and immediately. They often affect them
through the medium of their psychological causes. For example, the idea
of some particular pleasure may excite in different persons, even independ-
ently of habit or education, very different strengths of desire, and this may
be the effect of their different degrees or kinds of nervous susceptibility;.
LAWS OF MIND. 595
but these organic differences, we must remember, will render the pleasura-
ble sensation itself more intense in one of these persons than in the other ;
BO that the idea of the pleasure will also be an intenser feeling, and will, by
the operation of mere mental laws, excite an intenser desire, without its
being necessary to suppose that the desire itself is directly influenced by
the physical peculiarity. As in this, so in many cases, such differences in
the kind or in the intensity of the physical sensations as must necessarily
result from differences of bodily organization, will of themselves account
for many differences not only in the degree, but even in the kind, of the
other mental phenomena. So true is this, that even different qualities of
mind, different types of mental character, will naturally be produced by
mere differences of intensity in the sensations generally; as is well pointed
out in the able essay on Dr. Priestley, by Mr. Jdai'tineau, mentioned in a
former chapter :
"The sensations which form the elements of all knowledge are received
either simultaneously, or successively: when several are received simulta-
neously, as the smell, the taste, the color, the form, etc., of a fruit, their as-
sociation together constitutes our idea of an object; when received succes-
sively, their association makes up the idea of an event. Any thing, then,
which favors the associations of synchronous ideas will tend to produce a
knowledge of objects, a perception of qualities ; while any thing which fa-
vors association in the successive order, will tend to produce a knowledge
of events, of the order of occurrences, and of the connection of cause and
effect; in other words, in the one case a perceptive mind, with a discrimi-
nate feeling of the pleasurable and painful properties of things, a sense of
the grand and the beautiful will be the result: in the other, a mind atten-
tive to the movements and phenomena, a ratiocinative and philosophic in-
tellect. Now it is an acknowledged principle, that all sensations experi-
enced during the presence of any vivid impression become strongly asso-
ciated with it, and with each other; and does it not follow that the syn-
chronous feelings of a sensitive constitution (i. e., the one which has vivid
impressions) will be more intimately blended than in a differently formed
mind ? If this suggestion has any foundation in truth, it leads to an infer-
ence not unimportant; that where nature has endowed an individual with
great original susceptibility, he will probably be distinguished by fondness
for natural history, a relish for the beautiful and great, and moral enthusi-
asm; where there is but a mediocrity of sensibility, a love of science, of ab-
stract truth, with a deficiency of taste and of fei'vor, is likely to be the re-
sult."
We see from this example, that when the general laws of mind are more
accurately known, and, above all, more skillfully applied to the detailed ex-
planation of mental peculiarities, they will account for many more of those
peculiarities than is ordinarily supposed. Unfortunately the reaction of
the last and present generation against the philosophy of the eighteenth
century has produced a very general neglect of this great department of
analytical inquiry;- of which, consequently, the recent progress has been by
no means proportional to its early promise. The majority of those who
speculate on human nature prefer dogmatically to assume that the mental
differences which they perceive, or think they perceive, among human be-
ings, are ultimate facts, incapable of being either explained or altered, rath-
er than take the trouble of fitting themselves, by the requisite processes of
thought, for referring those mental differences to the outward causes by
which they are for the most part produced, and ou the removal of which
596 LOGIC OF THE MORAL SCIENCES.
they would cease to exist. The German school of metaphysical specula-
tion, which has not yet lost its temporary pvedominanoe in European
thought, has had this among many other injurious influences; and at the
opposite extreme of the psychological scale, no writer, either of early or of
recent date, is chargeable in a higher degree with this aberration from the
true scientific spirit, than M. Comte.
It is certain that, in human beings at least, differences in education and in
outward circumstances are capable of affording an adequate explanation of
by far the greatest portion of character; and that the remainder may be in
great part accounted for by physical differences in the sensations produced
in different individuals by the same external or internal cause. There are,
however, some mental facts which do not seem to admit of these modes of
explanation. Such, to take the strongest case, are the various instincts of
animals, and the portion of human nature which corresponds to those in-
stincts. No mode has been suggested, even by way of hypothesis, in which
these can receive any satisfactory, or even plausible, explanation from psy-
chological causes alone ; and there is great reason to think that they have
as positive, and even as direct and immediate, a connection with physical
conditions of the brain and nerves as any of our mere sensations have. A
supposition which (it is perhaps not superfluous to add) in no way conflicts
with the indisputable fact that these instincts may be modified to any ex-
tent, or entirely conquered, in human beings, and to no inconsiderable ex-
tent even in some of the domesticated animals, by other mental influences,
and by education.
Whether organic causes exercise a direct influence over any other classes
of mental phenomena, is hitherto as far from being ascertained as is the
precise nature of the organic conditions even in the case of instincts. The
physiology, however, of the brain and nervous system is in a state of such
rapid advance, and is continually bringing forth such new and interesting
results, that if there be really a connection between mental peculiarities and
any varieties cognizable by our senses in the structure of the cerebral and
nervous apparatus, the nature of that connection is now in a fair way of be-
ing found out. The latest discoveries in cerebral physiology appear to have
proved that any such connection which may exist is of a radically different
character from that contended for by Gall and his followers, and that, what-
ever may hereafter be found to be the true theory of the subject, phrenolo-
gy at least is untenable.
CHAPTER V.
OF ETHOLOGY, OR THB SCIENCE OP THE POEMATION OE CHAEACTBE.
§ 1. The laws of mind as characterized in the preceding chapter, com-
pose the universal or abstract portion of the philosophy of human nature ;
and all the truths of common experience, constituting a practical knowledge
of mankind, must, to the extent to which they are truths, be results or con-
sequences of these. Such familiar maxims, when collected a posteriori
from observation of life, occupy among the truths of the science the place
of what, in our analysis of Induction, have so often been spoken of under
the title of Empirical Laws.
An Empirical Law (it will be remembered) is a uniformity, whether of
ETHOLOGY. . 597
snccession or of co-existence, which holds true in all instances within our
limits of observation, but is not of a nature to afford any assurance that it
would hold beyond those limits ; either because the consequent is not really
the effect of the antecedent, but forms part along with it of a chain of ef-
fects flowing from prior causes not yet ascertained, or because there is
ground to believe that the sequence (though a case of causation) is resolv-
able into simpler sequences, and, depending therefore on a concurrence of
several natural agencies, is exposed to an unknown multitude of possibilities
of counteraction. In other words, an empirical law is a generalization, of
which, not content with finding it true, we are obliged to ask, why is it
true? knowing that its truth is not absolute, but dependent on some more
general conditions, and that it can only be relied on in so far as there is
ground of assurance that those conditions are realized.
'Now, the observations concerning human affairs collected from common
experience are precisely of this nature. Even if they were universally and
exactly true within the bounds of experience, which they never are, still
they are not the ultimate laws of human action ; they are not the principles
of human nature, but results of those principles under the circumstances in
which mankind have happened to be placed. When the Psalmist " said in
his haste that all men are liars," he enunciated what in some ages and coun-
tries is borne out by ample experience ; but it is not a law of man's natui-e
to lie ; though it is one of the consequences of the laws of human nature,
that lying is nearly universal when certain external circumstances exist uni-
versally, especially circumstances productive of habitual distrust and fear.
When the character of the old is asserted to be cautious, and of the young
impetuous, this, again, is but an empirical law ; for it is not because of their
youth that the young are impetuous, nor because of their age that the old
are cautious. It is chiefly, if not wholly, because the old, during their
many years of life, have generally had much experience of its various evils,
and having suffered or seen others suffer much from incautious exposure
to them, have acquired associations favorable to circumspection ; while the
young, as well from the absence of similar experience as from the greater
strength of the inclinations which urge them to enterprise, engage them-
selves in it more readily. Here, then, is the explanation of the empirical
law; here are the conditions which ultimately determine whether the law
holds good or not. If an old man has not been oftener than most young
men in contact with danger and difficulty, he will be equally incautious ; if
a youth has not stronger inclinations than an old man, he probably will be
as little enterprising. The empirical law derives whatever truth it has
from the causal laws of which it is a consequence. If we know those laws,
we know what are the limits to the derivative law; while, if we have not
yet accounted for the empirical law — if it rests only on observation— there
is no safety in applying it far beyond the limits of time, place, and circum-
stance in which the observations were made.
The really scientific truths, then, are not these empirical laws, but the
causal laws which explain them. The empirical laws of those phenomena
which depend on known causes, and of which a general theory can there-
fore be constructed, have, whatever may be their value in practice, no other
function in science than that of verifying the conclusions of theory. Still
more must this be the case when most of the empirical laws amount, even
within the limits of observation, only to approximate generalizations.
§ 2. This, however, is not, so much as is sometimes supposed, a peculiarity
598 LOGIC OF THE MORAL SCIENCES.
of the sciences called moral. It is only in the simplest branches of science
that empirical laws are ever exactly true; and not always in those. As-
tronomy, for example, is the simplest of all the sciences which explain, in
the concrete, the actual course of natural events. The causes or forces
on which astronomical phenomena depend, are fewer in number than those
which determine any other of the great phenomena of nature. According-
ly, as each effect results from the conflict of but few causes, a great degree
of regularity and uniformity might be expected to exist among the effects ;
and such is really the case : they have a fixed order, and return in cycles.
But propositions which should express, with absolute correctness, all the
successive positions of a planet until the cycle is completed, would be of al-
most unmanageable complexity, and could be obtained from theory alone.
The generalizations which can be collected on the subject from direct ob-
servation, even such as Kepler's law, are mere appi-oximations ; the planets,
owing to their perturbations by one another, do not move in exact ellipses.
Thus even in astronomy, perfect exactness in the mere empirical laws is
not to be looked for; much less, then, in more complex subjects of in-
quiry.
The same example shows how little can be inferred against the univer-
sality or even the simplicity of the ultimate laws, from the impossibility of
establishing any but approximate empirical laws of the effects. The laws
of causation according to which a class of phenomena are produced may
be very few and simple, and yet the effects themselves may be so various
and complicated that it shall be impossible to trace any regularity whatev-
er completely through them. For the phenomena in question may be of an
eminently modifiable character; insomuch that innumerable circumstances
are capable of influencing the effect, although they may all do it according
to a very small number of laws. Suppose that all which passes in the mind
of man is determined by a few simple laws ; still, if those laws be such that
there is not one of the facts surrounding a human being, or of the events
which happen to him, that does nCu influence in some mode or degree his
subsequent mental history, and if the circumstances of different human be-
ings are extremely different, it will be no wonder if very few propositions
can be made respecting the details of their conduct or feelings, which will
be true of all mankind.
Now, without deciding whether the ultimate laws of our mental nature
are few or many, it is at least certain that they are of the above description.
It is certain that our mental states, and our mental capacities and suscepti-
bilities, are modified, either for a time or permanently, by every thing which
happens to us in life. Considering, therefore, how much these modifying
causes differ in the case of any two individuals, it would be unreasonable
to expect that the empirical laws of the human mind, the generalizations
which can be made respecting the feelings or actions of mankind without
reference to the causes that determine them, should be any thing but ap-
proximate generalizations. They are the common wisdom of common life,
and as such are invaluable ; especially as they are mostly to be applied to
cases not very dissimilar to those from which they were collected. But
when maxims of this sort, collected from Englishmen, come to be applied
to Frenchmen, or when those collected from the present day are applied
to past or future generations, they are apt to be very much at fault. Un-
less we have resolved the empirical law into the laws of the causes on which
it depends, and ascertained that those causes extend to the case which we
have in view, there can be no reliance placed in our inferences. For every
ETHOLOGY.
599
individual is surrounded by circumstances different from those of every
other individual; every nation or generation of mankind from every other-
nation or generation : and none of these differences are without their influ-
ence in forming a different type of character. There is, indeed, also a cer-
tain general resemblance ; but peculiarities of circumstances are continually
constituting exceptions even to the propositions' which are true in the great
majority of cases.
Although, however, there is scarcely any mode of feeling or conduct which
is, in the absolute sense, common to all mankind ; and though the general-
izations which assert that any given variety of conduct or feeling will be
found universally (however nearly they may approximate to truth within
given limits of observation), will be considered as scientific propositions by
no one who is at all familiar with scientific investigation ; yet all modes of
feeling and conduct met with among mankind have causes which produce
them ; and in the propositions which assign those causes will be found the
explanation of the empirical laws, and the limiting principle of our reliance
on them. Human beings do not all feel and act alike in the same circum-
stances ; but it is possible to determine what makes one person, in a given
position, feel or act in one way, another in another ; how any given mode
of feeling and conduct, compatible with the general laws (physical and
mental) of human nature, has been, or may be, formed. In other words,
mankind have not one universal character, but there exist universal laws
of the Formation of Character. And since it is by these laws, combined
with the facts of each particular case, that the whole of the phenomena of
human action and feeling are produced, it is on these that every rational
attempt to construct the science of human nature in the concrete, and for
practical purposes, must proceed.
§ 3. The laws, then, of the formation of character being the principal ob-
ject of scientific inquiry into human nature, it remains to determine the
method of investigation best fitted for ascertaining them. And the logical
principles according to which this question is to be decided, must be those
which preside over every other attempt to investigate the laws of very com-
plex phenomena. For it is evident that both the character of any human
being, and the aggregate of the circumstances by which that character has
been formed, are facts of a high order of complexity. Now to such cases
we have seen that the Deductive Method, setting out from general laws,
and verifying their consequences by specific experience, is alone applicable.
The grounds of this great logical doctrine have formerly been stated ; and
its truth will derive additional support from a brief examination of the
specialties of the present case.
There are only two modes in which laws of nature can be ascertained —
•deductively and experimentally ; including under the denomination of ex-
perimental inquiry, observation as well as artificial experiment. Are the
Jaws of the formation of character susceptible of a satisfactory investigation
by the method of experimentation? Evidently not; because, even if we
suppose unlimited power of varying the experiment (which is abstractedly
possible, though no one but an Oriental despot has that powei', or, if he had,
would probably be disposed to exercise it), a still more essential condition
is wanting — the power of performing any of the experiments with scientifio
accuracy.
The instances requisite for the prosecution of a directly experimental in-
quiry into the formation of character, would be a number of human beings
600 LOGIC OF THE MORAL SCIENCES.
to bring up and educate, from infancy to mature age. And to perforin any
cue of these experiments with scientific propriety, it would be necessary to
know and record every sensation or impression received by the young pu-
pil from a period long before it could speak ; including its own notions re-
specting the sources of all those sensations and impressions It is not only
impossible to do this completely, but even to do so much of it as should
constitute a tolerable approximation. One apparently trivial circumstance
which eluded our vigilance might let in a train of impressions and associ-
ations sufficient to vitiate the experiment as an authentic exhibition of the
effects flowing from given causes. No one who has sufficiently reflected
on education is ignorant of this truth ; and whoever has not, will find it
most instructively illustrated in the writings of Rousseau and Helvetius on
that great subject.
Under this impossibility of studying the laws of the formation of char-
acter by experiments purposely contrived to elucidate them, there remain*
the resource of simple observation. But if it be impossible to ascertain
the influencing circumstances with any approach to completeness even
when we have the shaping of them ourselves, much more impossible is it
when the cases are further removed from our observation, and altogether
out of our control. Consider the difficulty of the very first step — of ascer-
taining what actually is the character of the individual, in each particular
case that we examine. There is hardly any person living concei'tiing some
essential part of whose character there are not differences of opinion even
among his intimate acquaintances ; and a single action, or conduct contin-
ued only for a short time, goes a very little way toward ascertaining it..
We can only make our observations in a I'ough way and en masse' not at-
tempting to ascertain completely in any given instance, what character has
been formed, and still less by what causes ; but only observing in what
state of previous circumstances it is found that certain marked mental
qualities or deficiencies oftenest exist. These conclusions, besides that they
are mere approximate generalizations, deserve no reliance, even as such,
unless the instances are sufficiently numerous to eliminate not only chance^
but every assignable circumstance in which a number of the cases ex-
amined may happen to have resembled one another. So numerous and
various, too, are the circumstances which form individual character, that
the consequence of any particular combination is hardly ever some definite
and strongly marked character, always fbund where that combination ex-
ists, and not otherwise. What is 'obtained, even after the most extensive
and accurate observation, is merely a comparative result ; as, for example,
that in a given number of Frenchmen, taken indiscriminately, there will be
found more persons of a particular mental tendency, and fewer of the con-
trary tendency, than among an equal number of Italians or English, simi-
larly taken ; or thus : of a hundred Frenchmen and an equal number of
Englishmen, fairly selected, and arranged according to the degree in which
they possess a particular mental characteristic, each number, 1, 2, 3, etc.^
of the one series, will be found to possess more of that characteristic than
the corresponding number of the other. Since, therefore, the comparison,
is not one of kinds, but of ratios and degrees; and since, in proportion as
the differences are slight, it requires a greater number of instances to elira
inate chance, it can not often happen to any one to know a sufficient num-
ber of cases with the accuracy requisite for making the sort of comparison
last mentioned ; less than which, however, would not constitute a real in-
duction. Accordingly, there is hardly one current opinion respecting the
ETHOLOGY. gQj
characters of nations, classes, or descriptions of persons, which is univer-
sally acknowledged as indisputable.*
And finally, if we could even obtain by way of experiment a much moie
satisfactory assurance of these generalizations than is really possible, they
would still be only empirical laws. They would show, indeed, that there
was some connection between the type of character formed and the cir-
cumstances existing in the case ; but not what the precise connection was,
nor to which of the peculiarities of those circumstances the effect was real-
ly owing. They could only, therefore, be received as results of causation,
requiring to be resolved into the general laws of the causes : until the de-
termination of which, we could not judge within what limits the derivative
laws might serve as presumptions in cases yet unknown, or even be de-
pended on as permanent in the very cases from which they were collected.
The French people had, or were supposed to have, a certain national char-
acter I but they drive out their royal family and aristocracy, alter their in-
stitutions, pass through a series of extraordinary events for the greater
part of a century, and at the end of that time their character is found to
have undergone important changes. A long \iSt of mental and moral dif-
ferences are observed, or supposed to exist between men and women ; but
at some future and, it may be hoped, not distant period, equal freedom
and an equally independent social position come to be possessed by both,
and their differences of character are either removed or totally altered.
But if the differences which we think we observe between French and
EngUsh, or between men and women, can be connected with more general
laws; if they be such as might be expected to be produced by the differ-
ences of government, former customs, and physical peculiarities in the two
nations, and by the diversities of education, ocicupations, personal inde-
pendence, and social privileges, and whatever original differences there
may be in bodily strength and nervous sensibility between the two sexes ;
then, indeed, the coincidence of the two kinds of evidence justifies us in
believing that we have both reasoned rightly and observed rightly. Our
observation, though not sufficient as proof, is ample as verification. And
having ascertained not only the empirical laws, but the causes, of the pe-
■culiarities, we need be under no difficulty in judging how far they may be
expected to be permanent, or by what circumstances they would be modi>
fed or destroyed.
§ 4. Since then it is impossible to obtain really accurate propositions
* The most favorable cases for making such approximate generalizations are what may be
termed collective instances ; where we are fortunately enabled to see the whole class respect-
ing which we are inquiring in action at once, and, from the qualities displayed by the col-
lective body, are able to judge what must be the qualities of the majority of the individuals
composing it. Thus the character of a nation is shown in its acts as a nation ; not so much
in the acts of its government, for those are much influenced by other causes ; but in the cur-
rent popular maxims, and other marks of the general direction of public opinion ; in the char-
acter of the persons or writings that are held in permanent esteem or admiration ; in laws and
institutions, so far as they are the work of the nation itself, or are acknowledged and support-
ed by it ; and so forth. But even here there is a large margin of doubt and uncertainty.
These things are liable to be influenced by many circumstances ; they are partially detei-mined
by the distinctive qualities of that nation or body of persons, but partly also by external causes
which would influence any other body of persons in the same manner. In order, therefore,
to make the experiment really complete, we ought to be able to try it without variation upon
other nations : to try how Englishmen would act or feel if placed in the same circumstances
in which we have supposed Frenchmen to be placed; to apply, in short, the Method of Dif-
ferences as well as that of Agi-eement. Now these experiments we can not try, nor even ap-
proximate to.
602 LOGIC OF THE MORAL SCIENCES.
respecting the formation of character from observation and experiment
alone, we are driven perforce to that which, even if it had not been the in-
dispensable, would have been the most perfect, mode of investigation, and
■which it is one of the principal aims of philosophy to extend ; namely, that
which tries its experiments not on the complex facts, but on the simple
ones of which they are coijipounded; and after ascertaining the laws of the
causes, the composition of which gives vise to the complex phenomena^
then considers whether these will not explain and account for the approx-
imate generalizations which have been framed empirically respecting the
sequences of those complex phenomena. The laws of the formation of
character are, in short, derivative laws, resulting from the general laws of
mind, and are to be obtained by deducing them from those general laws
by supposing any given set of circumstances, and then considering what,
according to the laws of mind, will be the iuflueijce of those circumstances
on the formation of character.
A science is thus formed, to which I would propose to give the name of
Ethology, or the Science of Character, from ^floe, a word more nearly cor-
responding to the term " cHaracter " as 1 hei-e >ise it, than any other word in
the same language. The name is perhaps etymologically applicable to the
entire science of our mental and moral nature ; but if, as is usual and con-
venient, we employ the name Psychology for the science of the elementary
laws of mind, Ethology will serve for the ulterior science which determines
the kind of character prodxiced in conformity to those general laws by any
set of circumstances, physical and moral. According to this definition.
Ethology is the science which corresponds to the art of education in the
widest sense of the term, including the formation of national or collective
character as well as individual. It would indeed be vain to expect (how-
ever completely the laws of the formation of character might be ascertain-
ed) that we could know so accurately the circumstances of any given case
as to be able positively to predict the character that would be produced in
that case. But we must remembei; that a degree of knowledge far short of
the power of actual prediction is often of much practical value. There
may be great power of influencing phenomena, with a very impei'fect
knowledge of the causes by which they are in any given instance deter-
mined. It is enough that we know that certain means have a tendency to
produce a given eifect, and that others have a tendency to fi'ustrate it.
When the circumstances of an individual or of a nation are in any consid-
erable degree under our control, we may, by oar knowledge of tendencies,
be enabled to shape those circumstances in a manner much more favorable
to the ends we desire, than the shape which they would of themselves as-
sume. This is, the limit of our power; but within this limit the power is
a most important one.
This science of Ethology may be called the Exact Science of Human Na^
ture; for its truths are not, like the empirical laws. which depend on thera,
approximate generalizations, but real laws. It is, however (as in all cases
of complex phenomena), necessary to the exactness of the propositions, that
they should be hypothetical only, and affirm tendencies, not facts. They
must not assert that something will always, or certainly, happen ; but only
that such and such will be the efBect of a given cause, so far as it operates
uncounteracted. It is a scientific proposition, that bodily strength tends t»
make men courageous ; not that it always makes them so : that an interest
on one side of a question tends to bias the judgment; not that it invaria-
bly does so': that experience tends to give wisdom; not that such is at
ETHOLOGY. 603
ways its effect. These propositions, being assertive only of tendencies, are
not the less universally true because the tendencies may be frustrated.
§ 5. While, on the one hand. Psychology is altogether, or principally, a
science of observation and experiment, Ethology, as I have conceived it, is,
as I have already remarked, altogether deductive. The one ascertains the
simple laws of Mind in general, the other traces their operation in complex
combinations of circumstances. Ethology stands to Psychology in a rela-
tion very similar to that in which the various branches of natural philoso-
phy stand to mechanics. The principles of Ethology are propei-ly the mid-
dle principles, the axiomata media (as Bacon would have said) of the sci-
ence of mind : as distinguished, on the one hand, from the empirical laws
resulting from simple observation, and, on the other, from the highest gen-
eralizations.
And this seems a suitable place for a logical remark, which, though of
general application, is of peculiar importance in reference to the present
subject. Bacon has judiciously observed that the axiomata media of ev-
ery science principally constitute its value. The lowest generalizations, un-
til explained by and resolved into the middle principles of which they are
the consequences, have only the imperfect accuracy of empirical laws;
while the most general laws are too general, and include too few circum-
stances, to give sufficient indication of what happens in individual cases,
where the circumstances are almost always immensely numerous. In the
importance, therefore, which Bacon assigns, in every science, to the middle
principles, it is impossible not to agree with him. But I conceive him to
have b^en radically wrong in his doctrine respecting the mode in which
these axiom,ata m,edia should be arrived at ; though there is no one propo-
sition laid down in his works for which he has been more extravagantly
eulogized. He enunciates as a universal rule that induction should pro-
ceed from the lowest to the middle principles, and from those to the high-
est, never reversing that order, and, consequentlj', leaving no room for the
discovery of new principles by way of deduction at all. It is not to be
conceived that a man of his sagacity could have fallen into this mistake if
there had existed in his time, among the sciences which treat of successive
phenomena, one single instance of a deductive science, such as mechanics,
astronomy, optics, acoustics, etc., now are. In those sciences it is evident
that the higher and middle principles are by no means derived from the
lowest, but the reverse. In some of them the very highest generalizations
were those earliest ascertained with any scientific exactness ; as, for exam-
ple (in mechanics), the laws of motion. Those general laws had not, in-
deed, at first the acknowledged universality which they acquired after having
been successfully employed to explain many classes of phenomena to which
they were not originally seen to be applicable ; as when the laws of motion
were employed, in conjunction with other laws, to explain deductively the
celestial phenomena. Still, the fact remains, that the propositions which
were afterward recognized as the most general truths of the science were,
of all its accurate generalizations, those earliest arrived at. Bacon's great-
est merit can not therefore consist, as we are so often told that it did, in ex-
ploding the vicious method pursued by the ancients of flying to the high-
est generalizations first, and deducing the middle principles from them;
since this is neither a vicious nor an exploded, but the universally accredited
method of modern science, and that to which it owes its greatest triumphs.
The error of ancient speculation did not consist in making the largest gen-
604 LOGIC OF THE MORAL SCIENCES.
eralizations first, but ia making them without the aid or warrant of rigor-
ous inductive methods, and applying them deductively without the needful
use of that important part of the Deductive Method termed Verification.
The order in which truths of the various degrees of generality should
be ascertained can not, I apprehend, be prescribed by any unbending rule.
I know of no maxim which can be laid down on the subject, but to obtain
those first in respect to which the conditions of a veal induction can be
first and most completely realized. Now, wherever our means of investi-
gation can reach causes, without stopping at the empirical laws of the ef-
fects, the simplest cases, being those in which fewest causes are simulta-
neously concerned, will bo most amenable to the inductive process; and
these are the cases which elicit laws of the greatest comprehensiveness.
In every science, therefore, which has reached the stage at which it be-
comes a science of causes, it will be usual as well as desirable first to ob-
tain the highest generalizations, and then deduce the more special ones
from them. Nor can I discover any foundation for the Baconian maxim,
so much extolled by subsequent writers, except this : That before we at-
tempt to explain deductively from more general laws any new class of phe-
nomena, it is desirable to have gone as far as is practicable in ascertaining
the empirical laws of those phenomena; so as to compare the results of
deduction, not with one individual instance after another, but with general
propositions expressive of the points of agreement which have been found
among many instances. For if Newton had been obliged to verify the
theory of gravitation, not by deducing from it Kepler's laws, but by de-
ducing all the observed planetary positions which had served Kepler to
establish those laws, the Newtonian theory would probably newjr have
emerged from the state of an hypothesis.*
The applicability of these remarks to the special case under considera-
tion can not admit of question. The science of the formation of character
is a science of causes. The subject is one to which those among the can-
ons of induction, by which laws of causation are ascertained, can be rigoi--
ously applied. It is, therefore, both natural and advisable to ascertain the
simplest, which are necessarily the most general, laws of causation first,
and to deduce the middle principles from them. In other words. Etholo-
gy, the deductive science, is a system of corollaries from Psychology, the
experimental science.
§ 6. Of these, the earlier alone has been, as yet, really conceived or stud-
ied as a science; the other. Ethology, is still to be created. But its cre-
ation has at length become practicable. The empirical laws, destined to
verify its deductions, have been formed in abundance by every successive
* " To which, " says Dr. Whewell, ' ' we maj' add, that it is certain, from the history of the
subject, that in that case the hypothesis would never have been framed at all."
Dr. Whewell {Philosophy of Discovery, pp. 277-282) defends Bacon's rule against the pre-
ceding strictures. But his defense consists only in asserting and exemplifying a proposition
which I had myself stated, viz., that though the largest generalizations may be the earliest
made, they are not at first seen in their entire generality, but acquire it by degrees, as they are
found to explain one class after another of phenomena. The laws of motion, for example,
were not known to extend to the celestial regions, until the motions of the celestial bodies
had been deduced from them. This, however, does not in any way affect the fact, that the
middle principles of astronomy, the central force, for example, and the law of the inverse
square, could not have been discovered, if the laws of motion, which are so much more uni-
versal, had not been known first. On Bacon's system of step-by-step generalization, it would
he impossible in any science to ascend higher than the empirical laws; a remark which Dr.
Whewell's own Inductive Tables, referred to by him in support of his argument, amply bear out.
ETHOLOGY. 605
age of humanity ; and the premises for the deductions are now sufficient-
ly complete. Excepting the degree of uncertainty which still exists as to
the extent of the natural differences of individual minds, and the physical
circumstances on which these may be dependent (considerations which are
of secondary importance when we are considering mankind in the average,
or en masse), I believe most competent judges will agree that the general
laws of the different constituent elements of human nature are even now
sufficiently understood to render it possible for a competent thinker to de-
duce from those laws, with a considerable approach to certainty, the par-
ticular type of character which would be formed in mankind generally by
any assumed set of circumstances. A science of Ethology, founded on the
laws of Psychology, is therefore possible; though little has yet been done,
and that little not at all systematically, toward forming it. The progress
of this important but most imperfect science will depend on a double proc-
ess: first, that of deducing theoretically the ethological consequences of
particular circumstances of position, and comparing them with the recog-
nized results of common experience ; and, secondly, the reverse operation ;
increased study of the various types of human natuie that are to be found
in the world ; conducted by persons not only capable of analyzing and re-
cording the circumstances in which these types severally prevail, but also
sufficiently acquainted with psychological laws to be able to explain and
account for the characteristics of the type, by the peculiarities of the cir-
cumstances : the residuum alone, when there proves to be any, being set
down to the account of congenital predispositions.
For the experimental or a posteriori part of this process, the materials
are continually accumulating by the observation of mankind. So far as
thought is concerned, the great problem of Ethology is to deduce the requi-
site middle principles from the general laws of Psychology. The subject
to be studied is, the origin and sources of all those qualities in human be-
ings which are interesting to us, either as facts to be produced, to be avoid-
ed, or merely to be understood; and the object is, to determine, from the
general laws of mind, combined with the general position of our species in
the universe, what actual or possible combinations of circumstances are
capable of promoting or of preventing the production of those qualities.
A science which possesses middle principles of this kind, arranged in the
order, not of causes, but of the effects which it is desirable to produce or
to prevent, is duly prepared to be the foundation of the corresponding
Art. And when Ethology shall be thus prepared, practical education will
be the mere transformation of those principles into a parallel system of
pi-ecepts, and the adaptation of these to the sum total of the individual cir-
cumstances which exist in each particular case.
It is hardly necessary again to repeat that, as in every other deductive
science, verification a posteriori must proceed pari passu with deduction
a priori. The inference given by theory as to the type of character which
would be formed by any given circumstances must be tested by specific
experience of those circumstances whenever obtainable; and_ the conclu-
sions of the science as a whole must undergo a perpetual verification and
correction from the general remarks afforded by common experience re-
specting human nature in our own age, and by history respecting times gone
by. The conclusions of theory can not be trusted, unless confirmed by ob-
servation ; nor those of observation, unless they can be affiliated to theory,
by deducing them from the laws of human nature, and from a close analysis
of the circumstances of the particular situation. It is the accordance of
606 LOGIC OF THE MORAL SCIENCES.
these two kinds of evidence separately taken — the consilience of a priori
reasoning and specific experience — which forms the only sufiicient ground
for the principles of any science so " immersed in matter," dealing with
such complex and concrete phenomena, as Ethology.
CHAPTER VI.
GENERAL CONSIDBEATIONS ON THE SOCIAL SCIENCE.
§ 1. Next after the science of individual man comes the science of man
in society — of the actions of collective masses of mankind, and the various
phenomena which constitute social life.
If the formation of individual character is already a complex subject of
study, this subject must be, in appearance at least, still more complex; be-
cause the number of concurrent causes, all exercising more or less influence
on the total effect, is greater, in the proportion in which a nation, or the
species at large, exposes a larger surface to the operation of agents, psy-
chological and physical, than any single individual. If it was necessary to
prove, in opposition to an existing prejudice, that the simpler of the tvs^o
is capable of being a subject of science, the prejudice is likely to be yet
stronger against the possibility of giving a scientific character to the study
of Politics, and of the phenomena of Society. It is, accordingly, but of
yestevday that the conception of a political or social science has existed
anywhere but in the mind of here and there an insulated thinker, generally
very ill prepared for its realization : though the subject itself has of all
others engaged the most general attention, and been a theme of interested
and earnest discussions, almost from the beginning of recorded time.
The condition, indeed, of politics as a branch of knowledge was, until
very lately, and has scarcely even yet ceased to be, that which Bacon ani-
madverted on, as the natural state of the sciences while their cultivation is
abandoned to practitioners ; not being carried on as a branch of speculative
inquiry, but only with a view to the exigencies of daily practice, and the
frucUfera experimenta, therefore, being aimed at, almost to the exclusion
of the lucifera. Such was medical investigation, before physiology and
natural history began to be cultivated as branches of general knowledge.
The only questions examined were, what diet is wholesome, or what medi-
cine will cure some given disease ; without any previous systematic inquiry
into the laws of nutrition, and of the healthy and morbid action of the
different organs, on which laws the effect of any diet or medicine must
evidently depend. And in politics the questions which engaged general
attention were similar : Is such an enactment, or such a form of govern-
ment, beneficial or the reverse — either universally, or to some particular
community? without any previous inquiry into the general conditions by
which the operation of legislative measures, or the effects produced by
forms of government, are determined. Students in politics thus attempted
to study the pa,thology and therapeutics of the social body, before they had
laid the necessary foundation in its physiology; to cure disease without
understanding the laws of health. And the result was such as it must al-
ways be when persons, even of ability, attempt to deal with the complex
questions of a science before its simpler and more elementary truths have
been established.
No wonder that, when the phenomena of society have so rarely beea
SOCIAL SCIENCE. 607
contemplated in the point of View cliaracteristio of science, the philosopliy
of society should have made little progress ; should contain few general
propositions sufficiently precise and certain for common inquirers to recog-
nize in them a scientific character. The vulgar notion accordingly is, that
all pretension to lay down general truths on politics and society is quack-
ery ; that no universality and no certainty are attainable in such matters.
What partly excuses this common notion is, that it is really not without
foundation' in one particular sense. A large proportion of those who have
laid claim to the character of philosophic politicians have attempted not
to ascertain universal sequences, but to frame universal precepts. They
have imagined some one form of government, or system of laws, to fit all
cases — a pretension well meriting the ridicule with which it is treated by
practitioners, and wholly unsupported by the analogy of the art to which,
from the nature of its subject, that of politics must be the most nearly
allied. No one now supposes it possible that one remedy can cui"e all
diseases, or even the same disease in all constitutions and habits of body.
It is not necessary even to the perfection of a science, that the corre-
sponding art should possess universal, or even general, rules. The phe-
nomena of society might not only be completely dependent on known
causes, but the mode of action of all those causes might be reducible to
laws of considerable simplicity, and yet no two cases might admit of being
treated in precisely the same manner. So great might be the variety of
circumstances on which the results in different cases depend, that the art
might not have a single general precept to give, except that of watching
the circumstances of the particular case, and adapting our measures to the
effects which, according to the principles of the science, result from those
circumstances. But although, in so complicated a class of subjects, it is
impossible to lay down practical maxims of universal application, it does
not follow that the phenomena do not conform to universal laws.
§ 2. All phenomena of society are phenomena of human nature, gener-
ated by the action of outward circumstances upon masses of human be-
ings ; and if, therefore, the phenomena of human thought, feeling, and ac-
tion are subject to fixed laws, the phenomena of society can not but con-
form to fixed laws, the consequence of the preceding. There is, indeed,
no hope that these laws, though our knowledge of them were as certain
and as complete as it is in astronomy, would enable us to predict the his-
tory of society, like that of the celestial appearances, for thousands of
years to come. But the difference of certainty is not in the laws them-
selves, it is in the data to which these laws are to be applied. In as-
tronomy the causes influencing the result are few, and change little, and
that little according to known laws ; we can ascertain what they are now,
and thence determine what they will be at any epoch of a distant future.
The data, therefore, in astronomy are as certain as the laws themselves.
The circumstances, on the contrary, which influence the condition and prog-
ress of society are innumerable, and perpetually changing; and though
they all change in obedience to causes, and therefore to laws, the multitude
of the causes is so great as to defy our limited powers of calculation. Not
to say that the impossibility of applying precise numbers to facts of such
a description would Set an impassable limit to the possibility of calcula-
ting them beforehand, even if the powers of the human intellect were other-
wise adequate to the task. . „ . ,
But, as before remarked, an amount of knowledge quite insuflicient tor
608 LOGIC OF THE MORAL SCIENCES.
prediction, may be most valuable for guidance. The science of society
would have attained a very high point of perfection if it enabled us, la
any given condition of social affairs, in the condition, for instance, of Eu-
rope or any European country at the present time, to understand by what
causes it had, in any and every particular, been made what it was; wheth-
er it was tending to any, and to what, changes ; what effects each feature
of its existing state was likely to produce in the future; and by what
means any of those effects might be prevented, modified, or accelerated, or
a different class of effects superinduced. There is nothing chimerical in
the hope that general laws, sufficient to enable us to answer these various
questions for any country or time with the individual circumstances of
which we are well acquainted, do really admit of being ascertained ; and
that the other branches of human knowledge, which this undertaking pr&
supposes, are so far advanced that the time is ripe for its commencement.
Such is the object of the Social Science.
That the nature of what I consider the true method of the science may
be made more palpable, by first showing what that method is not, it will
be expedient to characterize briefly two radical misconceptions of the
proper mode of philosophizing on society and government, one or other of
which is, either explicitly or more often unconsciously, entertained by al-
most all who have meditated or argued respecting the logic of politicSj
since the notion of treating it by strict rules, and on Baconian principles,
has been current among the more advanced thinkers. These erroneous
methods, if the word method can be applied to erroneous tendencies aris-
ing from the absence of any sufficiently distinct conception of method, may
be termed the Experimental, or Chemical, mode of investigation, and the
Abstract, or Geometrical, mode. We shall begin with the former.
CHAPTER VII.
OF THE CHEMICAL, OE EXPEBIMBNTAL, METHOD IN THE SOCIAL SCIENCE.
§ 1. The laws of the phenomena of society are, and can be, nothing but
the laws of the actions and passions of human beings united together in
the social state. Men, however, in a state of society are still men ; their
actions and passions are obedient to the laws of individual human nature.
Men are not, when brought together, converted into another kind of sub-
stance, with different properties ; as hydrogen and oxygen are different
from water, or as hydrogen, oxygen, carbon, and azote, are different from
nerves, muscles, and tendons. Human beings in society have no proper-
ties but those which are derived from, and may be resolved into, the laws
of the nature of individual man. In social phenomena the Composition of
Causes is the universal law.
Now, the method of philosophizing which may be termed chemical over-
looks this fact, and proceeds as if the nature of man as an individual were
not concerned at all, or were concerned in a very inferior degree, in the
operations of human beings in society. All reasoning in political or social
affairs, grounded on principles of human nature, is objected to by reason-
ers of this sort, under such names as " abstract theory." For the direc-
tion of their opinions and conduct, they profess to demand, in all cases
without exception, specific experience.
THE CHEMICAL METHOD. 60&
This mode of thinking is not only general with practitioners in poli-
tics, and with that very numerous class who (on a subject which no one,
however ignorant, thinks himself incompetent to discuss) profess to guide
themselves by common sense rather than by science; but is often counte-
tenanoed by persons with greater pretensions to instruction — persons who,
having sufficient acquaintance with books and with the current ideas to
have heard that Bacon taught mankind to follow experience, and to ground
their conclusions on facts instead of metaphysical dogmas, think that, by
treating political facts in as directly experimental a method as chemical
facts, they are showing themselves true Baconians, and proving their'ad-
versaries to be mere syllogizers and school-men. As, however, the notion
of the applicability of experimental methods to political philosophy can
not co-exist with any just conception of these methods themselves, the kind
of arguments from experience which the chemical theory brings forth as
its fruits (and which form the staple, in this country especially, of parlia-
mentary and hustings oratory), are such as, at no time since Bacon, would
have been admitted to be valid in chemistry itself, or in any other branch
of experimental science. They are such as these : that the prohibition of
foreign commodities must conduce to national wealth, because England
has flourished under it, or because countries in general which have adopt-
ed it have flourished ; that our laws, or our internal administration, or our
constitution, are excellent for a similar reason; and the etei'nal ai'guments
from historical examples, from Athens or Rome, from the fires in Smith-
field or the French Revolution.
I will not waste time in contending against modes of argumentation
which no person with the smallest practice in estimating evidence could
possibly be betrayed into; which draw conclusions of general application
from a single unanalyzed instance, or arbitrarily refer an effect to some
one among its antecedents, without any process of elimination or compari-
son of instances. It is a rule both of justice and of good sense to grapple
not with the absurdest, but with the most reasonable form of a wi'ong
opinion. We shall suppose our inquirer acquainted with the true condi-
tions of experimental investigation, and competent in point of acquire-
ments for realizing them, so far as they can be realized. He shall know
as much of the facts of history as mere erudition can teach — as much as
can be proved by testimony, without the assistance of any theory; and if
those mere facts, properly collated, can fulfill the conditions of a real in-
duction, he shall be qualified for the task.
But that no such attempt can have the smallest chance of success, has
been abundantly shown in the tenth chapter of the Third Book.* We
there examined whether effects which depend on a complication of causes
can be made the subject of a true induction by observation and experi-
ment; and concluded, on the most convincing grounds, that they can not.
Since, of all effects, none depend on so great a complication of causes as
social phenomena, we might leave our case to rest in safety on that previ-
ous showing. But a logical principle as yet so little familiar to the ordi-
nary run of thinkers, requires to be insisted on more than once, in order to
make the due impression ; and the present being the case which of all oth-
ers exemplifies it the most strongly, there will be advantage in re-f5tating
the grounds of the general maxim, as applied to the specialties of the
«lass of inquiries now under consideration.
* Supra, page 317 to the end of the chapter.
39
«10 LOGIC OF THE MOKAL SCIENCES.
§ 2. The first difficulty which meets lis in the attempt to apply experi-
mental methods for ascertaining the laws of social phenomena, is that we
are without the means of making artificial experiments. Even if we could
contrive experiments at leisure, and try them without limit, we should do
fio under immense disadvantage ; both from the impossibility of ascertain-
ing and taking note of all the facts of each case, and because (those facts
Tieing in a perpetual state of change), before sufficient time had elapsed to as-
certain the result of the experiment, some material circumstances would al-
ways have ceased to be the same. But it is unnecessary to consider the log-
ical'objections which would exist to the conclusiveness of our experiments,
since we palpably never have the power of trying any. We can only watch
those which nature produces, or which are produced for other reasons.
We can not adapt our logical means to our wants, by vaiying the circum-
stances as the exigencies of elimination may require. If the spontaneous
instances, formed by contemporary events and by the successions of phe-
nomena recorded in history, afford a sufficient variation of circumstances,
an induction from specific experience is attainable ; otherwise not. The
question to be resolved is, therefore, whether the requisites for induction
respecting the causes of political effects or the properties of political agents,
are to be met with in history ? including under the term, contemporary his-
tory. And in order to give fixity to our conceptions, it will be advisable
to suppose this question asked in reference to some special subject of po-
litical inquiry or controversy ; such as that frequent topic of debate in the
present century, the operation of restrictive and prohibitory commercial
legislation upon national wealth. Let this, then, be the scientific question
to be investigated by specific experience.
§ 3. In order to apply to the case the most perfect of the methods of ex-
perimental inquiry, the Method of Difference, we require to find two in-
stances which tally in every particular except the one which is the subject
of inquiry. If two nations can be found which are alike in all natural ad-
vantages and disadvantages; whose people resemble each other in every
quality, physical and inoral, spontaneous and acquired; whose habits,
usages, opinions, laws, and institutions are the same in all respects, except
that one of them has a more protective tariff, or in other respects interferes
more with the freedom of industry ; if one of these nations is found to be
rich and the other poor, or one richer than the other, this will be an expe-
rimentum crucis: a real proof by experience, which of the two systems is
most favorable to national riches. But the supposition that two such in-
stances can be met with is manifestly absurd. Nor is such a concurrence
even abstractedly possible. Two nations which agreed in every thing except
their commercial policy would agree also in that. Differences of legisla-
tion are not inherent and ultimate diversities ; are not properties of Kinds.
They are effects of pre-existing causes. If the two nations differ in this
portion of their institutions, it is from some difference in their position,
and thence in their apparent interests, or in some portion or other of their
opinions, habits, and tendencies ; which opens a view of further differences
■without any assignable limit, capable of operating on their industrial pros-
perity, as well as on every other feature of their condition, in more ways
than can be enumerated or imagined. There is thus a demonstrated im-
possibility of obtaining, in the investigations of the social science, the con-
ditions required for the most conclusive form of inquiry by specific experi-
ence.
THE CHEMICAL METHOD. qh
In the absence of the direct, we may next try, aa in other cases, the sup-
plementary resource, called in a former place the Indirect Method of Dif-
ference ; which, instead of two instances differing in nothing but the pres-
■ence or absence of- a given circumstance, compares two classes of instances
respectively agreeing in nothing but the presence of a circumstance on the
one side and its absence on the other. To choose the most advantageous
case conceivable (a case far too advantageous to be ever obtained), suppose
that we compare one nation which has a restrictive policy with two or
more nations agreeing in nothing but in permitting free trade. We need
oot now suppose that either of these nations agrees with the first in all its
<!ircumstances ; one may agree with it in some of its circumstances, and an-
other in the remainder. And it may be argued, that if these nations re-
main poorer than the restrictive nation, it can not be for want either of the
first or of the second set of circumstances, but it must be for want of the
protective system. If (we might say) the restrictive nation had prospered
from the one set of causes, the first of the free-trade nations would have
prospered equally ; if by reason of the other, the second would ; but nei-
ther has; therefore the prosperity was owing to the restrictions. This
will be allowed to be a very favorable specimen of an argument from spe-
oifio experience in politics, and if this be inconclusive, it would not be easy
to find another preferable to it.
Yet, that it is inconclusive, scarcely requires to be pointed out. Why
must the prosperous nation have prospered from one cause exclusively?
National prosperity is always the collective result of a multitude of favor-
able circumstances ; and of these, the restrictive nation may unite a greater
number than either of the others, though it may have all of those circum-j
stances in common with either one or the other of them. Its prosperity
may be partly owing to circumstances common to it with one of those na-
tions, and partly with the other, while they, having each of them only half
the number of favorable circumstances, have remained inferior. So that
the closest imitation which can be made, in the social science, of a legiti- .
mate induction from direct experience, gives but a specious semblance of
conclusiveness, without any real value.
§ 4. The Method of Difference in either of its forms being thus com-
pletely out of the question, there remains the Method of Agreement. But
we are already aware of how little value this method is, in cases admitting
Plurality of Causes ; and social phenomena are those in which the purality
prevails in the utmost possible extent.
Suppose that the observer makes the luckiest hit which could be given
by any conceivable combination of chances ; that he finds two nations which
agree in no circumstance whatever, except in having a restrictive system,
and in being prosperous ; or a number of nations, all prosperous, which
have no antecedent circumstances common to them all but that of having
a restrictive policy. It is unnecessary to go into the consideration of the
impossibility of ascertaining fi-om history, or even from contemporary ob-
servation, that such is really the fact ; that the nations agree in no other
circumstance capable of influencing the case. Let us suppose this impossi-
bility vanquished, and the fact ascertained that they agree only in a restrict-
ive system as an antecedent, and industrial prosperity as a consequent.
What degree of presumption does this raise that the restrictive system
caused the prosperity ? One so trifling as to be equivalent to none at all.
That some one antecedent is the cause of a given effect, because all othet
612 LOGIC OF THE MORAL SCIENCES.
antecedents have been found capable of being eliminated, is a just inference,
only if the effect can have but one cause. If it admits of several, nothing
is more natural than that each of these should separately admit of being
eliminated. Now, in the case of political phenomena, the supposition of
unity of cause is not only wide of the truth, but at an immeasurable dis-
tance from it. The causes of every social phenomenon which we are par-
ticularly interested about, security, wealth, freedom, good government, pub-
lic virtue, general intelligence, or their opposites, are infinitely numerous,
especially the external or remote causes, which alone are, for the most part,
accessible to direct observation. No one cause suflBces of itself to produce
any of these phenomena ; while there are countless causes which have some
influence over them, and may co-operate either in their production or in their
prevention. From the mere fact, therefore, of our having been able to elimi-
nate some circumstance, we can by no means infer that this cii'cumstance
was not instrumental to the effect in some of the very instances from which
we have eliminated it. We can conclude that the effect is sometimes pro-
duced without it ; but not that, when present, it does not contribute its share.
Similar objections will be found to apply to the Method of Concomitant
Variations. If the causes which act upon the state of any society produced
effects differing from one another in kind ; if wealth depended on one cause,
peace on another, a third made people virtuous, a fourth intelligent ; we
might, though unable to sever the causes from one another, refer to each of
them that property of the effect which waxed as it waxed, and which waned
as it waned. But every attribute of the social body is influenced by in-
numerable causes ; and such is the mutual action of the co-existing elements
of society, that whatever affects any one of the more important of them,
will by that alone, if it does not affect the others directly, affect them in-
directly. The effects, therefore, of different agents not being different in
quality, while the quantity of each is the mixed result of all the agents, the
variations of the aggregate can not bear a uniform proportion to those of
any one of its component parts.
_ § 5. There remains the Method of Residues ; which appears, on the first
view, less foreign to this kind of inquiry than the three other methods, be-
cause it only requires that we should accurately note the circumstances of
some one country, or state of society. Making allowance, thereupon, for
the effect of all causes whose tendencies are known, the residue which those
causes are inadequate to explain may plausibly be imputed to the remain-
der of the circumstances which are known to have existed in the case.-
Something similar to this is the method which Coleridge* describes him-
self as having followed in his political essays in the Morning Post. " On
every -great occurrence I endeavored to discover in past history the event
that most nearly resembled it. I procured, whenever it was possible, the
contemporary historians, memorialists, and pamphleteers. Then fairly sub-
tracting the points of difference from those of likeness, as the balance fa-
vored the former or the latter, I conjectured that the result would be the
sartie or different. As, for instance, in the series of essays entitled 'A Com-
parison of France under Napoleon with Rome under the first Caesars,' and
in those which followed, ' on the probable final restoration of the Bourbons.'
The same plan I pursued at the commencement of the Spanish Revolution,
and with the same success, taking the war of the United Provinces with.
* Biographia lAteraria, i. , 214.
THE CHEMICAL METHOD. 613
Philip II. as the groundwork of the comparison." In this inquiry he no
doubt employed the Method of Residues ; for, in " subtracting the points
of difference from those of likeness," he doubtless weighed, and did not
content himself with numbering, them : he doubtless took those points of
agreement only which he presumed fi-oin their own nature to be capable
of influencing the effect, and, allowing for that influence, concluded that the
remainder of the result would be referable to the points of difference.
Whatever may be the eflicaoy of this method, it is, as we long ago re-
marked, not a method of pure observation and experiment ; it concludes,
not from a comparison of instances, but from the comparison of an in-
stance with the result of a previous deduction. Applied to social phenom-
ena, it presupposes that the causes from which part of the effect proceeded
are already known ; and as we have shown that these can not have been
known by specific experience, they must have been learned by deduction
from principles of human nature ; experience being called in only as a sup-
plementary resource, to determine the causes which produced an unex-
plained residue. But if the principles of human nature may be had re-
course to for the establishment of some political truths, they may for all.
If it be admissible to say, England must have prospered by reason of
the prohibitory system, because after allowing for all the other tendencies
which have been operating, there is a portion of prosperity still to be ac-
counted for ; it must be admissible to go to the same source for the effect
of the prohibitory system, and examine what account the laws of human
motives and actions will enable us to give of its tendencies. Nor, in fact,
will the experimental argument amount to any thing, except in verification
of a conclusion drawn from those general laws. For we may subtract
the effect of one, two, three, or four causes, but we shall never succeed in
subtracting the effect of all causes except one; while it would be a cu-
rious instance of the dangers of too much caution if, to avoid depending
on a priori reasoning concerning the effect of a single cause, we should
oblige ourselves to depend on as many separate a priori reasonings as
there are causes operating concurrently with that particular cause in some
given instance.
We have now sufficiently characterized the gross misconception of the
mode of investigation proper to political phenomena, which I have termed
the Chemical Method. So lengthened a discussion would not have been
necessary, if the claim to decide authoritatively on political doctrines were
confined to persons who had competently studied any one of the higher
departments of physical science. But since the generality of those who
reason on political subjects, satisfactorily to themselves and to a more or
less numerous body of admirers, know nothing whatever of the methods of
physical investigation beyond a few precepts which they continue to par-
rot after Bacon, being entirely unaware that Bacon's conception of scien-
tific inquiry has done its work, and that science has now advanced into a
higher stage, there are probably many to whom such remarks as the fore-
going may still be useful. In an age in which chemistry itself, when at-
tempting to deal with the more complex chemical sequences — those of the
animal or even the vegetable organism — has found it necessary to become,
and has succeeded in becoming, a Deductive Science, it is not to be ap-
prehended that any person of scientific habits, who has kept pace with the
general progress of the knowledge of nature, can be in danger of applying
the methods of elementary chemistry to explore the sequences of the most
complex order of phenomena in existence.
614 LOGIC OF THE MORAL SCIENCES.
CHAPTER VIII.
OF THE GEOMETRICAL, OE ABSTRACT, METHOD,
§ 1. The misconception discussed in the preceding chapter Is, as wff
said, chiefly committed by persons not much accustomed to scientific in-
vestigation : practitioners in politics, who rather employ the commonplace*
of philosophy to justify their practice than seek to guide their practice by
philosophic principles ; or imperfectly educated persons, who, in ignorance-
of the careful selection and elaborate comparison of instances required for
the formation of a sound theory, attempt to found one upon a few coinci-
dences which they have casually noticed.
The erroneous method of which we are now to treat is, on the contrary,,
peculiar to thinking and studious minds. It never could bave suggested
itself but to persons of some familiarity with the nature of scientific re-
search ; who, being aware of the impossibility of establishing, by casual
observation or direct experimentation, a true theory of sequences so com-
plex as are those of the social phenomena, have recourse to the simpler
laws which are immediately operative in those phenomena, and which are
no other than the laws of the nature of the human beings therein concern-
ed. These thinkers perceive (what the partisans of the chemical or exper-
imental theory do not) that the science of society must necessarily be de-
ductive. But, from an insuflficient consideration of the specific nature of
the subject-matter — and often because (their own scientific education hav-
ing stopped short in too early a stage) geometry stands in their minds as
the type of air deductive science — it is to geometry, rather than to as-
tronomy and natural philosophy, that they unconsciously assimilate the-
deductive science of society.
Among the differences between geometry (a science of co-existent facts,
altogether independent of the laws of the succession of phenomena), and
those physical Sciences of Causation which have been rendered deductive^
the following is one of the most conspicuous : That geometry affords no
room for what so constantly occurs in mechanics and its applications, the
case of conflicting forces; of causes which counteract or modify one an-
other. In mechanics we continually find two or more moving forces pro-
ducing, not motion, but rest ; or motion in a different direction from that
which would have been produced by either of the generating forces. It
is true that the effect of the joint forces is the same when they act simul-
taneously, as if they had acted one after another, or by turns ; and it is
in this that the difference between mechanical and chemical laws consists.
But still the effects, whether produced by successive or by simultaneous
action, do, wholly or in part, cancel one another : what the one force does,,
the other, partly, or altogether undoes. There is no similar state of things
in geometiy. The result which follows from one geometrical principle has
nothing that conflicts with the result which follows from another. What
is proved true from one geometrical theoi-em, what would be true if no
other geometrical principles existed, can not be altered and made no longer
true by reason of some other geometrical principle. What is once proved
true is true in all cases, whatever supposition may be made in regard to
any other matter.
THE GEOMETRICAL METHOD. gjg,
Now a conception similar to this last would appear to have been form
ed of the social science, in the minds of the earlier of those who have at-
tempted to cultivate it by a deductive method. Mechanics would be a
science very similar to geometry, if every motion resulted from one force
alone, and not fi'om a conflict of forces. In the geometrical theory of so»
ciety, it seems to be supposed that this is really the case with the social
phenomena; that each of them results always from only one force one
single property of human nature. '
At the point which we have now reached, it can not be necessaiy to say
any thing either in proof or in illustration of the assertion that such is not.
the true character of the social phenomena. There is not, among these
most complex and (for that reason) most modifiable of all phenomena, any
one over which innumerable forces do not exei-cise influence; which does,
not depend on a conjunction of very many causes. We have not, there-
fore, to prove the notion in question to be an error, but to prove that the
error has been committed ; that so mistaken a conception of the mode in
which the phenomena of society are produced has actually been ascertained.
§ 2. One numerous division of the reasoners who have treated social
facts according to geometrical methods, not admitting any modification of
one law by another, must for the present be left out of consideration, be-
cause in them this error is complicated with, and is the effect of, another
fundamental misconception, of which we have already taken some notice,,
and which will be further treated of before we conclude. I speak of those,
who deduce political conclusions not from laws of nature, not from se-
quences of phenomena, real or imaginary, but from unbending practical
maxims. Such, for example, are all who found their theory of politics oa
what is called abstract right, that is to say, on universal precepts ; a pre-
tension of which we have already noticed the chimerical nature. Such, in
hke manner, are those who make the assumption of a social contract, or
any other kind of original obligation, and apply it to particular cases by
mere interpretation. But in this the fundamental error is the attempt to-
treat an art like a science, and to have a deductive art; the irrationality
of which will be shown in a futui-e chapter. It will be proper to take oui-
exemplification of the geometrical theory from those thinkers who hav&
avoided this additional error, and who entertain, so far, a juster idea of
the nature of political inquiry.
We may cite, in the first instance, those who assume as the principle of
their political philosophy that government is founded on fear; that the-
dread of each other is the one motive by which human beings wei-e origi-
nally brought into a state of society, and are still held in it. Some of the-
earlier scientific inquirers into politics, in particular Hobbes, assumed thif^
proposition, not by implication, but avowedly, as the foundation of their
doctrine, and attempted to build a complete philosophy of politics there-
upon. It is true that Hobbes did not find this one maxim sufiicient to
carry him through the whole of his subject, but was obliged to eke it out.
by the double sophism of an original contract. I call this a double soph-
ism; first, as passing off a fiction for a fact, and, secondly, assuming a
practical principle, or precept, as the basis of a theory ; which is a petitio-
principii, since (as we noticed in treating of that Fallacy) every j-ule of
conduct, even though it be so binding a one as the observance of a prom-
ise, must rest its own foundations on the theory of the subject; and the
theory, therefore, can not rest upon it.
616 LOGIC OF THE MORAL SCIENCES.
§ 3. Passing tjver less important instances, I shall come at once to the
most remarkable example afforded by our own times of the geometrical
method in politics; emanating from persons who are well aware of the
distinction between science and art ; who knew that rules of conduct must
iollow, not precede, the ascertainment of laws of nature, and that the lat-
ter, not the former, is the legitimate field for the application of the deduct-
ive method. I allude to the interest-philosophy of the Benthara school.
The profound and original thinkers who are commonly known under
this description, founded their general theory of government on one com-
ijirehensive premise, namely, that men's actions are always determined by
their interests. There is an ambiguity in this last expression ; for, as the
same philosophers, especially Bentham, gave the name of an interest to
anything which a person likes, the proposition may be understood to mean
only this, that men's actions are always determined by their wishes. In
this sense, however, it would not bear out any of the consequences which
these writers drew from it ; and the word, therefore, in their political
reasonings, must be understood to mean (which is also the explanation they
themselves, on such occasions gave of it) what is commonly termed private,
or worldly, interest.
Taking the doctrine, then, in this sense, an objection presents itself in
iimine which might be deemed a fatal one, namely, that so sweeping a
proposition is far from being universally true. Human beings are not
governed in all their actions by their worldly interests. This, however, is
by no means so conclusive an objection as it at first appears ; because in
politics we are for the most part concerned with the conduct, not of indi-
Tidual persons, but either of a series of persons (as a succession of kings),
or a body or mass of persons, as a nation, an aristocracy, or a representa-
tive assembly. And whatever is true of a large majority of mankind, may
without much error be taken for true of any succession of persons, con-
sidered as a whole, or of any collection of persons in which the act of the
majority becomes the act of the whole body. Although, therefore, the
maxim is sometimes expressed in a manner unnecessarily paradoxical, the
•consequences drawn from it will hold equally good if the assertion be lim-
ited as follows: Any succession of persons, or the majority of any body
of persons, will be governed in the bulk of their conduct by their personal*
interests. We are bound to allow to this school of thinkers the benefit of
this more rational statement of their fundamental maxim, which is also in
■strict conformity to the explanations which, when considered to be called
for, have been given by themselves.
The theory goes on to infer, quite correctly, that if the actions of man-
kind are determined in the main by their selfish interests, the only rulers
who will govern according to the interest of the governed, are those whose
selfish interests arciin accordance with it. And to this is added a third
proposition, namely, that no rulers have their selfish interest identical with
that of the governed, unless it be rendered so by accountability, that is,
by dependence on the will of the governed. In other words (and as the
result of the whole), that the desire of retaining or the fear of losing their
power, and whatever is thereon consequent, is the sole motive which can
be relied on for producing on the part of rulers a course of conduct in ac-
cordance with the general interest.
We have thus a fundamental theorem of political science, consisting of
three syllogisms, and depending chiefly on two general premises, in each of
■which a certain effect is considered as determined only by one cause, not
THE GEOMETRICAL METHOD.
617
by a concurrence of causes. In the one, it is assumed that the actions of
average rulers ai-e determined solely by self-interest; jn the other, that the
sense of identity of interest with the governed, is produced and producible
by no other cause than responsibility.
Neithei- of these propositions is by any means true ; the last is extreme-
ly wide of the truth.
It is not true that the actions even of average rulers are wholly, or any
thing approaching to wholly, determined by their personal interest, or even
by their own opinion of their personal interest. I do not speak of the in-
fluence of a sense of duty, or feelings of philanthropy, motives never to be
mainly relied on, though (except in countries or during periods of great
moral debasement) they influence almost all rulers in some degree, and
some rulers in a very great degree. But I insist only on what is true of all
rulers, viz., that the character and course of their actions is largely influ-
enced (independently of personal calculation) by the habitual sentiments
and feelings, the general modes of thinking and acting, which prevail
throughout the community of which they are members ; as well as by the
feelings, habits, and modes of thought which characterize the particular class
in that community to which they themselves belong. And no one will un-
derstand or be able to decipher their system of conduct, who does not take-
all these things into account. They are also much influenced by the max-
ims and traditions which have descended to them from other rulers, their
predecessors ; which maxims and traditions have been known to retain an
ascendancy during long periods, even in opposition to the private interests,
of the rulers for the time being. I put aside the influence of other less gen-
eral causes. Although, therefore, the private interest of the rulers or of
the ruling class is a very powerful force, constantly in action, and exer-
cising the most important influence upon their conduct, there is also, in
what they do, a large portion which that private interest by no means af-
fords a sufficient explanation of ; and even the particulars which constitute
the goodness or badness of their government, are in some, and no small
degree, influenced by those among the circumstances acting upon them,,
which can not, with any propriety, be included in the term self-interest.
Turning now to the other proposition, that responsibility to the govern-
ed is the only cause capable of producing in the rulers a sense of identity
of interest with the community, this is still less admissible as a universal
truth, than even the former. I am not speaking of perfect identity of in-
terest, which is an impracticable chimera ; which, most assuredly, responsi-
bility to the people does not give. I speak of identity in essentials ; and
the essentials are different at different places and times. There are a large
number of cases in which those things which it is most for the general inter-
est that the rulers should do, are also those which they are prompted to do
by their strongest personal interest, the consolidation of their power. The-
suppression, for instance, of anarchy and resistance to law — the complete
establishment of the authority of the central government, in a state of so-
ciety like that of Europe in the Middle Ages — is one of the strongest inter-
ests of the people, and also of the rulers simply because they are the rul-
ers ; and responsibility on their part could not strengthen, though in many
conceivable ways it might weaken, the motives prompting them to pursue
this object. During the greater part of the reign of Queen Elizabeth, and
of many other monarchs who might be named, the sense of identity of in-
terest between the sovereign and the majority of the people was probably
stronger than it usually is in responsible governments ; every thing that
€18 LOGIC OF THE MORAL SCIENCES.
the people had most at heart, the monarch had at heart too. Had Peter
the Great, or the rugged savages whom he began to civilize, the truest
inclination toward the things which were for the real interest of those
savages ?
I am not here attempting to establish a theory of government, and am
not called upon to determine the proportional weight which ought to be
given to the circumstances which this school of geometrical politicians left
out of their system, and those which they took into it. I am only con-
cerned to show that their method was unscientific; not to measure the
amount of error which may have affected their practical conclusions.
It is but justice to them, however, to remark, that their mistake was not
so much one of substance as of form, and consisted in presenting in a
systematic shape, and as the scientific treatment of a great philosophical
question, what should have passed for that which it really was, the mere
polemics of the day. Although the actions of rulers are by no means
wholly determined by their selfish interests, it is chiefly as a security
against those selfish interests that constitutional checks are required; and
ior that purpose such checks, in England, and the other nations of modern
Europe, can in no manner be dispensed with. It is likewise true, that in
these same nations, and in the present age, responsibility to the governed
is the only means practically available to create a feeling of identity of
interest, in the cases, and on the points, where that feeling does not suffi-
•ciently exist. To all this, and to the arguments which may be founded on
it in favor of measures for the correction of our representative system, I
have nothing to object; but I confess ray regret, that the small though
highly important portion of the philosophy of government, which was
wanted for the immediate purpose of serving the cause of parliamentary
reform, should have been held forth by thinkers of such eminence as a
-complete theory.
It is not to be imagined possible, nor is it true in point of fact, that
these philosophers regarded the few premises of their theory as including
all that is required for explaining social phenomena, or for detei-mining
the choice of forms of government and measures of legislation and admin-
istration. They were too highly instructed, of too comprehensive intellect,
and some of them of too sober and practical a character, for such an error.
They would have applied, and did apply, their principles with innumerable
allowances. But it is not allowances that are wanted. There is little
■chance of making due amends in the superstructure of a theory for the
want of sufficient breadth in its foundations. It is unphilosophical to con-
struct a science out of a few of the agencies by which the phenomena are
•determined, and leave the rest to the routine of practice or the sagacity of
•conjecture. We either ought not to pretend to scientific forms, or we
•ought to study all the determining agencies equally, and endeavor, so far
as it can be done, to include all of them within the pale of the science;
■else we shall infallibly bestow a disproportionate attention upon those
which our theory takes into account, while we misestimate the rest, and
probably underrate their importance. That the deductions should be
from the whole and not from a part only of the laws of nature that are
concerned, would be desirable even if those omitted were so insignificant
in comparison with the others, that they might, for most purposes and on
most occasions, be left out of the account. But this is far indeed from be-
ing true in the social science. The phenomena of society do not depend,
in essentials, on some one agency or law of human nature, with only incon-
PHYSICAL METHOD. 619
fiiderablc modifications from others. The whole of the qualities of human
nature influence those phenomena, and there is not one which influences
them in a small degree. There is not one, the removal or any great alter-
ation of which would not materially affect the whole aspect of society,
and change more or less the sequences of social phenomena generally.
The theory which has been the subject of these remarks is, in this coun-
try at least, the principal contemporary example of what I have styled the
geometrical method of philosophizing in the social science ; and our ex-
amination of it has, for this reason, been more detailed than would other-
wise have been suitable to a work like the present. Having now suflS-
ciently illustrated the two erroneous methods, we shall pass without fur-
ther preliminary to the true method ; that which proceeds (conformably
to the practice of the more complex physical sciences) deductively indeed,
but by deduction from many, not from one or a very few, original prem-
ises ; considering each effect as (what it really is) an aggregate result of
many causes, operating sometimes through the same, sometimes through
different mental agencies, or laws of human nature.
CHAPTER IX.
OF THE PHYSICAL, OK CONCRETE DEDUCTIVE, METHOD.
§ 1. After what has been said to illustrate the nature of the inquiry
into social phenomena, the general character of the method proper to that
inquiry is sufficiently evident, and needs only to be I'ecapitulated, not
proved. However complex the phenomena, all their sequences and co-ex-
istences result from the laws of the separate elements. The effect pro-
duced, in social phenomena, by any complex set of circumstances, amounts
precisely to. the sum of the effects of the circumstances taken singly ; and
the complexity does not arise from the number of the laws themselves,
which is not remarkably great, but from the extraordinary number and
variety of the data or elements — of the agents which, in obedience to that
small number of laws, co-operate toward the effect. The Social Science,
therefore (which, by a convenient barbarism, has been termed Sociology),
is a deductive science ; not, indeed, after the model of geometry, but after
that of the more complex physical sciences. It infers the law of each ef-
fect from the laws of causation on which that effect depends; not, how-
ever, from the law merely of one cause, as in the geometrical method, but
by considering all the causes which conjunctly influence the effect, and
compounding their laws with one another. Its method, in short, is the
Concrete Deductive Method : that of which astronomy furnishes the most
perfect, natural philosophy a somewhat less perfect, example, and the em-
ployment of which, with the adaptations and precautions required by the
subject, is beginning to regenerate physiology.
Nor does it admit of doubt, that similar adaptations and precautions are
indispensable in sociology. In applying to that most complex of all stud-
ies what is demonstrably the sole method capable of throwing the light
of science even upon phenomena of a far inferior degree of complication,
we ought to be aware that the same superior complexity which renders the
instrument of Deduction more necessary, renders it also more precarious ;
and we must be prepared to meet, by appropriate contrivances, this in-
crease of difficultv.
620 LOGIC OF THE MORAL SCIENCES.
The actions and feelings of human heings in the social state, are, no
doubt, entirely governed by psychological and ethological laws: whatever
influence any cause exercises upon the social phenomena, it exercises-
through those laws. Supposing therefore the laws of human actions and
feelings to be sufficiently known, there is no extraordinary difficulty in de-
termining from those laws, the nature of the social effects which any given
cause tends to produce. But when the question is that of compounding
several tendencies together, and computing the aggregate result of many
co-existent causes ; and especially when, by attempting to predict what wilL
actually occur in a given case, we incur the obligation of estimating and
compounding the influences of all the causes which happen to exist in that
case, we attempt a task to proceed far in which, surpasses the compass of
the human faculties.
If all the resources of science are not sufficient to enable us to calculate,
a priori, with complete precision, the mutual action of three bodies gravita-
ting toward one another, it may be judged with what prospect of success
we should endeavor to calculate the result of the conflicting tendencies-
which are acting in a thousand different directions and promoting a thou-
sand different changes at a given instant in a given society; although we-
might and ought to be able, from the laws of human nature, to distinguish
correctly enough the tendencies themselves, so far as they depend on causes
accessible to our observation ; and to determine the direction which each
of them, if acting alone, would impress upon society, as well as, in a gener-
al way at least, to pronounce that some of these tendencies are more pow-
erful than others.
But, without dissembling the necessary imperfections of the a priori
method when applied to such a subject, neither ought' we, on the other
hand, to exaggerate them. The same objections which apply to the Meth-
od of Deduction in this its most difficult employment, apply to it, as we
formerly showed,* in its easiest; and would even there have been insuper-
able, if there had not existed, as was then fully explained, an appropriate
remedy. This remedy consists in the process which, under the name of
Verification, we have characterized as the third essential constituent part
of the Deductive Method ; that of collating the conclusions of the ratioci-
nation either with the concrete phenomerfS themselves, or, when such are
obtainable, with their empirical laws. The ground of confidence in any
concrete deductive science is not the a priori reasoning itself, but the ac-
cordance between its results and those of observation a posteriori. Either
of these processes, apart. from the other, diminishes in value as the subject
increases in complication, and this is in so rapid a ratio as soon to become
entirely worthless; but the reliance to be placed in the concurrence of the
two sorts of evidence, not only does not diminish in any thing like the
same proportion, but is not necessarily much diminished at all. Nothing
more results than a disturbance in the order of precedency of the two
processes, sometimes amounting to its actual inversion : insomuch that in-
stead of deducing our conclusions by reasoning, and verifying them by ob-
servation, we in some cases begin by obtaining them provisionally from,
specific experience, and afterward connect them with the principles of hu-
man nature by a priori reasonings, which reasonings are thus a real Verifi-
cation.
The only thinker who, with a competent knowledge of scientific methods
' Supra, p. 321.
PHYSICAL METHOD. 621
in general, has attempted to characterize the Method of Sociology, M.
•Comte, considers this inverse order as inseparably inherent in the nature of
sociological speculation. He looks upon the social science as essentially
consisting of generalizations from history, verified, not originally suggest-
ed, by deduction from the laws of human nature. Though there is a truth
contained in this opinion, of which I shall presently endeavor to show the
importance, I can not but think that this truth is enunciated in too unlim-
ited a manner, and that there is considerable scope in sociological inquiry
for the direct, as well as for the inverse, Deductive Method.
It will, in fact, be shown in the next chapter, that there is a kind of soci-
ological inquiries to which, from their prodigious complication, the method
of direct deduction is altogether inapplicable, while by a happy compensa-
tion it is precisely in these cases that we are able to obtain the best empir-
ical laws : to these inquiries, therefore, the Inverse Method is exclusively
adapted. But there are also, as will presently appear, other cases in which
it is impossible to obtain from direct observation any thing worthy the
name of an empirical law ; and it fortunately happens that these are the
very cases in which the Direct Method is least affected by the objection
which undoubtedly must always affect it in a certain degree.
We shall begin, then, by looking at the Social Science as a science of di-
rect Deduction, and considering what can be accomplished in it, and under
what limitations, by that mode of investigation. We shall, then, in a sep-
arate chapter, examine and endeavor to characterize the inverse process.
§ 2. It is evident, in the first place, that Sociology, considered as a sys-
tem of deductions a priori, can not be a science of positive predictions,
but only of tendencies. We may be able to conclude, from the laws of hu-
man nature applied to the circumstances of a given state of society, that a
particular cause will operate in a certain manner unless counteracted ; but
we can never be assui-ed to what extent or amount it will so operate, or
aflSrm with certainty that it will not be counteracted ; because we can sel-
dom know, even approximately, all the agencies which may co-exist with it,
and still less calculate the collective result of so many combined elements.
The remark, however, must here be once more repeated, that knowledge
insufficient for prediction may Jjie most valuable for guidance. It is not
necessary for the wise conduct of the affairs of society, no more than of
any one's private concerns, that we should be able to foresee infallibly the
results of what we do. We must seek our objects by means which may
perhaps be defeated, and take precautions against dangers which possibly
may never be realized. The aim of practical politics is to surround any
given society with the greatest possible number of circumstances of which
the tendencies are beneficial, and to remove or counteract, as far as practi-
cable, those of which the tendencies are injurious. A knowledge of the
tendencies only, though without the power of accurately predicting their
conjunct result, gives us to a considerable extent this power.
It would, however, be an error to suppose that even with respect to tend-
encies we could arrive in this manner at any great number of proposi-
tions which will be true in all societies without exception. Such a suppo-
sition would be inconsistent with the eminently modifiable nature of the
social phenomena, and the multitude and variety of the circumstances by
which they are modified — circumstances never the same, or even nearly the
same, in two different societies, or in two different periods of the same
society. This would not be so serious an obstacle if, though the causes
622 tOGIC OF THE MORAL SCIENCES.
acting upon society in general are numerous, those which influence any one
feature of society were limited in number ; for we might then insulate any
particular social phenomenon, and investigate its laws without disturbance
from the rest. But the truth is the very opposite of this. Whatever af-
fects, in an appreciable degree, any one element of the social state, affects
through it all the other elements. The mode of production of all social
phenomena is one great case of Intermixture of Laws. We can never ei-
ther understand in theory or command in practice the condition of a so-
ciety in any one respect, without taking into consideration its condition ia
all other respects. There is no social phenomenon which is not more or
less influenced by every other part of the condition of the same society,
and therefore by every cause which is influencing any other of the contem-
poraneous social phenomena. There is, in short, what physiologists term
a consensus, similar to that existing among the various organs and func-
tions of the physical frame of man and the more perfect animals ; and con-
stituting one of the many analogies which have rendered universal such
expressions as the " body politic " and " body natural." It follows from
this consensus, that unless two societies could be alike in all the circum-
stances which surround and influence them (which would imply their be-
ing alike in their previous history), no portion whatever of the phenomena
will, unless by accident, precisely correspond ; no one cause will produce
exactly the same effects in both. Every cause, as its effect spreads through
society, comes somewhere in contact with different sets of agencies, and
^thus has its effects on some of the social phenomena differently modified;
and these differences, by their reaction, produce a difference even in those
of the effects which would otherwise have been the same. We can never,
therefore, affirm with certainty that a cause which has a particular tend-
ency in one people or in one age will have exactly the same tendency in
another, without referring back to our premises, and performing over again
for the second age or nation, that analysis of the whole of its influencing
circumstances which we had already performed for the first. The deduct-
ive science of society will not lay down a theorem, asserting in a univer-
sal manner the effect of any cause ; but will rather teach us how to frame
the proper theorem for the circumstances of any given case. It will not
give the laws of society in general, but tha means of determining the phe-
nomena of any given society from the particular elements or data of that
society.
All the general propositions which can be framed by the deductive sci-
ence, are therefore, in the strictest sense of the word, hypothetical. They
are grounded on some suppositious set of circumstances, and declare how
some given cause would operate in those circumstances, supposing that no
others were combined with thera. If the set of circumstances supposed
have been copied from those of any existing society, the conclusions will
be true of that society, provided, and in as far as, the effect of those cir-
cumstances shall not be modified by others which have not been taken into
the account. If we desire a nearer approach to concrete truth, we can only
aim at it by taking, or endeavoring to take, a greater number of individ-
ualizing circumstances into the computation.
Considering, however, in how accelerating a ratio the uncertainty of our
conclusions increases as we attempt to take the effect of a greater number
of concurrent causes into our calculations, the hypothetical combinations
of circumstances on which we construct the general theorems of the sci-
ence, can not be made very complex, without so rapidly accumulating a
PHYSICAL METHOD. 62a
liability to error as must soon deprive our conclusions of all value. This
mode of inquiry, considered as a means of obtaining general propositions,
must, therefore, on pain of frivolity, be limited to those classes of social
facts which, though influenced like the rest by all sociological agents, are
under the immecliate influence, principally at least, of a few only.
§ 3. Notwithstanding the universal consensus of the social phenomena
whereby nothing which takes place in any part of the operations of society
is without its share of influence on every other part; /and notwithstanding
the paramount ascendancy which the general state of civilization and social
progress in any given society must hence exei-cise over all the partial and
subordinate phenomena ; it is not the less true that different species of so-
cial facts are in the main dependent, immediately and in the first resort,
on different kinds of causes ; and therefore not only may with advantage,
but must, be studied apart: just as in the natural body we study separate-
ly the physiology and pathology of each of the principal organs and tis-
sues, though every one is acted upon by the state of all the others ; and
though the peculiar constitution and general state of health of the organ-
ism co-operates with, and often preponderates over, the local causes, in de-
termining the state of any particular organ.
On these considerations is grounded the existence of distinct and sep.
arate, though not independent, bi'anches or departments of sociological
speculation.
There is, for example, one large class of social phenomena in which the
immediately determining causes are principally those which act through
the desire of wealth, and in which the psychological law mainly concerned
is the familiar one, that a greater gain is preferred to a smaller. I mean,
of course, that portion of the phenomena of society which emanate from
the industrial, or productive, operations of mankind ; and from those of
their acts through which the distribution of the products of those indus-
trial operations takes place, in so far as not effected by force, or modified
by voluntary gift. . By reasoning from that one law of human nature, and
from the principal outward circumstances (whether universal or confined
to particular states of society) which operate upon the human mind through
that law, we may be enabled to explain and predict this portion of the phe-
nomena of society, so far as they depend on that class of circumstances-
only; overlooking the influence of any other of the circumstances of socie-
ty ; and therefore neither tracing back the circumstances which we do take
into account, to their possible origin in some other facts in the social state,
nor making allowance for the manner in which any of those other circum-
stances may interfere with, and counteract or modify, the effect of the
former. A department of science may thus be constructed, which has re-
ceived the name of Political Economy.
The motive which suggests the separation of this portion of the social
phenomena from the rest, and the creation of a distinct branch of science
relating to them is — that they do mainly depend, at least in the first resort,
on one class of circumstances only; and that even when other circum-
stances interfere, the ascertainment of the effect due to the one class of
circumstances alone, is a suificiently intricate and difficult business to make
it expedient to perform it once for all, and then allow for the effect of the
modifying circumstances; especially as certain fixed combinations of the
former are apt to recur often, in conjunction with ever-varying circum-
stances of the latter class.
624 LOGIC OF THE MORAL SCIENCES.
Political Economy, as I have said on another occasion, concerns itself
only with " such of the phenomena of the social state as take place in con-
sequence of the pursuit of wealth. It makes entire abstraction of every
other human passion or motive; except those which may be regarded as
perpetually antagonizing principles to the desire of wealth, namely, aversion
to labor, and desire of the present enjoyment of costly indulgences. These
it takes, to a certain extent, into its calculations, because these do not
merely, like our other desires, occasionally conflict with the pursuit of
wealth, but accompany it always as a drag or impediment, and are there-
fore inseparably mixed up in the consideration of it. Political Economy
considers mankind as occupied solely in acquiring and consuming wealth ;
and aims at showing what is the course of action into which mankind,
living in a state of society, would be impelled, if that motive, except in the
•degree in which it is checked by the two perpetual counter-motives above
adverted to, were absolute ruler of all their actions. Tinder the influ-
■ence of this desire, it shows mankind accumulating wealth, and employing
that wealth in the production of other wealth ; sanctioning by mutual
agreement the institution of property; establishing laws to prevent indi-
viduals from encroaching upon the pi'operty of others by force or fraud ;
adopting various contrivances for increasing the productiveness of their
labor; settling the division of the produce by agreement, under the influ-
ence of competition (competition itself being governed by certain laws,
which laws are therefore the ultimate regulators of the division of the
produce) ; and employing certain expedients (as money, credit, etc.) to
facilitate the distribution. All these operations, though many of them are
really the result of a plurality of motives, are considered by political econ-
omy as flowing solely from the desire of wealth. The science then pro-
ceeds to investigate the laws which govern these several operations, under
the supposition that man is a being who is determined, by the necessity
of his nature, to prefer a greater portion of wealth to a smaller, in all oases,
without any other exception than that constituted by the two counter-
motives already specified. Not that any political economist was ever so
absurd as to suppose that mankind are really thus constituted, but because
this is the mode in which science must necessarily proceed. When an
effect depends on a concurrence of causes, these causes must be studied
one at a time, and their laws separately investigated, if we wish, through
the causes, to obtain the power of either predicting or controlling the
effect ; since the law of the effect is compounded of the laws of all the
causes which determine it. The law of the centripetal and that of the
projectile force must have been known, before the motions of the earth
and planets could be explained, or many of them predicted. The same is
the case with the conduct of man in society. In order to judge how he
will act under the variety of desires and aversions which are concurrently
operating upon him, we must know how he would act under the exclusive
influence of each one in particular. There is, perhaps, no action of a man's
life in which he is neither under the immediate nor under the remote in-
fluence of any impulse but the mere desire of wealth. With respect to
those parts of human conduct of which wealth is not even the f)rincipal
object, to these political economy does not pretend that its conclusions are
applicable. But there are also certain departments of human affairs, in
which the acquisition of wealth is the main and acknowledged end. It is
only of these that political economy takes notice. The manner in which it
necessarily proceeds is that of treating the main and acknowledged end as
PHYSICAL METHOD. 625
if it were the sole end ; which, of all hypotheses equally simple, is the near-
«8t_to the truth. The political economist inquires, what are the actions
which would be produced by this desire, if within the departments in
question it were unimpeded by any other. In this way a nearer approx-
imation is obtained than would otherwise be practicable to the real order
of human affairs in those departments. This appi-oximation has then to
be corrected by making proper allowance for the effects of any impulses
of a different description, which can be shown to interfere with the result
in any particular case. Only in a few of the most striking cases (such as
the important one of the principle of population) are these corrections in-
terpolated into the expositions of political economy itself; the strictness
of puroly scientific arrangement being thereby somewhat departed from,
for the sake of practical utility. So far as it is known, or may be pre-
sumed, that the conduct of mankind in the pursuit of wealth is under the
collateral influence of any other of the properties of our nature than the
desire of obtaining the greatest quantity of wealth with the least labor
and self-denial, the conclusions of political economy will so far fail of being
applicable to the explanation or prediction of real events, until they are
modified by a correct allowance for the degree of influence exercised by
the other cause."*
Extensive and important practical guidance may be derived, in any given
state of society, from general propositions such as those above indicated ;
even though the modifying influence of the miscellaneous causes which the
theory does not take into account, as well as the effect of the general social
changes in progress, be provisionally overlooked. And though it has been
a very common error of political economists to draw conclusions from the
elements of one state of society, and apply them to other states in which
many of the elements are not the same, it is even then not difficult, by
tracing back the demonstrations, and introducing the new premises in
their proper places, to make the same general course of argument which
served for the one case, serve for the others too.
For example, it has been greatly the custom of English political econ-
omists to discuss the laws of the distribution of the produce of industry,
on a supposition which is scarcely realized anywhere out of England and
Scotland, namely, that the produce is " shared among three classes, altogeth-
■er distinct from one another, laborers, capitalists, and landlords ; and that
all these are free agents, permitted in law and in fact to set upon their la-
bor, their capital, and their land, whatever price they are able to get for it.
The conclusions of the science, being all adapted to a society thus consti-
tuted, require to be revised whenever they are applied to any other. They
are inapplicable where the only capitalists are the landlords, and the labor-
ers are their property, as in slave countries. They are inapplicable where
the almost universal landlord is the state, as in India. They are inappli-
cable where the argricultural laborer is generally the owner both of the land
itself and of the capital, as frequently in France, or of the capital only, as
in Ireland." But though it may often be very justly objected to the ex-
isting race of political economists " that they attempt to construct a per-
manent fabric out of transitory materials ; that they take for granted the
immutabiUty of arrangements of society, many of which are in their nature
fluctuating or progressive, and enunciate with as little qualification as if
they were universal and absolute truths, propositions which are perhaps
* Essays on some Unsettled Questions of Political Economy, pp. 137-140.
40
626 LOGIC OF THE MORAL SCIENCES.
applicable to no state of society except the pavticular one in which the
writer happened to live;" this does not take away the value of the proposi-
tions, considered with reference to the state of society from which they
were drawn. And even as applicable to other states of society, " it must
not be supposed that the science is so incomplete and unsatisfactory as this^
might seem to prove. Though many of its conclusions are only locally
true, its method of investigation is applicable universally ; and as whoever
has solved a certain number of algebraic equations, can without difficulty
solve all others of the same kind, so whoever knows the political economy
of England, or even of Yorkshire, knows that of all nations, actual or pos-
sible, provided he have good sense enough not to expect the same conclu-
sion to issue from varying premises." Whoever has mastered with the
degree of precision which is attainable the laws which, under free competi-
tion, determine the rent, profits, and wages, received by landlords, capital-
ists, and laborers, in a state of society in which the three classes are com-
pletely separate, will have no difficulty in determining the very different
laws which regulate the distribution of the produce among the classes in-
terested in it in any of the states of cultivation and landed property set
forth in the foregoing extract.*
§ 4. I would not here undertake to decide what Other hypothetical or
abstract sciences similar to Political Economy, may admit of being carved
out of the general body of the social science ; what other portions of the
social phenomena are in a sufficiently close and complete dependence, in the
first resort, on a peculiar class of causes, to make it convenient to create a
preliminary science of those causes ; postponing the consideration of the
causes which act through them, or in concurrence with them, to a later
period of the inquiry. There is, however, among these separate depart-
ments one which can not be passed over in silence, being of a more com-
prehensive and commanding character than any of the other branches into
which the social science may admit of being divided. Like them, it is di-
rectly conversant with the causes of only one class of social facts, but a class
which exercises, immediately or remotely, a paramount influence over the
test. I allude to what may be termed Political Ethology, or the theory of
the causes which determine the type of character belonging to a people or
to an age. Of all the subordinate branches of the social science, this is
the most completely in its infancy. The causes of national character are
scarcely at all understood, and the effect of institutions or social arrange-
ments upon the character of the people is generally that portion of their
effects which is least attended to, and least comprehended. Nor is this
wonderful, when we consider the infant state of the science of Ethology
itself, from whence the laws must be drawn, of which the truths of polit-
ical ethology can be but results and exemplifications.
Yet, to whoever well considers the matter, it must appear that the laws
of national (or collective) character are by far the most important class of
sociological laws. In the first place, the character which is formed by any
state of social circumstances is in itself the most interesting phenomenon
which that state of society can possibly present. Secondly, it is also a fact
which enters largely into the production of all the other phenomena. And
above all, the character, that is, the opinions, feelings, and habits, of the
people, though greatly the results of the state of society which precedes
* The quotations in this paragraph are from a paper written by the author, and published
in a periodical in 1834. > r
PHYSICAL METHOD. 627
them, are also greatly the causes of the state of society which follows them ;
and are the power by which all those of the circumstances of society which
are artificial, laws and customs for instance, are altogether moulded: cus-
toms evidently, laws no less really, either by the direct influence of public
sentiment upon the ruling powers, or by the effect which the state of na-
tional opinion and feeling has in determining the form of government and
shaping the character of the governors.
As might be expected, the most imperfect part of those branches' of social
inquiry which have been cultivated as separate sciences, is the theory of the
manner in which their conclusions are affected by ethological considerations.
The omission is no defect in them as abstract or hypothetical sciences, but
it vitiates them in their practical application as branches of a comprehen-
sive social science. In political economy, for instance, empirical laws of hu-
man nature are tacitly assumed by English thinkers, which are calculated
only for Great Britain and the United States. Among other things, an in-
tensity of competition is constantly supposed, which, as a general mercan-
tile fact, exists in no country in the world except those two. An English
political economist, like his countrymen in general, has seldom learned that
it is possible that men, in conducting the business of selling their goods
over a counter, should care more about their ease or their vanity than about
their pecuniary gain. Yet those who know the habits of the continent of
Europe are aware how apparently small a motive often outweighs the desire
of money getting, even in the operations which have money getting for their
direct object. The more highly the science of ethology is cultivated, and
the better the diversities of individual and national character are under-
stood, the smaller, probably, will the number of propositions become, which
it will be considered safe to build on as universal principles of human na<"
ture.
These considerations show that the process of dividing off the social
science into compartments, in order that each may be studied separately,
and its conclusions afterward corrected for practice by the modifications
supplied by the others, must be subject to at least one important limitation.
Those portions alone of the social phenomena can with advantage be made
the subjects, even provisionally, of distinct branches of science, into which
the diversities of character between different nations or different times en-
ter as influencing causes only in a secondary degree. Those phenomena,
on the contrary, with which the influences of the ethological state of the
people are mixed up at every step (so that the connection of effects and
causes can not be even rudely marked out without taking those influences
into consideration) could not with any advantage, nor without great disad-
vantage, be treated independently of political ethology, nor, therefore, of all
the circumstances by which the qualities of a people are influenced. For
this reason (as well as for others which will hereafter appear) there can be
no separate Science of Government ; that being the fact which, of all oth-
ers, is most mixed up, both as cause and effect, with the qualities of the par-
ticular people or of the particular age. All questions respecting the tend-
encies of forms of government must stand part of the general science of
society, not of any separate branch of it.
This general Science of Society, as distinguished from the separate de-
partments of the science (each of which asserts its conclusions only con-
ditionally, subject to the paramount control of the laws of the general sci-
ence) now remains to be characterized. And as will be shown presently,
nothing of a really scientific character is here possible, except by the invers.a
628 LOGIC OF THE MORAL SCIENCES.
deductive method. But before we quit the subject of those sociological
speculations which proceed by way of direct deduction, we must examine
in what relation they stand to that indispensable element in all deductive
sciences, Verification by Specific Experience — comparison between the con-
clusions of reasoning and the results of observation.
8 5. We have seen tha,t, in most deductive sciences, and among the rest
in Ethology itself, which is the immediate foundation of the Social Science,
a preliminary work of preparation is performed on the observed facts, to
fit them for being rapidly and accurately collated (sometimes even for
being collated at all) with the conclusions of theory. This preparatory
treatment consists in finding general propositions which express concisely
what is common to large classes of observed facts ; and these are called the
empirical laws of the phenomena. We have, therefore, to inquire, whether
any similar preparatory process can be performed on the facts of the social
science ; whether there are any empirical laws in history or statistics.
In statistics, it is evident that empirical laws may sometimes be traced ;
and the tracing them forms an important part of that system of indirect
observation on which we must often rely for the data of the Deductive
Science. The process of the science consists in inferring effects from their
causes ; but we have often no means of observing the causes, except through
the medium of their effects. In such cases the deductive science is unable
to predict the effects, for want of the necessary data; it can determine
what causes are capable of producing any given effect, but not with what
frequency and in what quantities those causes exist. An instance in point
is afforded by a newspaper now lying before me. A statement was fur-
nished by one of the official assignees in bankruptcy showing among the
various bankruptcies which it had been his duty to investigate, in how
many cases the losses had been caused by misconduct of different kinds,
and in how many by unavoidable misfortunes. The result was, that the
number of failures caused by misconduct greatly preponderated over those
arising from all other causes whatever. Nothing but specific experience
could have given sufficient ground for a conclusion to this purport. To
collect, therefore, such empii-ical laws (which are never more than approx-
imate generalizations) from direct observation, is an important part of the
process of sociological inquiry.
The experimental process is not here to be regarded as a distinct road to
the truth, but as a means (happening accidentally to be the only, or the best,
available) for obtaining the necessary data for the deductive science. When
the immediate causes of social facts are not open to direct observation, the
empirical law of the effects gives us the empirical law (which in that case
is all that we can obtain) of the causes likewise. But those immediate
causes depend on remote causes ; and the empirical law, obtained by this
indirect mode of observation, can only be relied on as applicable to unob-
served cases, so long as there is reason to think that no change has taken
place in any of the remote causes on which the immediate causes depend.
In making use, therefore, of even the best statistical generalizations for the
purpose of inferring (though it be only con jectur ally) that the same em-
pirical laws will hold in any new case, it is necessary that we be well ac-
quainted with the remoter causes, in order that we may avoid applying the
empirical law to cases which differ in any of the circumstances on which
the truth of the law ultimately depends. And thus, even where conclU"
sions derived from specific observation are available for practical infer-
PHYSICAL METHOD. 629
ences in new cases, it is necessary that the deductive science should stand
sentinel over the whole process ; that it should be constantly referred to,
and its sanction obtained to every inference.
The same thing holds true of all generalizations which can be grounded
on history. Not only there are such generalizations, but it will presently
be shown that the general science of society, which inquires into the laws
of succession and co-existence of the great facts constituting the state of
society and civilization at any time, can proceed in no other manner than
by making such generalizations — afterward to be confirmed by connecting
them with the psychological and ethological laws on which they must
really depend.
§ 6. But (reserving this question for its proper place) in those more special
inquiries which form the subject of the separate branches of the social sci-
ence, this twofold logical process and reciprocal verification is not possible ;
specific experience affords nothing amounting to empii-ical laws. This is
particularly the case where the object is to determine the effect of any one
social cause among a great number acting simultaneously ; the effect, for
example, of corn laws, or of a prohibitive commercial system generally.
Though it may be perfectly certain, from theory, what Jcind of effects corn
laws must produce, and in what general direction their influence must tell
upon industrial prosperity, their effect is yet of necessity so much dis-
guised by the similar or contrary effects of other influencing agents, that
specific experience can at most only show that on the average of some
great number of instances, the cases where there were corn laws exhibited
the effect in a greater degree than those where there were not. Now the
number of instances necessary to exhaust the whole round of combinations
of the various influential circumstances, and thus afford a fair average, nev-
er can be obtained. Not only we can never learn with sufficient authen-
ticity the facts of so many instances, but the world itself does not afford
them in sufficient numbers, within the limits of the given state of society
and civilization which such inquiries always presuppose. Having thus no
previous empirical generalizations with which to collate the conclusions of
theory, the only mode of direct verification which remains is to compare
those conclusions with the result of an individual experiment or instance.
But here the difficulty is equally great. For in order to verify a theory by
an experiment, the circumstances of the experiment must be exactly the
same with those contemplated in the theory. But in social phenomena the
circumstances of no two cases are exactly alike. A trial of corn laws in an-
other country, or in a former generation, would go a very little way toward
verifying a conclusion drawn respecting their effect in this generation and
in this country. It thus happens, in most cases, that the only individual
instance really fitted to verify the predictions of theory is the very instance
for which the predictions were made; and the verification comes too late
to be of any avail for practical guidance.
Although, however, direct verification is impossible, there is an indirect
verification, which is scarcely of less value, and which is always practica-
ble. The conclusion drawn'as to the individual case can only be directly
verified in that case; but it is verified indirectly, by the verification of other
conclusions, drawn in other individual cases from the same laws. The ex-
perience which comes too late to verify the particular proposition to_ which
it refers, is not too late to help toward verifying the general sufficiency
of the theory. The test of the degree in which the science affords safe
630 LOGIC OP THE MORAL SCIENCES.
ground for predicting (and consequently for practically dealing with) what
has not yet happened, is the degree in which it would have enabled us to
predict what has actually occurred. Befoi'e our theory of the influence of
a particular cause, in a given state of circumstances, can be entirely trust-
ed, we must be able to explain and account for the existing state of all
that portion of the social phenomena which that cause has a tendency to
influence. If, for instance, we would apply our speculations in political
economy to the prediction or guidance of the phenomena of any country,
we must be able to explain all the mercantile or industrial facts of a gen-
-eral character, appertaining to the present state of that country ; to point
out causes sufficient to account for all of them, and prove, or show good
ground for supposing, that these causes have really existed. If we can
not do this, it is a proof either that the facts which ought to be taken into
account are not yet completely known to us, or that although we know the
facts, we are not masters of a sufficiently perfect theory to enable us to
assign their consequences. In either case we are not, in the present state
of our knowledge, fully competent to draw conclusions, speculative or
practical, for that country. In like manner, if we would attempt to judge
of the effect which any political institution would have, supposing that it
could be introduced into any given country, we must be able to show that
the existing state of the practical government of that country, and of
whatever else depends thereon, together with the particular character and
tendencies of the people, and their state in respect to the various elements
of social well-being, are such as the institutions they have lived under, in
conjunction with the other circumstances of their nature or of their posi-
tion, were calculated to produce.
To prove, in short, that our science, and our knowledge of the particu-
lar case, render us competent to predict the future, we must show that
they would have enabled us to predict the present and the past. If there
be any thing which we could not have predicted, this constitutes a resid-
ual phenomenon, requiring further study for the purpose of explanation ;
and we must either search among the circumstances of the particular case
until we find one which, on the principles of our existing theory, accounts
for the unexplained phenomenon, or we must turn back, and seek the ex-
planation by an extension and improvement of the theoiy itself.
CHAPTER X.
OP THB lUTBRSE DEDUCTIVE, OE HISTORICAL, METHOD.
§ 1. There are two kinds of sociological inquiry. In the first kind, the
question proposed is, what effect will follow from a given cause, a certain
general condition of social circumstances being presupposed. As, for ex-
ample, what would be the effect of imposing or of repealing corn laws, of
abolishing monarchy or introducing universal suffrage, in the present con-
dition of society and civilization in any European country, or under any
other given supposition with regard to the circumstances of society in gen-
eral, without reference to the changes which might take place, or which
may already be in progress, in those circumstances. But there is also a
second inquiry, namely, what are the laws which determine those general
circumstances themselves. In this last the question is, not what will be
the effect of a given cause in a certain state of society, but what are the
HISTORICAL METHOD. 631
causes which produce, and the phenomena which characterize, states of
society generally. In the solution of this question consists the general
Science of Society ; by which the conclusions of the other and more spe-
cial kind of inquiry must be limited and controlled.
' § 2. In order to conceive correctly the scope of this general science, and
■distinguish it from the subordinate departments of sociological specula-
tion, it is necessary to fix the ideas attached to the phrase, "A State of So-
ciety." What is called a state of society, is the simultaneous state of all
.the greater social facts or phenomena. Such are : the degree of knowl-
edge, and of intellectual and moral culture, existing in the community, and
in every class of it ; the state of industry, of wealth and its distribution ;
the habitual occupations of the community ; their division into classes, and
the relations of those classes to one another; the common beliefs which
they entertain on all the subjects most important to mankind, and the de-
gree of assurance with which those beliefs are held ; their tastes, and the
^iharacter and degree of their aesthetic development; their form of govern-
ment, and the more important of their laws and customs. The condition of
all these things, and of many more which will readily suggest themselves,
•constitute the state of society, or the state of civilization, at any given time.
When states of society, and the causes which produce them, are spoken
■of as a subject of science, it is implied that there exists a natural correla^
tion among these different elements; that not eveiy variety of combina-
tion of these general social facts is possible, but only certain combinations ;
that, in short, there exist Uniformities of Co-existence between the states
oi the various social phenomena. And such is the truth; as is indeed a
necessary consequence of the influence exercised by every one of those
phenomena over every other. It is a fact implied -in the consensus of the
various parts of the social body.
States of society are like different constitutions or different ages in the
physical frame ; they are conditions not of one or a few organs or func-
tions, but of the wholfe organism. Accordingly, the information which we
•possess respecting past ages, and respecting the various states of society
flow existing in different regions of the earth, does, when duly analyzed,
•exhibit uniformities. It is found that when one of the features of society
da in a particular state, a state of many other features, more or less precise-
ly determinate, always or usually co-exists with it.
But the uniformities of co-existence obtaining among phenomena which
are effects of causes, must (as we have so often observed) be corollaries
from the laws of causation by which these phenomena are really deter-
mined. The mutual correlation between the different elements of each
■state of society, is, therefore, a derivative law, resulting from the laws
which regulate the succession between one state of society and another ;
for the proximate cause of every state of society is the state of society
immediately preceding it. The fundamental problem, therefore, of the
social science, is to find the laws according to which any state of society
produces the state which succeeds it and takes its place. This opens the
great and vexed question of the progi-essiveness of man and society; an
idea involved in every just conception of social phenomena as the subject
■of a science.
' § 8. It is one of the characters, not absolutely peculiar to the sciences
of human nature and society, but belonging to them in a peculiar degree,
632 LOGIC OF THE MORAL SCIENCES.
to be conversant with a subject-matter whose properties are changeable.
I do not mean changeable from day to day, but from age to age ; so that
not only the qualities of individuals vary, but those of the majority are
not the same in one age as in another.
The principal cause of this peculiarity is the extensive and constant re-
action of the effects upon their causes. The circumstances in which man-
kind are placed, operating according to their own laws and to the laws
of human nature, form the characters of the human beings ; but the human
beings, in their turn, mould and shape the circumstances for themselves
and for those who come after them. From this reciprocal action there,
must necessarily result either a cycle or a progress. In astronomy also,
every fact is. at once effect and cause; the successive positions of the vari-
ous heavenly bodies produce changes both in the direction and in the inten-
sity of the forces by which those positions are determined. But in the
case of the solar system, these mutual actions bring around again, after a
certain number of changes, the former state of circumstances ; which, of
course, leads to the perpetual recurrence of the same series in an unvarying
order. Those bodies, in short, revolve in orbits : but there are (or, con-
formably to the laws of astronomy, there might be) others which, instead of
an orbit, describe a trajectory — a course not returning into itself. One or
other of these must be the type to which human affairs must conform.
One of the thinkers who earliest conceived the succession of historical
events as subject to fixed laws, and endeavored to discover these laws by
an analytical survey of history, Vico, the celebrated author of the Scienza
N'uova, adopted the former of these opinions; He conceived the phenom-
ena of human society as revolving in an orbit ; as going through periodic-
ally the same series of changes. Though there were not wanting circum-
stances tending to give some plausibility to this view, it would not bear
a close scrutiny : and those who have succeeded Vico in this kind of spec-
ulations have universally adopted the idea of a trajectory or progress, in
lieu of an orbit or cycle.
The words Progress and Progressiveness are not here to be understood
as synonymous with improvement and tendency to improvement. It i»
conceivable that the laws of human nature might determine, and even ne-
cessitate, a certain series of changes in man and society, which might not
in every case, or which might not on the whole, be improvements. It is
my belief, indeed, that the general tendency is, and will continue to be,,
saving occasional and temporary exceptions, one of improvement ; a tend-
ency toward a better and happier state. This, however, is not a question
of the method of the social science, but a theorem of the science itself..
For our purpose it is sufficient that there is a progressive change both in
the character of the human race and in their outward circumstances, so far
as moulded by themselves ; that in each successive age the principal phe-
nomena of society are different from what they were in the age preceding,,
and still more different from any previous age: the periods which most
distinctly mark these successive changes being intervals of one generation,,
during which a new set of human beings have been educated, have grown
up from childhood, and taken possession of society.
The progressiveness of the human race is the foundation on which a ■
method of philosophizing in the social science has been of late years erect-
ed, far superior to either of the two modes which had previously been
prevalent, the chemical or experimental, and the geometrical modes. This
method, which is now generally adopted by the most advanced thinkers.
HISTORICAL METHOD.
633
on the Continent, consists in attempting, by a study and analysis of the
general facts of history, to discover (what these philosophers term) the law
of progress : which law, once ascertained, must according to them enable
us to predict future events, just as after a few terras of^an infinite series
in algebra we are able to detect the principle of regularity in their forma-
tion, and to pi-edict the rest of the series to any number of terms we please.
The principal aim of historical speculation in France, of late years, has
been to ascertain this law. But while I gladly acknowledge the great serv-
ices which have been rendered to historical knowledge by this school, I
oan not but deem them to be mostly chargeable with a fundamental mis-
conception of the true method of social philosophy. The misconception
consists in supposing that the order of succession which we may be able
to trace among the different states of society and civilization which history
presents to us, even if that order were more rigidly uniform than it has
yet been proved to be, could ever amount to a law of nature. It can only
be an empirical law. The succession of states of the human mind and of
human society can not have an independent law of its own ; it must de-
pend on the psychological and ethological laws which govern the action of
circumstances on men and of men on circumstances. It is conceivable
that those laws might be such, and the general circumstances of the human
race such, as to determine the successive transformations of man and society
to one given and unvarying order. But even if the case were so,"it can not
be the ultimate aim of science to discover an empirical law. Until that
law could be connected with the psychological and ethological laws on
which it must depend, and, by the consilience of deduction a priori with
historical evidence, could be converted from an empirical law into a scien-
tific one, it could not be relied on for the prediction of future events, be-
yond, at most, strictly adjacent cases. M. Comte alone, among the new
historical school, has seen the necessity of thus connecting all our generali-
zations from history with the laws of human nature.
§ 4. But, while it is an imperative rule never to introduce any generali-
zation from history into the social science unless sufficient grounds can
be pointed out for it in human nature, I do not think any one will contend
that it would have been possible, setting out from the principles of human
nature and from the general circumstances of the position of our species, to
determine a^nonthe order in which human development must take place,
and to predict, consequently, the general facts of history up to the pres-
ent time. After the first few terms of the series, the influence exercised
over each generation by the generations which preceded it, becomes (as is
well observed by the writer last referred to) more and more preponder-
ant over all other influences ; until at length what we now are and do, is in
a very small degree the result of the universal circumstances of the human
race, or even of our own circumstances acting through the original quali'
ties of our species, but mainly of the qualities produced in us by the whole
previous history of humanity. So long a series of actions and reactions
between Circumstances and Man, each successive term being composed of
an ever greater number and variety of parts, could not possibly be com-
puted by human faculties from the elementary laws which produce it. The
mere length of the series would be a sufficient obstacle, since a slight errbr
in any one of the terms would augment in rapid progression at every sub-
sequent step.
If, therefore, the series of the effects themselves did not, when examined
634 LOGIC OF THE MORAL SCIENCES.
as a whole, manifest any regularity, we should in, vain attempt to construct
a general science of society. We must in that case have contented our-
selves with that subordinate order of sociological speculation formerly no-
ticed, namely, with endeavoring to ascertain what would be the effect of
the introduction of any new cause, in a state of society supposed to be fix-
ed— a knowledge sufficient for the more common exigencies of daily polite
ical practice, but liable to fail in all cases in which the progressive move-
ment of society is one of the influencing elements; and therefore more
precarious in proportion as the case is more important. But since both the
natural varieties of mankind, and the original diversities of local circum-
stances, are much less considerable than the points of agreement, there will
naturally be a certain degree of uniformity in the progressive development
of the species and of its works. And this uniformity tends to become
greater, not less, as society advances ; since the evolution of each people,
which is at first determined exclusively by the nature and circumstances
of that people, is gradually brought under the influence (which becomes,
stronger as civilization advances) of the other nations of the earth, and of
the circumstances by which they have been influenced. History accord-/
ingly does, when judiciously examined, afford Empirical Laws of Society/
And the problem of general sociology is to -ascertain these, and connect
them with the laws of human nature, by deductions showing that such
were the derivative laws naturally to be expected as the consequences of
those ultimate ones.
It is, indeed, hardly ever possible, even after history has suggested the
derivative law, to demonstrate a priori that such was the only order of
succession or of co-existence in which the effects could, consistently with
the laws of human nature, have been produced. We can at most make out
that there were strong a priori reasons for expecting it, and that no other
order of succession or co-existence would have been so likely to result from
the nature of man and the general circumstances of his position. Often
we can not do even this ; we can not even show that what did take place
was probable a priori, but only that it was possible. This, however —
which, in the Inverse Deductive Method that we are now characterizing, is
a real process of verification — is as indispensable, as vei'ification by specific
experience has been shown to be, where the conclusion is originally obtain-
ed by the direct way of deduction. The empirical laws must be the result
of but a few instances, since few nations have ever attained at all, and still
fewer by their own independent development, a high stage of social prog-
ress. If, therefore, even one or two of these few instances be insufficientry
known, or imperfectly analyzed into their elements, and therefore not ade-
quately compared with other instances, nothing is more probable than that
a wrong empirical law will emerge instead of the right one. Accordingly,
the most erroneous generalizations are continually made from the course of
history ; not only in this country, where history can not yet be said to be
at all cultivated as a science, but in other countries where it is so culti-
vated, and by persons well versed in it. The only check or corrective is,
constant verification by psychological and ethological laws. We may add
to this, that no one but a person competently skilled in those laws is
capable of preparing the materials for historical generalization, by analyz-
ing the facts of history, or even by observing the social phenomena of his
own time. No other will be aware of the comparative importance of dif-
ferent facts, nor consequently know what facts to look for, or to observe^
still less will he be capable of estimating the evidence of facts which, as is
HISTORICAL METHOD. 635
the case with most, can not be ascertained by direct observation or learned
from testimony, but must be inferred from marks.
§ 5. The Empirical Laws of Society are of two kinds ; some are uni
formities of co-existence, some of succession. According as the science is
occupied in ascertaining and verifying the former sort of uniformities or
the latter, M. Comte gives it the title of Social Statics, or of Social Dy-
namics ; conformably to the distinction in mechanics between the condi-
tions of equilibrium and those of movement; or in biology, between the
laws of organization and those of life. The first branch of the science as-
certains the conditions of stability in the social union ; the second, the laws
of progress. Social Dynamics is the theory of Society considered in a
state of progressive movement; while Social Statics is the theory of the
consensus already spoken of as existing among the different parts of the
social organism ; in other words, the theory of the mutual actions and re-
actions of contemporaneous social phenomena; "making* provisionally, as
far as possible, abstraction, for scientific pui-poses, of the fundamental move-
ment which is at all times gradually modifying the whole of them.
" In this first point of view, the provisions of sociology will enable us to
infer one from another (subject to ulterior verification by direct observa-
tion) the various characteristic marks of each distinct mode of social ex-
istence, in a manner essentially analogous to what is now habitually prac-
ticed in the anatoniy of the physical body. This preliminary aspect, there-
fore, of political science, of necessity supposes that (contrary to the exist-
ing habits of philosophers) each of the numerous elements of the social
state, ceasing to be looked at independently and absolutely, shall be al-
ways and exclusively considered relatively to all the other elements, with
the whole of which it is united by mutual interdependence. It would be
superfluous to insist here upon the great and constant utility of this branch
of sociological speculation. It is, in the first place, the indispensable basis
of the theory of social progress. It may, moreover, be employed, immedi-
ately, and of itself, to supply the place, provisionally at least, of direct ob-
servation, which in many cases is not always practicable for some of the
elements of society, the real condition of which may, however, be sufficient-
ly judged of by means of the relations which connect them with others
previously known. The history of the sciences may give us some notion
of the habitual importance of this auxiliary resource, by reminding us, for
example, how the vulgar errors of mere erudition concerning the pretend-
ed acquirements of the ancient Egyptians in the higher astronomy were
irrevocably dissipated (even before sentence had been passed on them by
a sounder erudition) from the single consideration of the inevitable con-
nection between the general state of astronomy and that of abstract ge-
ometry, then evidently in its infancy. It would be easy to cite a multi-
tude of analogous cases, the character of which could admit of no dispute.
In order to avoid exaggeration, however, it should be remarked, that these
necessary relations among the diffei-ent aspects of society can not, from
their veiy nature, be so simple and precise that the results observed could
only have arisen from some one mode of mutual co-ordination. Such a
notion, already too narrow in the science of life, would be completely at
variance with the still more complex nature of sociological speculations.
But the exact estimation of these limits of variation, both in the healthy
* Caurs de Philosophie Positive, iv., 325-29.
636 ' LOGIC OF THE MORAL SCIENCES.
and in the morbid state, constitutes, at least as much as in the anatomy of
the natural body, an indispensable complement to every theory of Socio-
logical Statics; without which the indirect exploration above spoken of
would often lead into error.
"This is not the place for methodically demonstrating the existence of
a necessary relation among all the possible aspects of the same social or-
ganism ; a point on which, in principle at least, there is now little difference
of opinion among sound thinkers. From whichever of the social elements
we choose to set out, we may easily recognize that it has always a connec-
tion, more or less immediate, with all the other elements, even with those
which at first sight appear the most independent of it. The dynamic-
al consideration of the progressive development of civilized humanity, af-
fords, no doubt, a still more efficacious means of effecting this interesting
verification of the consensus of the social phenomena, by displaying the
manner in which every change in any one part, opel'ates immediately, or
very speedily, upon all the rest. But this indication may be preceded, or
at all events followed, by a confirmation of a purely statical kind ; for, in
politics as in mechanics, the communication of motion from one object to
another proves a connection between them. Without descending to the
minute interdependence of the different branches of any one science or
art, is it not evident that among the different sciences, as well as among
most of the arts, there exists such a connection, that if the state of any one
well-marked division of them is sufficiently known to us, we can with real
scientific assurance infer, from their necessary correlation, the contempo-
raneous state of every one of the others ? By a further extension of this
consideration, we may conceive the necessary relation which exists be-
tween the condition of the sciences in general and that of the arts in gen-
eral, except that the mutual dependence is less intense in proportion as it
is more indirect. The same is the case, when, instead of considering the
aggregate of the social phenomena in some one people, we examine it si-
multaneously in different contemporaneous nations; between which the
perpetual reciprocity of influence, especially in modern times, can not be
contested, though the consensus must in this case be ordinarily of a less
decided character, and must decrease gradually with the affinity of the
cases and the multiplicity of the points of contact, so as at last, in some
cases, to disappear almost entirely ; as for, example, between Western Eu-
rope and Eastern Asia, of which the various general states of society ap-
pear to have been hitherto almost independent of one another.
These remarks are followed by illustrations of one of the most impor-
tant, and until lately, most neglected, of the general principles which, in
this division of the social science, may be considered as established ; name-
ly, the necessary correlation between the form of government existing in
any society and the contemporaneous state of civilization : a natural law
which stamps the endless discussions and innumerable theories respecting
forms of government in the abstract, as fruitless and worthless, for any
other purpose than as a preparatory treatment of materials to be after-
ward used for the construction of a better philosophy.
As already reniarked, one of the main results of the science of social
statics would be to ascertain the requisites of stable political union. There
are some circumstances which, being found in all societies without excep-
tion, and in the greatest degree where the social union is most complete,
may be considered (when psychological and ethological laws confirm the
indication) as conditions of the existence of the complex phenomena called
HISTORICAL METHOD. 637
a State. For example, no numerous society has ever been held together
without laws, or usages equivalent to them ; without tribunals, and an or-
ganized force of some sort to execute their decisions. There have always
been public authorities whom, with more or less strictness and in cases
more or less accurately defined, the rest of the community obeyed, or ac-
cording to general opinion were bound to obey. By following out this
course of inquiry we shall find a number of requisites, which have been
present in every society that has maintained a collective existence, and on
the cessation of which it has either merged in some other society, or re-
constructed itself on some new basis, in which the conditions were con-
formed to. Although these results, obtained by comparing different forms
and states of society, amount in themselves only to empirical laws ; some
of them, when once suggested, are found to follow with so much proba-
bility from general laws of human nature, that the consilience of the two
processes raises the evidence to proof, and the generalizations to the rank
of scientific truths.
This seems to be affirmable (for instance) of the conclusions arrived at
in the following passage, extracted, with some alterations, from a criticism
on the negative philosophy of the eighteenth century,* and which I quote,
though (as in some former instances) from myself, because I have no bet-
ter way of illustrating the conception I have formed of the kind of theo-
rems of which sociological statics would consist.
"The very first element of the social union, obedience to a government
of some sort, has not been found so easy a thing to establish in the world.
Among a timid and spiritless race like the inhabitants of the vast plains of
tropical countries, passive obedience may be of natural growth ; though
even there we doubt whether it has ever been found among any people with
whom fatalism, or in other words, submission to the pressure of circum-
stances as a divine decree, did not prevail as a religious doctrine. But the
difficulty of inducing a brave and warlike race to submit their individual
arhitrium to any common umpire, has always been felt to be so great, that
nothing short of supernatural power has been deemed adequate to over-
come it; and such tribes have always assigned to the first institution of
civil society a divine origin. So differently did those judge who knew
savage men by actual experience, from those who had no acquaintance
with them except in the civilized state. In modern Europe itself, after the
fall of the Roman empire, to subdue the feudal anarchy and bring the
whole people of any European nation into subjection to government
(though Christianity in the most concentrated form of its influence was
co-operating in the work) required thrice as many centuries as have elapsed
Bmce that time.
"Now if these philosophers had known human nature under any other
type than that of their own age, and of the particular classes of society
among whom they lived, it would have occurred to them, that wherever
this habitual submission to law and government has been firmly and du-
rably established, and yet the vigor and manliness of character which re-
sisted its establishment have been in any degree preserved, certain requi-
sites have existed, certain conditions have been fulfilled, of which the fol-
lowing may be regarded as the principal.
" First : there has existed, for all who were accounted citizens — foi
,all who were not slaves, kept dowji by brute force — a system of education,
* Since reprinted entire in Dissertations and Discussions, as the concluding paper of the first
volume.
638 LOGIC OF THE MORAL SCIENCES.
beginning with infancy and continued through life, of which whatever else
it might include, one main and incessant ingredient was restraining disci-
pline. To train the human being in the habit, and thence the power, of
subordinating his personal impulses and aims to what were considered the
ends of society ; of adhering, against all temptation, to the course of con-
duct which those ends prescribed ; of controlling in himself all feelings
which were liable to militate against those ends, and encouraging all such
as tended toward them ; this was the purpose, to which every outward
motive that the authority directing the system could command, and every
inward power or principle which its knowledge of human nature enabled
it to evoke, were endeavored to be rendered instrumental. The entire civ-
il and military policy of the ancient commonwealths was such a system,
of training ; in modern nations its place has been attempted to be supplied,
principally, by religious teaching. And whenever and in proportion as the
strictness of the restraining discipline was relaxed, the natural tendency
of mankind to anarchy re-asserted itself; the state became disorganized
from within; mutual conflict for selfish ends, neutralized the energies
which were required to keep up the contest against natural causes of evil ;
and the nation, after a longer or briefer interval of progressive decline, be-
came either the slave of a despotism, or the prey of a foreign invader.
" The second condition of permanent political society has been found to
be, the existence, in some form or other, of the feeling of allegiance or loy-
alty. This feeling may vary in its objects, and is not confined to any par-
ticular form of government; but whether in a democracy or in a mon-
archy, its essence is always the same ; viz., that there be in the constitution
of the state something which is settled, something permanent, and not to
be called in question ; something which, by general agreement, has a right
to be where it is, and to be secure against disturbance, whatever else may
change. This feeling may attach itself, as among the Jews (and in most
of the commonwealths of antiquity), to a common God or gods, the pro-
tectors and guardians of their state. Or it may attach itself to certain per-
sons, who are deemed to be, whether by divine appointment, by long pre-
scription, or by the general recognition of their superior capacity and
worthiness, the rightful guides and guardians of the rest. Or it may con-
nect itself with laws; with ancient liberties or ordinances. Or, finally,
(and this is the only shape in which the feeling is likely to exist hereafter),
it may attach itself to the principles of individual freedom and political and
social equality, as I'ealized in institutions which as yet exist nowhere, or ex-
ist only in a rudimentary state. But in all political societies which have
had a durable existence, there has been some fixed point : something which
people agreed in holding sacred; which, wherever freedom of discussion
was a recognized principle, it was of course lawful to contest in theory, but
which no one could either fear or hope to see shaken in practice; which, in
short (except perhaps during some temporally crisis), was in the common
estimation placed beyond discussion. And the necessity of this may easily
be made evident. A state never is, nor until mankind are vastly improved,
can hope to be, for any long time exempt from internal dissension ; for
there neither is nor has ever been any state of society in which collisions
did not occur between the immediate interests and passions of powerful
sections of the people. "What, then, enables nations to weather these
storms, and pass through turbulent times without any permanent weaken-
ing of the securities for peaceable existence? Precisely this — that how-
ever important the interests about which men fell out, the conflict did not
HISTORICAL METHOD. 639
affect the fundamental principle of the system of social union which hap-
pened to exist; nor threaten large portions of the community with the
subversion of that on which they had built their calculations, and with
which their hopes and aims had become identified. But when the ques-
tioning of these fundamental principles is (not the occasional disease, or
salutary medicine, but) the habitual condition of the body politic, and when
all the violent animosities are called forth, which spring naturally from such
a situation, the state is virtually in a position of civil war ; and can never
long remain free from it in act and fact.
" The third essential condition of stability in political society, is a strong
and active principle of cohesion among the members of the same commu-
nity or state. We need scarcely say that we do not mean nationality, in
the vulgar sense of the term ; a senseless antipathy to foreigners ; indiffer-
ence to the general welfare of the human race, or an unjust preference of
the supposed interests of our own country ; a cherishing of bad pecuUari-
ties because they are national, or a refusal to adopt what has been found
good by other countries. "We mean a principle of sympathy, not of hostil-
ity; of union, not of separation. We mean a feeling of common interest
among those who live under the same government, and are contained with-
in the same natural or historical boundaries. We mean, that one part of
the community do not consider themselves as foreigners with regard to an-
other part; that they set a value on their connection — ^feel that they are
one people, that their lot is cast together, that evil to any of their fellow-
countrymen is evil to themselves, and do not desire selfishly to free them-
selves from their share of any common inconvenience by severing the con-
nection. How strong this feeUng was in those ancient commonwealths
■which attained any durable greatness, every one knows. How happily
Home, in spite of all her tyranny, succeeded in establishing the feeling of a
common country among the provinces of her vast and divided empire, will
appear when any one who has given due attention to the subject shall take
the trouble to point it out. In modern times the countries which have had
that feeling in the strongest degree have been the most powerful countries :
England, France, and, in proportion to their territory and resources, Hol-
land and Switzerland ; while England in her connection with Ireland is one
of the most signal examples of the consequences of its absence. Every
Italian knows why Italy is under a foreign yoke; every German knows
what maintains despotism in the Austrian empire ;* the evils of Spain flow
as much from the absence of nationality among the Spaniards themselves,
as from the presence of it in their relations with foreigners : while the com-
pletest illustration of all is afforded by the republics of South America,
where the pai-ts of one and the same state adhere so slightly together, that
no sooner does any province think itself aggrieved by the general govern-
ment than it proclaims itself a separate nation."
§ 6. While the derivative laws of social statics are ascertained by an-
alyzing different states of society, and comparing them with one another,
without regard to the order of their succession, the consideration of the
successive order is, on the contrary, predominant in the study of social
dynamics, of which the aim is to observe and explain the sequences of so-
cial conditions. This branch of the social science would be as complete aa
it can be made, if every one of the leading general circumstances of each
* Written and first published in 1840.
generation were traced to its causes in the generation immediately preced-
ing. But the consensus is so complete (especially in modern history), that
in the filiation of one generation and another, it is the whole which pro-
duces the whole, rather than any part a part. Little progress, therefore,
can be made in establishing the filiation, directly "from laws of human na-
ture, without having first ascertained the immediate or derivative laws ac-
cording to which social states generate one another as society advances j
the axiomata media of General Sociology.
The empirical laws which are most readily obtained by generalization
from history do not amount to this. They are not the " middle princi-
ples " themselves, but only evidence toward the establishment of such prin-
ciples. They consist of certain general tendencies which may be perceived
in society ; a progressive increase of some social elements, and diminution
of others, or a gradual change in the general character of certain elements.
It is easily seen, for instance, that as society advances, mental tend more
and more to prevail over bodily qualities, and masses over individuals;
that the occupation of all that portion of mankind who are not under ex-
ternal restraint is at first chiefly military, but society becomes progressive-
ly more and more engrossed with productive pursuits, and the military
spirit gradually gives way to the industrial ; to which many similar truths
might be added. And with generalizations of this description, ordinary
inquirers, even of the historical school now predominant on the Continent,
are satisfied. But these and all such results are still at too great a dis-
tance from the elementary laws of human nature on which they depend —
too many links intervene, and the concurrence of causes at each link is far
too complicated^ to enable these propositions to be .presented as direct
corollaries from those elementary principles. They have, therefore, in the
minds of most inquirers, remained in the state of empirical laws, applica-
ble only within the bounds of actual observation; without any means of
determining their real limits, and of judging whether the changes which
have hitherto been in progress are destined to continue indefinitely, or to
terminate, or even to be reversed.
§ 1. In order to obtain better empirical laws, we must not rest satisfied
with noting the progressive changes which manifest themselves in the sep-
arate elements of society, and in which nothing is indicated but the rela-
tion of fragments of the effect to corresponding fragments of the cause..
It is necessary to combine the statical view of social phenomena with
the dynamical, considering not only the progressive changes of the differ-
ent elements, but the contemporaneous condition of each ; and thus obtain
empirically the law of correspondence not only between the simultaneous
states, but between the simultaneous changes, of those elements. This
law of correspondence it is, which, duly verified a priori, would become
the real scientific derivative law of the development of humanity and hu-
man afEairs.
In the difficult process of observation and comparison which is here re-
quired, it would evidently be a great assistance if it should happen to be
the fact, that some one element in the complex existence of social man is
pre-eminent over all others as the prime agent of the social movement.
For we could then take the progress of that one element as the central
chain, to each successive link of which, the corresponding links of all the
other progressions being appended, the succession of the facts would by
this alone be presented in a kind of spontaneous order, far more nearly ap*
HISTORICAL METHOD. g4j
proaching to the real order of their filiation than could be obtained by any
other merely empirical process.
Now, the evidence of history and that of human nature combine, by a
striking instance of consilience, to show that there really is one social ele-
ment which is thus predominant, and almost paramount, among the agents
of the social progression. This is, the state of the speculative faculties of
mankind; including the nature of the beliefs which by any means they
have arrived at, concerning themselves and the world by which they are
surrounded.
It would be a great error, and one very little likely to be committed, to
assert that speculation, intellectual activity, the pursuit of truth, is among
the more powerful propensities of human nature, or holds a predominating
place in the lives of any, save" decidedly exceptional, individuals. But, not-
withstanding the relative weakness of this principle among other sociolog-
ical agents, its influence is the main determining cause of the social prog-
ress; all the other dispositions of our nature which contribute to that
progress being dependent on it for the means of accomplishing their share
of the work. Thus (to take the most obvious case first), the impelling
force to most of the improvements effected in the arts of life, is the desire
of increased material comfort ; but as we can only act upon external ob-
jects in proportion to our knowledge of them, the state of knowledge at
any time is the limit of the industi ial improvements possible at that time ;
and the progress of industry must follow, and depend on, the progress of
knowledge. The same thing may be shown to be true, though it is not
quite so obvious, of the progress of the fine arts. Further, as the strong-
est propensities of uncultivated or half-cultivated human nature (being the
purely selfish ones, and those of a sympathetic character which partake
most of the nature of selfishness) evidently tend in themselves to disunite
mankind, not to unite them — to make them rivals, not confederates, so-
cial existence is only possible by a disciplining of those more powerful
propensities, which consists in subordinating them to a common system of
opinions. The degree of this subordination is the measure of the com-
pleteness of the social union, and the nature of the common opinions de-
termines its kind. But in order that mankind should conform their ac-
tions to any set of opinions, these opinions must exist, must be believed
by them. And thus, the state of the speculative faculties, the character of
the propositions assented to by the intellect, essentially determines the
moral and political state of the community, as we have already seen that
it determines the physical.
These conclusions, deduced from the laws of human nature, are in entire
accordance with the general facts of history. Every considerable change
historically known to us in the condition of any portion of mankind, when
not brought about by external force, has been preceded by a change, of
proportional extent, in the state of their knowledge, or in their prevalent
beliefs. As between any given state of speculation, and the correlative
state of every thing else, it was almost always the former which first show-
ed itself; though the effects, no doubt, reacted potently upon the cause.
Every considerable advance in material civilization has been preceded by
an advance in knowledge: and when any great social change has come to
pass, either in the way of gradual development or of sudden conflict, it has
had for its precursor a great change in the opinions and modes of thinking
of society. Polytheism, Judaism, Christianity, Protestantism, the critical
philosophy of modern Europe, and its positive science — each of these has
41
«42 LOGIC OF THE MORAL SCIENCES.
been a primaiy agent in making society what it was at each successive pe-
riod, while society was but secondarily instrumental in making^hem, each
of them (so far as causes can be assigned for its existence) being mainly
an emanation not from the practical life of the period, but from the pre-
vious state of belief and thought. The weakness of the speculative pro-
pensity in mankind generally has not, therefore, prevented the progress of
speculation from governing that of society at large ; it has only, and too
often, pi-evented progress altogether, where the intellectual progression has
<5ome to an early stand for want of sufficiently favorable circumstances.
From this accumulated evidence, we are justified in concluding, that the
order of human progression in all respects will mainly depend on the or-
der of progression in the intellectual convictions of mankind, that is, on the
law of the successive transformations of human opinions. The question
remains, whether this law can be determined; at first from history as an
empirical law, then converted into a scientific thearem by deducing it a
priori from the principles of human nature. As the progress of knowl-
edge and the changes in the opinions of mankind are very slow, and mani-
fest themselves in a well-defined manner only at long intervals, it can not
be expected that the general order of sequence should be discoverable from
the examination of less than a very considerable part of the duration of the
social progress. It is necessary to take into consideration the whole of
past time, from the first recorded condition of the human race, to the mem-
orable phenomena of the last and present generations.
§ 8. The investigation which I have thus endeavored to characterize,
has been systematically attempted, up to the present time, by M. Comte
alone. His work is hitherto the only known example of the study of social
phenomena according to this conception of the Historical Method. With-
out discussing here the worth of his conclusions, and especially of his pre-
dictions and recommendations with respect to the Future of society, which
appear to me greatly inferior in value to his appreciation of the Past, I
shall confine myself to mentioning one important generalization, which
M. Comte regards as the fundamental law of the progress of human knowl-
edge. Speculation he conceives to have, on every subject of human in-
quiry, three successive stages ; in the first of which it tends to explain the
phenomena by supernatural agencies, in the second by metaphysical ab-
stractions, and in the third or final state confines itself to ascertaining their
laws of succession and similitude. This generalization appears to me to
have that high degree of scientific evidence which is derived from the eon-
currence of the indications of history with the probabilities derived from
the constitution of the human mind. Nor could it be easily conceived,
irom the mere enunciation of such a proposition, what a flood of light it
lets in upon the whole course of history, when its consequences are traced,
by connecting with each of the three states of human intellect which it dis-
tinguishes, and with each successive modification of those three states, the
correlative condition of other social phenomena.*
* This great generalization is often unfavorably criticised (as by Dr.Whewell, for instance)
Tinder a misapprehension of its real innport. The doctrine, that the theological explanation
of phenomena belongs only to the infancy of our knowledge of them, ought not to be con-
strued as if it was equivalent to the assertion, that mankind, as their knowledge advances,
will necessarily cease to believe in any kind of theology. This was M. Comte's opinion ; but
it is by no means implied in his fundamental theorem. All that is implied is, that in an ad-
vanced state of human knowledge, no other Ruler of the World will be acknowledged than
one who rules by universal laws, and does not at all, or does not unless in very peculiar cases,
HISTORICAL METHOD. 643
But whatever decision competent judges may pronounce on the results
arrived at by any individual inquirer, the method now characterized is that
by which the derivative laws of social order and of social progress must
be sought. By its aid we may hereafter succeed not only in looking far
forward into the future history of the human race, but in determining what
artificial means may be used, and to what extent, to accelerate the natural
progress in so far as it is beneficial; to compensate for whatever may be
its inherent inconveniences or disadvantages ; and to guard against" the
•dangers or accidents to which our species is exposed from the necessary
incidents of its progression. Such practical instructions, founded on the
-highest branch of speculative sociology, will form the noblest and most
beneficial portion of the Political Art.
That of this science and art even the foundations are but beginning to
be laid, is sufficiently evident. But the superior minds are fairly turning
themselves toward that object. It has become the aim of really scientific
thinkers to connect by theories the facts of universal history : it is acknowl-
edged to be one of the requisites of a general system of social doctrine,
that it should explain, so far as the data exist, the main facts of history ;
and a Philosophy of History is generally admitted to be at once the verifi-
cation, and the initial form, of the Philosophy of the Progress of Society.
If the endeavors now making in all the more cultivated nations, and be-
ginning to be made even in England (usually the last to enter into the gen-
eral movement of the European mind) for the construction of a Philosophy
of History, shall be directed and controlled by those views of the nature of
sociological evidence which I have (very briefly and imperfectly) attempt-
ed to characterize ; they can not fail to give birth to a sociological system
widely removed from the vague and conjectural character of all former at-
tempts, and worthy to take its place, at last, among the sciences. When
this time shall come, no important branch of human affairs will be any
longer abandoned to empiricism and unscientific surmise : the circle of hu-
man knowledge will be complete, and it can only thereafter receive further
enlargement by perpetual expansion from within.
produce events by special intei-positions. Originally all natural events were ascribed to such
interpositions. At present every educated person rejects this explanation in regard to all
classes of phenomena of which the laws have been fully ascertained ; though some have not
yet reached the point of referring all phenomena to the idea of Law, but believe that rain and
sunshine, famine and pestilence, victory and defeat, death and life, are issues which the Cre-
ator does not leave to the operation of his general laws, but reserves to be decided by express
acts of volition. M. Comte's theory is the negation of this doctrine.
Dr. Whewell equally misunderstands M. Comte's doctrine respecting the second or meta.
physical stage of speculation. M. Comte did not mean that "discussions concerning ideas"
are limited to an early stage of inquiry, and cease when science enters into the positive stage.
(Philosophy of Discovery, pp. 226 et seq.) In all M. Comte's speculations as much stress is
laid on the process of clearing up our conceptions as on the ascertainment of facts. When
M. Comte speaks of the metaphysical stage of speculation, he means the stage in which men
speak of "Nature" and other abstractions as if they were ttctive forces, producing effects,-
when Nature is said to do this, or forbid that ; when Nature's horror of a vacuum. Nature's
non-admission of a break, Nature's vis medicatrix, were offered as explanations of phenome-
na ; when the qualities of things were mistaken for real entities dwelling in the things ; when
the phenomena of living bodies were thought to be accounted for by being referred to a " vi-
tal force;" when, in short, the abstract names of phenomena were mistaken for the causes of
their existence. In this sense of the word it can not be reasonably denied that the meta-
physical explanation of phenomena, equally with the theological, gives way before the ad-
vance of real science.
That the final, or positive stage, as conceived by M. Comte, has been equally misunderstood,
and that, notwithstanding some expressions open to just criticism, M. Comte never dreamed
of denying the legitimacy of inqniiy into all causes which are accessible to human investiga-
tion, I have pointed out in a former place.
644 LOGIC OF THE MORAL SCIENCES.
CHAPTER XI.
ADDITIONAL ELUCIDATIONS OF THE SCIENCE OF HISTOBT.
§ 1. The doctrine which the preceding chapters were intended to enforce
and elucidate — that the collective series of social phenomena, in other worda
the course of history, is subject to general laws, which philosophy may pos-
sibly detect — has been familiar for generations to the scientific thinkers
of the Continent, and has for the last quarter of a century passed out of
their peculiar domain, into that of newspapers and ordinary political dis-
cussion. In our own country, however, at the time of the first publication
of this Treatise, it was almost a novelty, and the prevailing habits of thought
on historical subjects were the very reverse of a preparation for it. Since
then a great change has taken place, and has been eminently promoted by
the important work of Mr. Buckle ; who, with characteristic energy, flung
down this great principle, together with many striking exemplifications of
it, into the arena of popular discussion, to be fought over by a sort of com-
batants, in the presence of a sort of spectators, who would never even have
been aware that there existed such a principle if they had been left to learn
its existence from the speculations of pure science. And hence has arisen
a considerable amount of controversy, tending not only to make the prin-
ciple rapidly familiar to the majority of cultivated minds, but also to clear
it from the confusions and misunderstandings by which it was but natural
that it should for a time be clouded, and which impair the worth of the
doctrine to those who accept it, and are the stumbling-block of many who
do not.
Among the impediments to the general acknowledgment, by thoughtful
minds, of the subjection of historical facts to scientific laws, the most fun-
damental continues to be that which is grounded .on the doctrine of Free
Will, or, in other words, on the denial that the law of invariable Causation
holds true of human volitions ; for if it does not, the course of history, being
the result of human volitions, can not be a subject of scientific laws, since
the volitions on which it depends can neither be foreseen, nor reduced to
any canon of regularity even after they have occurred. I have discussed
this question, as far as seemed suitable to the occasion, in a former chapter ;
and I only think it necessary to repeat, that the doctrine of the Causation
of human actions, improperly called the doctrine of Necessity, afiirms no
mysterious nexus, or overruling fatality : it asserts only that men's actions
are the joint result of the general laws and circumstances of human na-
ture, and of their own particular characters; those characters again being
the consequence of the natural and artificial circumstances that constituted
their education, among which circumstances must be reckoned their own
conscious efforts. Any one who is willing to take (if the expression may
be permitted) the trouble of thinking himself into the doctrine as thus
stated, will find it, I believe, not only a faithful interpretation of the uni-
versal experience of human conduct, but a correct representation of the
mode in which he himself, in every particular case, spontaneously interprets
his own experience of that conduct.
But if this principle is trug of individual man, it must be true of collect
SCIENCE OF HISTORY. 645
ive man. If it is the law of human life, the law must be realized in history.
The experience of human affairs when looked at en masse, must be in &&.
■cordance with it if true, or repugnant to it if false. The support which
this a posteriori verification affords to the law, is the part of the case which
has been most clearly and triumphantly brought out by Mr. Buckle.
The facts of statistics, since they have been made a subject of careful re-
cordation and study, have yielded conclusions, some of which have been very
startling to persons not accustomed to I'egard moral actions as subject to uni-
form laws. The very events which in their own nature appear most capri-
cious and uncertain, and which in any individual. case no attainable degree
•of knowledge would enable us to foresee, occur, when considerable numbers
are taken into the account, with a degree of regularity approaching to math-
ematical. What act is there which all would consider as more completely
dependent on individual character, and on the exercise of individual free
will, than that of slaying a fellow-creature ? Yet in any large country, the
number of murders, in proportion to the population, varies (it has been
found) very little from one year to another, and in its variations never de-
viates widely from a certain average. What is still more remarkable, there
is a similar approach to constancy in the proportion of these murders an-
nually committed with every particular kind of instrument. There is a
like approximation to identity, as between one year and another, in the com-
parative number of legitimate and of illegitimate births. The same thing
is found true of suicides, accidents, and all other social phenomena of which
the registration is sufficiently perfect ; one of the most cui-iously illustrative
examples being the fact, ascertained by the registers of the London and
Paris post-offices, that the number of letters posted which the writers have
forgotten to direct, is nearly the same, in proportion to the whole number
■of letters posted, in one year as in another. " Year after year," says Mr.
Buckle, " the same proportion of lettei--writers forget this simple act ; so
that for each successive period we can actually foretell the number of per-
sons whose memory will fail them in regard to this trifling, and as it tfiight
appear, accidental occurrence."*
This singular degree of regularity en wiasse, combined with the extreme
of irregularity in the cases composing the mass, is a felicitous verification
a posteriori of the law of causation in its application to human conduct.
Assuming the truth of that law, every human action, every murder, for in-
stance, is the concurrent result of two sets of causes. On the one part, the
general circumstances of the country and its inhabitants; the moral, educa-
tional, economical, and other influences operating on the whole people, and
constituting what we term the state of civilization. On the other part, the
great variety of influences special to the individual : his temperament, and
other peculiarities of organization, his parentage, habitual associates, temp-
tations, and so forth. If we now take the whole of the instances which oc-
cur within a sufficiently large field to exhaust all the combinations of these
special influences, or, in other words, to eliminate chance ; and if all these
instances have occurred within such narrow limits of time, that no material
change can have taken place in the general influences constituting the state
of civilization of the country ; we may be certain, that if human actions are
governed by invariable laws, the aggregate result will be something like a
leonstant quantity. The number of murders committed within that space
and time, being the effect partly of general causes which have not varied,
* Buckle's History of Civilization, i. , 30.
646 LOGIC OP THE MORAL SCIENCES.
and partly of partial causes the whole round of whose variations has beer*
included, will be, practically speaking, invariable.
Literally and mathematically invariable it is not, and could not be expect-
ed to be: because the period of a year is too short to include all the possi.
ble combinations of partial causes, while it is, at the same time, sufficiently"
long to make it probable that in some years at least, of every sei-ies, there
will have been introduced new influences of a more or less general charac-
ter; such as a more vigorous or a more relaxed police; some temporary
excitement from political or religious causes ; or some incident generally
notorious, of a nature to act morbidly on the imagination. That in spite of
these unavoidable imperfections in the data, there should be so very trifling-
a margin of variation in the annual results, is a brilliant confirmation of the-
general theory.
§ 2. The same considerations which-'thus strikingly corroborate the evi-
dence of the doctrine, that historical facts are the invariable effects of
causes, tend equally to clear that doctrine from various misapprehensions,,
the existence of which has been put in evidence by the recent discussions.
Some persons, for instance, seemingly imagine the doctrine to imply, not
merely that the total number of murders committed in a given space and
time is entirely the effect of the general circumstances of society, but that
every particular murder is so too — that the individual murderer is, so to
speak, a mere instrument in the hands of general causes that he himself
has no option, or, if he has, and chose to exercise it, some one else would
be necessitated to take his place; that if any one of the actual murderers
had abstained from the crime, some person who would otherwise have re-
mained innocent, would have committed an extra murder to make up the
average. Such a corollary would certainly convict any theory which nec-
essarily led to it of absurdity. It is obvious, however, that each particular
murder depends, not on the general state of society only, but on that com-
bined with causes special to the case, which are generally much more pow-
erful; and if these special causes, which have greater influence than the
general ones in causing every particular murder, have no influence on the
number of murders in a given period, it is because the field of observation
is so extensive as to include all possible combinations of the special causes
— all varieties of individual character and individual temptation compatible
•with the general state of society. The collective experiment, as it may be
termed, exactly separates the effect of the general from that of the special
causes, and shows the net result of the former ; but it declares nothing at
all respecting the amount of influence of the special causes, be it greater or
smaller, since the scale of the experiment extends to the number of cases
within which the effects of the special causes balance one another, and dis-
appear in that of the general causes.
I will not pretend that all the defenders of the theory have always kept
their language free from this same confusion, and have shown no tendency
to exalt the influence of general causes at the expense of special. I am of
opinion, on the contrary, that they have done so in a very great degree,
and by so doing have encumbered their theory with diflSculties, and laid it
open to objections, which do not necessarily affect it. Some, for example
(among whom is Mr. Buckle himself), have inferred, or allowed it to be
supposed that they inferred, from the regularity in the recurrence of events
which depend on moral qualities, that the moral qualities of mankind are
little capable of being improved, or are of little importance in the general
- SCIENCE OF HISTORY. g4ij
progi-ess of society, compared with intellectual or economic causes. But
to draw this inference is to forget that the statistical tables, from which
the invariable averages are deduced, were compiled from facts occurring
withm narrow geographical limits and in a small number of successive
years ; that is, from a field the whole of which was under the operation of
the same general causes, and during too short a time to allow of much
change therein. All moral causes but those common to the country gen-
erally, have been eliminated by the great number of instances taken ; and
those which are common to the whole country have not varied considera-
bly, in the short space of time comprised in the observations. If we admit,
the supposition that they have varied ; if we compare one age with anoth-
er, or one country with another, or even one part of a country with an-
other, differing in position and character as to the moral elements, the
crimes committed within a year give no longer the same, but a widely
different numerical aggregate. And this can not but be the case : for,,
inasmuch as every single crime committed by an individual mainly depends-
on his moral qualities, the crimes committed by the entire population of
the country must depend in an equal degree on their collective moral quali-
ties. To render this element inoperative upon the large scale, it would
be necessary to suppose that the general moral average of mankind does
not vary froni country to country or from age to age ; which is not true^
and, even if it were true, could not possibly be proved by any existing^
statistics. I do not on this account the less agree in the opinion of Mr..
Buckle, that the intellectual element in mankind, including in that expres-
sion the nature of their beliefs, the amount of their knowledge, and the-
development of their intelligence, is the predominant circumstance in de-
termining their progress. But I am of this opinion, not because I regard
their moral or economical condition either as less powerful or less variable
agencies, but because these are in a great degree the consequences of the
intellectual condition, and are, in all cases, limited by it ; as was observed
in the preceding chapter. The intellectual changes are the most conspicu-
ous agents in history, not from their superior force, considei'ed in them-
selves, but because practically they work with the united power belonging
to all three.*
§ 3. There is another distinction often neglected in the discussion of this-
subject, which it is extremely important to observe. The theory of the
* I hare been assured by an intimate friend of Mr. Buckle that he would not have with-
held his assent from these remarks, and that he never intended to affirm or imply that man-
kind are not progressive in their moral as well as in their intellectual qualities. " In dealing
with his problem, he availed himself of the artifice resorted to by the Political Economist,
who leaves out of consideration the generous and benevolent sentiments, and founds his sci-
ence on the proposition that mankind are actuated by acquisitive propensities alone, " not be-
cause such is the fact, but because it is necessary to begin by treating the principal influence-
as if it was the sole one, and make the due corrections afterward. "He desired to make-
abstraction of the intellect as the determining and dynamical element of the progression, elimi-
nating the more dependent set of conditions, and treating the more active one as if it were air
entirely independent variable."
The same friend of Mr. Buckle states that when he used expressions which seemed to ex-
aggerate the influence of general at the expense of special causes, and especially at the ex-
pense of the influence of individual minds, Mr. Buckle really intended no more than to affirm
emphatically that the greatest men can not effect great changes in human affairs unless the.
general mind has been in some considerable degree prepared for them by the general circum-
stances of the age ; a truth which, of course, no one thinks of denying. And there certainly-
are passages in Mr. Buckle's writings which speak of the influence exercised by great indi-
Tidnal intellects in as strong terms as could be desired.
«48 LOGIC OF THE MOKAL SCIENCES.
subjection of social progress to invariable laws, is often held in conjunc-
tion with the doctrine, that social progress can not be materially influenced
by the exertions of individual persons, or by the acts of governments.
But though these opinions ■ are often held by the same persons, they are
two very different opinions, and the confusion between them is the eter-
nally recurring error of confounding Causation with Fatalism. Because
whatever happens will be the effect of causes, human volitions among the
rest, it does not follow that volitions, even those of peculiar individuals,
are not of great efficacy as causes. If any on6 in a storm at sea, because
about the same number of persons in every year perish by shipwreck,
should conclude that it was useless for him to attempt to save his own life,
we should call him a Fatalist; and should remind him that the efforts of
shipwrecked persons to save their lives are so far from being immaterial,
that the average amount of those efforts is one of the causes on which the
ascertained annual number of deaths by shipwreck depend. However uni-
versal the laws of social development may be, they can not be more univer-
sal or more rigorous than those of the physical agencies of nature; yet
human will can convert these into instruments of its designs, and the ex-
tent to which it does so makes the chief difference between savages and
the most highly civilized people. Human and social facts, from their more
complicated nature, are not less, but more, modifiable than mechanical and
■cheiuical facts ; human agency, therefore, has still greater power over them.
And accordingly, those who maintain that the evolution of society depends
■exclusively, or almost exclusively, on general causes, always include among
these the collective knowledge and intellectual development of the race.
But if of the race, why not also of some powerful monarch or thinker, or
of the ruling portion qi some political society, acting through its govern-
ment? Though the varieties of character among ordinary individuals neu-
tralize one another on any large scale, exceptional individuals in important
positions do not in any given age neutralize one another; there was not
another Themistocles, or Luther,, or Julius CsBsar, of equal powers and
contrary dispositions, who exactly balanced the given Themistocles, Luther,
and Csesar, and prevented them from having any permanent effect. More-
over, for aught that appears, the volitions of exceptional persons, or the
•opinions and purposes of the individuals who at some particular time com-
pose a government, may be indispensable links in the chain of causation by
which even the general causes produce their effects; and I believe this to
be the only tenable form of the theory.
Lord Macaulay, in a celebrated passage of one of his early essays (let
me add that it was one which he did not himself choose to reprint), gives
•expression to the doctrine of the absolute inoperativeness of great men,
more unqualified, I should think, than has been given to it by any writer
of equal abilities. He compares them to persons who merely stand on a
loftier height, and thence receive the sun's rays a little earlier, than the
rest of the human race. " The sun illuminates the hills while it is still be-
low the horizon, and truth is discovered by the highest minds a little be-
fore it becomes manifest to the multitude. This is the extent of their su-
pei-iority. They are the first to catch and reflect a light which, without
their assistance, must in a short time be visible to those who lie far be-
neath them."* If this metaphor is to be carried out, it follows that if
there had been no Newton, the world would not only have had the New
* Essay on Dryden, in Miscellaneous Writings, i., 186.
SCIENCE OF HISXOKY. 649
tonian system, but would have had it equally soon ; as the sun would have
risen just as early to spectators in the plain if there had been no mountain
at hand to catch still earlier rays. And so it would be, if truths, like the
~sun, rose by their own proper motion, without human effort ; but not oth-
erwise. I believe that if Newton had not lived, the world must have wait-
ed for the Newtonian philosophy until there had been another Newton,.
or his equivalent. No ordinary man, and nQjracoession of ordinary men,
could have achieved it. I will not go the length of saying that what New-
ton did in a single life, might not have been done in successive steps by
some of those who followed him, each singly inferior to him in genius.
But even the least of those steps required a man of great intellectual supe-
riority. Eminent men do not merely see the coming light from the hill-
top, they mount on the hill-top and evoke it ; and if no one had ever as-
cended thither, the light, in many cases, might never have risen upon the-
plain at all. Philosophy and religion are abundantly amenable to general
causes ; yet few will doubt that, had there been no Socrates, no Plato, and
no Aristotle, there would have been no philosophy for the next two thou-
sand years, nor in all probability then ; and that if there had been no-
Christ, and no St. Paul, there would have been no Christianity.
The point in which, above all, the influence of remarkable individuals is-
decisive, is in determining the celerity of the movement. In most states
of society it is the existence of great men which decides even whether there
shall be any progress. It is conceivable that Greece, or that Christian
Europe, might have been progressive in certain periods of their history
through general causes only : but if there had been no Mohammed, would
Arabia have produced Avicenna or Averroes, or Caliphs of Bagdad or of
Cordova ? In determining, however, in what manner and order the prog-
ress of mankind shall take place if it take place at all, much less depends,
on the character of individuals. There is a sort of necessity established in
this respect by the general laws of human nature — by the constitution of
the human mind. Certain truths can not be discovered, nor inventions-
made, unless certain others have been made first; certain social improve-
ments, from the nature of the case, can only follow, and not precede, others..
The order of human progress, therefore, may to a certain extent have defi-
nite laws assigned to it: while as to its celerity, or even as to its taking
place at all, no generalization, extending to the human species generally, can
poBsibly be made; but only some very precarious approximategeneraliza-
tions, cQnfined to the small portion of mankind in whom there has been
any thing like consecutive progress within the historical period, and de-
duced from their special position, or collected from their particular history.
Even looking to the manner of progress, the order of succession of social
states, there is need of great flexibility in our generalizations. The limits,
of variation in the possible development of social, as of animal life, are a
subject of which little is yet understood, and are one of the great problems
in social science. It is, at all events, a fact, that different portions of man-
kind, under the influence of different circumstances, have developed them-
selves in a more or less different manner and into different forms; and
among these determining circumstances, the individual character of their
great speculative thinkers or practical organizers may well have been one.
Who can tell how profoundly the whole subsequent history of China may^
have been influenced by the individuality of Confucius ? and of Sparta (and
hence of Greece and the world) by that of Lycurgus ?
Concerning the nature and extent of what a great man under favorable-
€50 LOGIC OF THE MORAL SCIENCES.
■circumstances can do for mankind, as well as of what a government can do
for a nation, many different opinions are possible ; and every shade of opin-
ion on these points is consistent with the fullest recognition that there are
invariable laws of historical phenomena. Of course the degree of influence
which has to be assigned to these more special agencies, makes a great dif-
ference in the precision which can be given to the general laws, and in the
confidence with which predictions can be grounded on them. Whatever
■depends on the peculiarities of individuals, combined with the accident of
the positions they hold, is necessarily incapable of being foreseen. Un-
doubtedly these casual combinations might be eliminated like any others,
by taking a sufficiently large cycle : the peculiarities of a great historical
character make their influence felt in history sometimes for several thou-
sand years, but it is highly probable that they will make no difference at
all at the end of fifty millions. Since, however, we can not obtain an aver-
age of the vast length of time necessary to exhaust all the possible combi-
nationg of great men and circumstances, as much of the law of evolution of
human affairs as depends upon this average, is and remains inaccessible to
lis; and within the next thousand years, which are of considerably more
importance to us than the whole remainder of the fifty millions, the favor-
able and unfavorable combinations which will occur will be to us purely
accidental. We can not foresee the advent of great men. Those who in-
troduce new speculative thoughts or great practical conceptions into the
world, can not have their epoch fixed beforehand. What science can do,
is this. It can trace through past history the general causes which had
brought mankind into that preliminary state which, when the right sort of
:great man appeared, rendered them accessible to his influence. If this
«tate continues, experience renders it tolerably certain that in a longer or
■shorter period the great man will be produced ; provided that the general
•circumstances of the country and people are (which very often they are
not) compatible with his existence; of which point also, science can in
46ome measure judge. It is in this manner that the results of progress, ex-
cept as to the celerity of their production, can be, to a certain extent, re-
duced to regularity and law. And the belief that they can be so, is equal-
ly consistent with assigning very great, or very little efficacy, to the influ-
ence of exceptional men, or of thie acts of governments. And the same
may be said of all other accidents and disturbing causes.
ft
§ 4. It would nevertheless be a great error to assign only a trifling im-
portance to the agency of eminent individuals, or of governments. It must
not be concluded that the influence of either is small, because they can not
■bestow what the general circumstances of society, and the course of its
■previous history, have not prepared it to receive. Neither thinkers nor
governments effect all that they intend, but in compensation they often
produce important results which they did not in the least foresee. Great
men, and great actions, are seldom wasted ; they send forth a thousand un-
:seen influences, more effective than those which are seen; and though nine
out of every ten things done, with a good pui-pose, by those who are in
advance of their age, produce no material effect, the tenth thing produces
effects twenty times as great as any one would have dreamed of predict-
ing from it. Even the men who for want of sufficiently favorable circum-
«tances left no impress at all upon their own age, have often been of the
greatest value to posterity. Who could appear to have lived more entire-
ly in vain than some of the early heretics? They were burned or mas-
SCIENCE OF HISTORY. 651
sacred, their writings extirpated, their memory anathematized, and their
■very names and existence left for seven or eight centuries in the obscuri-
ty of musty manuscripts— their history to be gathered, perhaps, only from
the sentences by which they were condemned. Yet the memoi-y of these
men — men who resisted certain pretensions or certain dogmas of the
Church in the very age in which the unanimous assent of Christendom
was afterward claimed as having been given to them, and asserted as the
ground of their authority — broke the chain of tradition, established a se-
ries of precedents for resistance, inspired later Reformers with the cour-
age, and armed them with the weapons, which they needed when mankind
were better prepared to follow their impulse. To this example from men,
let us add another from governments. The comparatively enlightened
rule of which Spain had the benefit during a considerable part of the
«ighteenth century, did not correct the fundamental defects of the Spanish
people ; and in consequence, though it did great temporary good, so much
of that good perished with it, that it may plausibly be aflBrmed to have
had no permanent effect. The case has been cited as a proof how little
governments can do in opposition to the causes which have determined
' the general character of the nation. It does show how much there is
which they can not do; but not that they can do nothing. Compare what
Spam was at the beginning of that half-century of liberal government,
with what she had become at its close. That period fairly let in the light
of European thought upon the more educated classes ; and it never after-
ward ceased to go on spreading. Previous to that time the change was
in an inverse direction ; culture, light, intellectual and even material activ-
ity, were becoming extinguished. Was it nothing to arrest this down-
ward and convert it into an upward course ? How much that Charles the
Third and Aranda could not do, has been the ultimate consequence of
what they did ! To that half-century Spain owes that she has got rid of
the Inquisition, that she has got rid of the monks, that she now has parlia-
ments and (save in exceptional intervals) a free press, and the feelings of
freedom and citizenship, and is acquiring railroads and all the other con-
stituents of material and economical progress. In the Spain which pre-
ceded that era, there was not a single element at work which could have
led to these results in any length of time, if the country had continued to
be governed as it was by the last princes of the Austrian dynasty, or if
the Bourbon rulers had been from the first what, both in Spain and in Na-
ples, they afterward became.
And if a government can do much, even when it seems to have done
little, in causing positive improvement, still greater are the issues depend
ent on it in the way of warding off evils, both internal and external, which
«l8e would stop improvement altogether. A good or a bad counselor, in a
single city at a particular crisis, has affected the whole subsequent fate of
the world. It is as certain as any contingent judgment respecting histor-
ical events can be, that if there had been no Themistocles there would
have been no victory of Salamis ; and had there not, where would have
been all our civilization ? How different, again, would have been the issue
if Epaminondas, or Timoleon, or even Iphicrates, instead of Chares and Ly-
sicles, had commanded at Chseroneia. As is well said in the second of two
Essays on the Study of History,* in my judgment the soundest and most
philosophical productions which the recent controversies on this subject
* In the Comhill Magazine for June and July, 1861.
652 LOGIC OF THE MORAL SCIENC:eS.
have called forth, historical science authorizes not absolute, but only con-
ditional predictions. General causes count for much, but individuals also
" produce great changes in history, and color its whole complexion long^
after their death No one can doubt that the Roman republic would
have subsided into a military despotism if Julius Caesar had never lived "
(thus much was i-endered practically certain by general causes) ; " but is
it at all clear that in that case Gaul would ever have formed a province of
the empire? Might not Varus have lost his three legions on the banks of
the Rhone ? and might not that river have become the frontier instead of
the Rhine? This might well have happened if Csesar and Crassus had
changed provinces; and it is surely impossible to say that in such an
event the venue (as lawyers say) of European civilization might not have-
been changed. The Norman Conquest in the same way was as much the
act of a single man, as the writing of a newspaper article; and knowing
as we do the history of that man and his family, we can retrospectively
predict with all but infallible certainty, that no other person " (no other in
that age, I presume, is meant) " could have accomplished the enterprise.
If it had not been accomplished, is there any ground to suppose that either
our history or our national character would have been what they are ?"
As is most truly remarked by the same writer, the whole stream of Gre-
cian history, as cleared up by Mr. Grote, is one series of examples how oft-
en events on which the whole destiny of subsequent civilization turned,
were dependent on the personal character for good or evil of some one in-
dividual. It must be said, however, that Greece furnishes the most extreme
example of this nature to be found in history, and is a very exaggerated
specimen of the general tendency. It has happened only that once, and
will probably never happen again, that the fortunes of mankind depended
upon keeping a certain order of things in existence in a single town, or a 4
country scarcely larger than Yorkshire; capable of being ruined or saved
by a hundred causes, of very slight magnitude in comparison with the gen-
eral tendencies of human affairs. Neither ordinary accidents, nor the char-
acters of individuals, can ever again be so vitally important as they then
were. The longer our species lasts, and the more civilized it becomes, the
more, as Comte remarks, does the influence of past generations over the
present, and of mankind en masse over every individual in it, predominate
over other forces ; and though the course of affairs never ceases to be sus-
ceptible of alteration both by accidents and by personal qualities, the in-
creasing preponderance of the collective agency of the species over all
minor causes, is constantly bringing ths general evolution of the race into-
something which deviates less from a certain and preappointed track. His-
torical science, therefore, is always becoming moi-e possible ; not solely be-
cause it is better studied, but because, in every generation, it becomes bet-
ter adapted for study.
CHAPTER XII.
OP THE LOGIC OP PEAOTICE, OK ART ; INCLUDING MORALITY AND POLIOTr
§ 1. In the preceding chapters we have endeavored to characterize the
present state of those among the branches of knowledge called Moral, which
are sciences in the only proper sense of the term, that is, inquiries into the
course of nature. It is customary, however, to include under the term
LOGIC OF PRACTICE, OR ART. 653
moral knowledge, and even (though improperly) under that of moral science,
an inquiry the results of which do not express themselves in the indica-
tive, but in the imperative mood, or in periphrases equivalent to it; what
is called the knowledge of duties; practical ethics, or morality.
Now, the imperative mood is the characteiistic of art, as distinguished
from science. Whatever speaks in rules, or precepts, not in assertions re-
specting matters of fact, is art ; and ethics, or morality, is properly a por-
tion of the art corresponding to the sciences of human nature and society.*
The Method, therefore, of Ethics, can be no other than that of Art, or
Practice, in general ; and the portion yet uncompleted of the task which
we proposed to ourselves in the concluding Book, is to characterize the gen-
eral Method of Art, as distinguished from Science.
§ 2. In all branches of practical business there are cases in which indi-
viduals are bound to conform their practice to a pre-established rule, while
there are others in which it is part of their task to find or construct the
Tule by which they are to govern their conduct. The first, for example, is
the case of a judge, under a definite written code. The judge is not called
upon to determine what course would be intrinsically the most advisable
in the particular case in hand, but only within what rule of law it falls ;
what the legislature has ordained to be done in the kind of case, and must
therefore be presumed to have intended in the individual case. The meth-
od must here be wholly and exclusively one of ratiocination, or syllogism ;
and the process is obviously, what in our analysis of the syllogism we
showed that all ratiocination is, namely the interpretation of a formula.
In order that our illustration of the opposite case may be taken from the
same class of subjects as the former, we will suppose, in contrast with the
situation of the judge, the position of the legislator. As the judge has laws
for his guidance, so the legislator has rules, and maxims of policy ; but it
would be a manifest error to suppose that the legislator is bound by these
maxims in the same manner as the judge is bound by the laws, and that all
he has to do is to argue down from them to the particular case, as the judge
; does from the laws. The legislator is bound to take into consideration the
reasons or grounds of the maxim; the judge has nothing to do with those
of the law, except so far as a consideration of them may throw light upon
the intention of the law-maker, where his words have left it doubtful. To
the judge, the rule, once positively ascertained, is final ; but the legislator,
or other practitioner, who goes by rules rather than by their reasons, like
the old-fashioned German tacticians who were vanquished by Napoleon,
or the physician who preferred that his patients should die by rule rather
than recover contrary to it, is rightly judged to be a mere pedant, and the
slave of his formulas.
Now, the reasons of a maxim of policy, or of any other rule of art, can
be no other than the theoi'ems of the corresponding science.
The relation in which rules of art stand to doctrines of science may be
thus characterized. The art proposes to itself an end to be attained, de-
fines the end, and hands it over to the science. The science receives it, con-
siders it as a phenomenon or effect to be studied, and having investigated
its causes and conditions, sends it back to art with a theorem of the com-
* It is almost superfluous to observe, that there is another meaning of the word Art, in
which it may be said to denote the poetical department or aspect of things in general, in con-
tradistinction to the scientific. In the text, the word is used in its older, and I hope, not yet
obsolete sense.
654 LOGIC OF THE MORAL SCIENCES.
bination of circumstances by which it could be produced. Art then exam-
ines these combinations of circumstances, and according as any of them are
or are not in human power, pronounces the end attainable or not. The only
one of the premises, therefore, which Art supplies, is the original major
premise, which asserts that the attainment of the given end is desirable.
Science then lends to Art the proposition (obtained by a series of induc-
tions or of deductions) that the performance of certain actions will attain
the end. From these premises Art concludes that the performance of these
actions is desirable, and finding it also practicable, converts the theorem
into a rule or precept.
§ 3. It deserves particular notice, that the theorem or speculative truth
is not ripe for being turned into a precept, until the whole, and not a part
merely, of the operation which belongs to science, has been performed.
Suppose that we have completed the scientific process only up to a certain
point ; have discovered that a particular cause will produce the desired ef-
fect, but have not ascertained all the negative conditions which are neces-
sary, that is, all the circumstances which, if present, would prevent its pro-
duction. If, in this imperfect state of the scientific theory, we attempt to
frame a rule of art, we perform that operation prematurely. Whenever any
counteracting cause, overlooked by the theorem, takes place, the rule will be
at fault ; we shall employ the means and the end will not follow. No ar-
guing from or about the rule itself will then help us through the diflficultyj
there is nothing for it but to turn back and finish the scientific process
which should have preceded the formation of the rule. We must re-open
the investigation to inquire into the remainder of the conditions on which
the effect depends ; and only after we have ascertained the whole of these-
are we prepared to transform the completed law of the effect into a pre-
cept, in which those circumstances or combinations of circumstances which;
the science exhibits as conditions are prescribed as means.
It is. true that, for the sake of convenience, rules must be formed from
something less than this ideally perfect theory : in the first place, because
the theory can seldom be made ideally perfect; and next, because, if all the
counteracting contingencies, whether of frequent or of rare occurrence,,
were included, the rules would be too cumbrous to be apprehended and re-
membered by ordinary capacities, on the common occasions of life. The
rules of art do not attempt to comprise more conditions than require to be
attended to in ordinary cases ; and are therefore always imperfect. In the
manual arts, where the requisite conditions are not numerous, and where
those which the rules do not specify are generally either plain to common
observation or speedily learned from practice, rules may often be safely act-
ed on by persons who know nothing more than the rule. But in the com-,
plicated affairs of life, arid still more in those of states and societies, rules-
can not be relied on, without constantly referring back to the scientific laws
on which they are founded. To know what are the practical contingen-
cies which require a modification of the rule, or which are altogether ex-
ceptions to it, is to know what combinations of circumstances would in-
terfere with, or entirely counteract, the consequences of those laws ; and.
this can only be learned by a reference to the theoretic grounds of the rule.
By a wise practitioner, therefore, rules of conduct will only be consider-
ed as provisional. Being made for the most numerous cases, or for those
of most ordinary occurrence, they point out the manner in which it will be
least perilous to act, where time or means do not exist for analyzing the
LOGIC OF PRACTICE, OR ART. 655
actual circumstances of the case, or where we can not trust our judgment
in estimating them. But they do not at all supersede the propriety of go-
ing through, when circumstances pennit, the scientific process requisite
for framing a rule from the data of the particular case before us. At the
same time, the common rule may very properly serve as an admonition that
a certain mode of action has been found by ourselves and others to be well
adapted to the cases of most common occurrence ; so that if it be unsuita-
ble to the case in hand, the reason of its being so will be likely to arise
from some unusual circumstance.
§ 4. The error is therefore apparent of those who would deduce the line
of conduct proper to particular cases from supposed universal practical
maxims, overlooking the necessity of constantly referring back to the prin-
ciples of the speculative science, in order to be sure of attaining even the
specific end which the rules have in view. How much greater still, then,
must the error be, of setting up such unbending principles, not merely as
universal rules for attaining a given end, but as rules of conduct generally,
without regard to the possibility, not only that some modifying cause may
prevent the attainment of the given end by the means which the rule pre-
scribes, but that success itself may conflict with some other end, which may
possibly chance to be more desirable.
This is the habitual error of many of the political speculators whom I
h^ve characterized as the geometrical school; especially in France, where
ratiocination from rules of practice forms the staple commodity of journal-
ism and political oratory — a misapprehension of the functions of Deduction
which has brought much discredit, in the estimation of other countries,
upon the spirit of generalization so honorably characteristic of the French
mind. The commonplaces of politics in France are large and sweeping
practical maxims, from which, as ultimate premises, men reason downward
to particular applications ; and this they call being logical and consistent.
For instance, they are perpetually arguing that such and such a measure
ought to be adopted, because it is a consequence of the principle on which
the form of government is founded ; of the principle of legitimacy, or the
principle of the sovereignty of the people. To which it may be answered,
that if these be really practical principles, they must rest on speculative
grounds ; the sovereignty of the people, for example, must be a right foun-
dation for government, because a government thus constituted tends to pro-
duce certain beneficial effects. Inasmuch, however, as no government pro-
duces all possible beneficial effects, but all are attended with more or few-
er inconveniences, and since these can not usually be combated by means
drawn from the very causes which produce them, it would be often a much
- stronger recommendation of some practical arrangement, that it does not
follow from what is called the general principle of the government, than
that it does. Under a government of legitimacy, the presumption is far
rather in favor of institutions of popular origin ; and in a democracy, in
favor of arrangements tending to check the impetus of popular will. The
line of augmentation so commonly mistaken in France for pohtical philoso-
phy, tends to the practical conclusion that we should exert our utmost ef-
forts to aggravate, instead of alleviating, whatever are the characteristic
imperfections of the system of institutions which we prefer, or under which
we happen to live.
§ 5. The grounds, then, of every rule of art, are to be found in the the-
656 LOGIC OF THE MORAL SCIENCES.
•orems of science. An art, or a body of art, consists of the rules, together
with as much of the speculative propositions as comprises the justification^
of those rules. The complete art of any matter includes a selection of
soch a portion from the science as is necessary to show on what condi-
tions the effects, which the art aims at producing, depend. And Art in
general, consists of the truths of Science, arranged in the most convenient
•order for practice, instead of the order which is the most convenient for
thought. Science groups and arranges its truths, so as to enable us to
take in at one view as much as possible of the general order of the uni-
verse. Art, though it must assume the same general laws, follows th^pi
■only into such of their detailed consequences as have led to the formation
of rules of conduct; and brings together from parts of the field of science
most remote from one another, the truths relating to the production of the
different and heterogeneous conditions necessary to each effect which the
exigencies of practical life require to be produced.*
Science, therefore, following one cause to its various effects, while art
traces one effect to its multiplied and diversified causes and conditions,
there is need of a set of intermediate scientific truths, derived from the
higher generalities of science, and destined to serve as the generalia or
first principles of the various arts. The scientific operation of framing
these intermediate principles, M. Comte characterizes as one of those re-
sults of philosophy which are reserved for futurity. The only complete
example which he points out as actually realized, and which can be held
tip as a type to be imitated in more important matters, is the general the-
ory of the art of Descriptive Geometry, as conceived by M. Monge. It is
not, however, difficult to understand what the nature of these intermediate
principles must generally be. After framing the most comprehensive pos-
sible conception of the end to be aimed at, that is, of the effect to be pro-
duced, and determining in the same comprehensive manner the set of con-
ditions on which that effect depends, there remains to be taken, a general
survey of the resources which can be commanded for realizing this set of
conditions ; and when the result of this survey has been embodied in the
fewest and most extensive propositions possible, those propositions will
•express the general relation between the available means and the end, and
will constitute the general scientific theory of the art, from which its
practical methods will follow as corollaries.
§ 6. But though the reasonings which connect the end or purpose of ev-
ery art with its means belong to the domain of Science, the definition of
the end itself belongs exclusively to Art, and forms its peculiar province.
Every art has one first principle, or general major premise, not borrowed
from science ; that which enunciates the object aimed at, and aflSrms it to
be a desirable object. The builder's art assumes that it is desirable to
have buildings ; architecture, as one of the fine arts, that it is desirable
to have them beautiful or imposing. The hygienic and medical arts as-
sume, the one that the preservation of health, the other that the cure of
disease, are fitting and desirable ends. These are not propositions of sci-
ence. Propositions of science assert a matter of fact : an existence, a co-
existence, a succession, or a resemblance. The propositions now spoken
of do not assert that any thing- is, but enjoin or recommend that something
should be. They are a class by themselves. A proposition of which the
* Professor Bain and others call the selection from the truths of science made for the pur'
poses of an art, a Practical Science, and confine the name Art to the actual rules.
LOGIC OF PRACTICE, OR ART. 657
predicate is expressed by the words ought or should be, is generically dif-
Jerent from one which is expressed by is, or will be. It is true, that in the
largest sense of the words, even these propositions assert something as a
matter of faot. The fact afSrmed in them is, that the conduct recommend-
ed excites in the speaker's mind the feeling of approbation. This, how-
ever, does not go to the bottom of the matter ; for the speaker's approba^
tion is no sufficient reason why other people should approve ; nor ought it
to be a conclusive reason even with himself. For the purposes of practice,
every one must be required to justify his approbation ; and for this there
is need of general premises, determining what are the proper objects of ap-
probation, and what the' proper order of precedence among those objects.
These genei-al premises, together with the principal conclusions which may
be deduced from them, form (or rather might form) a body of doctrine,
which is properly the Art of Life, in its three departments, Morality, Pru-
dence or Policy, and Esthetics ; the Right, the Expedient, and the Beau-
tiful or Noble, in human conduct and works. To this art (which, in the
main, is unfortunately still to be created), all other arts are subordinate ;
since its principles are those which must determine whether the special aim
of any particular art is worthy and desirable, and what is its place in the
scale of desirable things. Every art is thus a joint result of laws of nature
disclosed by science, and of the general principles of what has been called
Teleology, or the Doctrine of Ends;* which, borrowing the language of the
German metaphysicians, may also be termed, not improperly, the principles
of Practical Reason.
A scientific observer or reasoner, merely as such, is not an adviser for
practice. His part is only to show that certain consequences follow from
certain causes, and that to obtain certain ends, certain means are the most ef-
PIII fectual. Whether the ends themselves are such as ought to be pursued, and
'■'■ if so, in what cases and to how gi-eat a length, it is no part of his business
as a cultivator of science to decide, and science alone will never qualify him
for the decision. In purely physical science, there is not much temptation
to assume this ulterior office; but those who treat of human nature and so-
ciety invariably claim it : they always undertake to say, not merely what
. is, but what ought to be. To entitle them to do this, a complete doctrine
. . .. of Teleology is indispensable. A scientific theory, however perfect, of the
subject-matter, considered merely as part of the order of nature, can in no
degree serve as a substitute. In this respect the various subordinate arts
afford a misleading analogy. In them there is seldom any visible necessity
for justifying the end, since in general its desirableness is denied by nobody,
and it is only when the question of precedence is to be decided between
that end and some other, that the general principles of Teleology have to
be called in ; but a writer on Morals and Politics requires th9se principles
at every step. The most elaborate and well - digested exposition of the
laws of succession and co-existence among mental or social phenomena, and
of their relation to one another as causes and effects, will be of no avail
toward the art of Life or of Society, if the ends to be aimed at by that art
are left to the vague suggestions of the intellectus sibi permissus, or are
taken for granted without analysis or questioning.
§ 7. There is, then, a, philosophia prima peculiar to Art, as there is one
which belongs to Science. There are not only first principles of Knowl-
* The word Teleology is also, but inconveniently and improperly, employed by some writei-s
as a name for the attempt to explain the phenomena of the universe from final causes.
42
658 LOGIC OF THE MORAL SCIENCES.
edge, but first principles of Conduct. Tiiere must be some standard by
whicb to determine the goodness or badness, absolute and comparative, of
ends, or objects of desire. And whatever that standard is, there can be but
one ; for if there were several ultimate principles of conduct, the same con-
duct might be approved by one of those principles and condemned by an-
other ; and there would be needed some more general principle, as umpire
between them.
Accordingly, writers on Moral Philosophy have mostly felt the necessity
not only of referring all rules of conduct, and all judgments of praise and
blame, to principles, but of referring them to some one principle ; some
rule, or standard, with which all other rules of conduct were required to be
consistent, and from which by ultimate consequence they could all be de-
duced. Those who have dispensed with the assumption of such a universal
standard, have only been enabled to do so by supposing that a moral sense,
or instinct, inherent in our constitution, informs us, both what principles of
conduct we are bound to observe, and also in what order these should be
subordinated to one another.
The theory of the foundations of morality is a subject which it would be
out of place, in a work like this, to discuss at large, and which could not to
any useful purpose be treated incidentally. I shall content myself, therefore,
with saying, that the doctrine of intuitive moral principles, even if true,
would provide only for that portion of the field of conduct which is prop-
erly called moral. For the remainder of the practice of life some general
principle, or standard, must still be sought ; and if that principle be rightly
chosen, it will be found, I apprehend, to serve quite as well for the ultimate
principle of Morality, as for that of Prudence, Policy, or Taste.
Without attempting in this place to justify my opinion, or even to define
the kind of justification which it adnlits of, I merely declare ray conviction,
that the general principle to which all rules of practice ought to conform,
and the test by which they should be tried, is that of oonduciveness to the
happiness of mankind, or rather, of all sentient beings; in other words, that
the promotion of happiness is the ultimate principle of Teleology.*
I do not mean to assert that the promotion of happiness should be itself
the end of all actions, or even of all rules of action. It is the justification,
and ought to be the controller, of all ends, but it is not itself the sole end.
There are many virtuous actions, and even virtuous modes of action (though
the cases are, I think, less frequent than is often supposed), by which hap-
piness in the particular instance is sacrificed, more pain being produced
than pleasure. But conduct of which this can be truly asserted, admits of
justification only because it can be shown that, on the whole, more happiness
will exist in the world, if feelings are cultivated which will make people, in
certain cases, regardless of happiness. I fully admit that this is true; that
the cultivation of an ideal nobleness of will and conduct should be to indi-
vidual human beings an end, to which the specific pursuit either of their
own happiness or of that of others (except so far as included in that idea)
should, in any case of conflict, give way. But I hold that the very .ques-
tion, what constitutes this elevation of character, is itself to be decided by
a reference to happiness as the standard. The character itself should be,
to the individual, a paramount end, simply because the existence of this
ideal nobleness of character, or of a near approach to it, in any abundance,
would go farther than all things else toward making human life happy,
* For an express discussion and vindication of this principle, see the little volume entitled
"Utilitarianism."
LOGIC OF PRACTICE, OR ART. 659
"both in the comparatively humble sense of pleasure and freedom from
pain, and in the higher meaning, of rendering life, not what it now is almost
universally, puerile and insignificant, but such as human beings with high-
ly developed faculties can care to have.
§ 8. With these remarks we must close this summary view of the appli-
cation of the general logic of scientific inquiry to the moral and social de-
partments of science. Notwithstanding the extreme generality of the
principles of method which I have laid down (a generality which, I trust,
is not, in this instance, synonymous with vagueness), I have indulged the
hope that to some of those on whom the task will devolve of bringing those
most important of all sciences into a more satisfactory state, these observa-
tions may be useful, both in removing erroneous, and in clearing up the
true, conceptions of the means by which, on subjects of so high a degree of
complication, truth can be attained. Should this hope be realized, what is
probably destined to be the great intellectual achievement of the next two
or three generations of European thinkers will have been in some degree
forwarded.
THE END.
Live Music
Archive
Librivox
Free Audio
Metropolitan Museum
Cleveland
Museum of Art
Internet
Arcade
Console Living Room
Open Library
American
Libraries
TV News
Understanding
9/11